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ANALYSIS OF TWOLANE ROADWAY LANE CLOSURE OPERATIONS UNDER FLAGGING CONTROL By THOMAS HILES A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2008 2008 Thomas Hiles To My Parents ACKNOWLEDGMENTS I thank Dr. Scott Washburn (my supervisory committee chair) and the other committee members (Dr. Lily Elefteriadou and Dr. Kevin Heaslip) for their mentoring and support. I would like to thank Catherine for helping me through my graduate work. I would finally like to thank my parents and grandmother for their loving support. TABLE OF CONTENTS page A C K N O W L E D G M E N T S ..............................................................................................................4 LIST O F TA BLE S ......... .... ........................................................................... 7 LIST OF FIGURES .................................. .. ..... ..... ................. .8 ABSTRAC T ......................................................................................... CHAPTER 1 INTRODUCTION ............... .............................. ........................ .... 11 B a c k g ro u n d .........................................................................................................................1 1 Problem Statem ent ........................ ........................... ... .............. ................ 11 Research Objective and Supporting Tasks................................ ................... .............. 12 D ocum ent O organization ............................................................................ ....................13 2 L ITE R A TU R E R E V IE W ......................................................................... ........................ 14 In tro du ctio n ................................................................................ 14 B a ck g ro u n d ................................................................................14 P reviou s R research ................................................................................ 15 C assidy and Son .........................................................15 Calculation procedure outline ....................... ......................................... 16 F ie ld d a ta .................................................................................................... 1 6 Sim ulation data ................................... ................ ............... .... 17 F D O T P ro ce d u re ................................................................................................. 18 Q u ickZ on e .................................................................................................... 2 0 C olorado D O T ................................................................22 Sum m ary and C conclusions ............................................................22 3 RESEARCH APPROACH ........................ ........ .... ........25 Introduction .............. ........... ................................ ............................25 M ethodological A approach ........................................................................................... 2 5 Sim u nation .................. ..................................... ............................... 2 7 Program D evelopm ent ...........................................................28 V vehicle distribution............................................... 28 Vehicle properties ................ ........ ........ ........29 V vehicle arriv als ............................................................2 9 Initial speed ................. ................. .........30 Carfollowing model ............... ..... ........ ...............31 Q ueue arrival and discharge.............................................. 33 Flagging operations................................................. 34 Startup lost tim e ..................................................................................... .. .......34 F lag g in g m eth o d s ....................................................................................... 3 5 U ser In terface ................................................................................ 3 5 A n im atio n ............................................................3 6 O utputs of the sim ulation....................................................... .... ........... 36 Sim u nation C alib ration ................................................................. .. ...................3 8 Sensitivity A analysis ................. ........ .......................... .... ........ .......... ...... 39 Experim ental D esign................................. .. .......... ....... .... 41 V ariab le S election ........... ............................................................ ........ .......... 4 1 Setting V ariable L evels.................................................. ............................... 45 N um ber of R eplications ........................................................................... 46 4 CALCULATION PROCEDURE DEVELOPMENT..........................................................53 In tro d u ctio n ............................................................................................5 3 W ork Z one Speed M odel ......................................................................... ....................53 Saturation Flow R ate M odel ........................................... .................. ............... 54 C capacity C calculation ......... ...................... ...................... .. .. .. ....... ..............56 Queue Delay and Queue Length Models............................................................... 59 Queue D elay M odel .................................. .. ... ........ ............ 59 Q ueue Length M odel ......................................... ................... ........ 60 M o d e l V alid atio n ............................................................................................................... 6 1 Cassidy and Son Com prison ............................................................................ 61 Uniform D elay and Queue Length .................................................. ............... 62 Analytical Procedure Compared to FlagSim ................................. ................ 64 5 CONCLUSIONS AND RECOMMENDATIONS...................................... ............... 72 S u m m a ry ....................... ............................................................................................... 7 2 Conclusions ................................ ....................... ...............72 Recommendations for Further Research................................................................... 73 A PPEN D IX Sum m ary Output File........ ........................... .................................. ............... 75 R E F E R E N C E S ..........................................................................76 B IO G R A PH IC A L SK E T C H .............................................................................. .....................78 6 LIST OF TABLES Table Page 21 FD O T w ork zone factor. ......................................................................... .....................24 41 W ork Z one Speed M odel ......................................................................... ....................68 42 Saturation F low M odel ............................................................................ ....................68 43 Queue Delay M odel ..................................... ... .. .......... ....... ...... 68 44 Q u eu e L length M odel .............................................................................. ..................... 68 45 Parameter revisions made to Cassidy and Son method to facilitate more direct comparison to the Analytical Procedure. ........................................ ........................ 69 46 Comparison of Cassidy and Son with FlagSim and generated models ...........................70 47 Comparison of uniform delay and queue length equations ................. .................71 LIST OF FIGURES Figure page 31 Twolane work zone operated with flagging control.............. .....................................47 32 K value location used in sim ulation ...................................................... ............... 47 33 Screen shot of the program main user interface............................. ............48 34 Screen shot of vehicle parameter setting window..........................................................48 35 Screen shot of the multiple run input form ................................... .......... ...... .. ....... 49 36 Screen shot of anim ation w indow ......................................................................... ...... 49 37 Relationship of work zone speed to capacity..................................................................50 39 Relationship of green tim e to capacity............................................................................50 310 Relationship of work zone length to capacity ......................................... ...............51 311 Relationship of heavy vehicle percentage to capacity ..................................................51 41 Modelestimated queue delay versus simulation queue delay ........................................66 42 Modelestimated queue length versus simulation queue length. .....................................67 A1 Sample of the Summary Output File .............................................................................75 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering ANALYSIS OF TWOLANE ROADWAY LANE CLOSURE OPERATIONS UNDER FLAGGING CONTROL By Thomas Hiles December 2008 Chair: Dr. Scott Washburn Major: Civil Engineering With an aging roadway infrastructure and continual urban development, construction work zones are a common fixture on our roadway system. Work zone delays have a negative effect on not only the transportation network, but also on the national economy as well. While there have been a number of studies conducted on roadway work zone operations, very few of them have focused on twolane roadway work zones, where one lane is closed and traffic flow must alternate on one lane. These types of work zones usually rely on the use of flagging personnel to alternate the flow of traffic on the single open lane. Thus, the analysis of this type of work zone is quite different from that of multilane roadways. While a couple of analysis methods do exist for this type of work zone, there is no commonly accepted or nationally adopted method. The Florida Department of Transportation (FDOT) developed their own method, which is included in their Plans Preparation Manual (PPM). This method is fairly simple and considers a limited number of factors. Consequently, there is a very limited range of field conditions for which this method will yield reasonably accurate results. Furthermore, the only output from method is work zone capacity. The objective of this project was to develop an analysis procedure for twolane roadway work zones (with a lane closure) that was more robust, both in terms of inputs and outputs, than the FDOT's current PPM method. The FDOT also had the requirement that this new procedure still be easy to use. A custom microscopic simulation program was developed to generate the data used in the development of the models contained in the new analysis procedure. Specifically, models were developed to estimate saturation flow rate/capacity, queue delay, and queue length. The analysis procedure also employs calculation elements consistent with the analysis of signalized intersections. The analysis procedure has been implemented into an easy to use spreadsheet format. This procedure is much more robust than the current PPM procedure, and the results match well with the simulation data. For situations that are not handled by the analytical procedure, such as oversaturated conditions, the simulation program can be used instead. CHAPTER 1 INTRODUCTION Background With an aging roadway infrastructure and increase in city sprawl, construction work zones are a common fixture on our roadway system. Work zone delays have a negative effect on not only the transportation network, but also on the national economy, as well. On September 9, 2004, the Federal Highway Administration (FHWA) updated its 'Work Zone Safety and Mobility' rule. This rule mandates that states develop an agencylevel work zone safety and mobility policy. The states' policies must include plans to minimize the congestion impacts to the public, and address all types of roadway facilities and construction operations on a corridor, and network level. From freeways to rural twolane roads, each construction project must develop a plan to lower the cost of congestion. Over the past 20 years, there have been numerous research projects on estimating motorist delays for freeway work zones. However, few research projects have been conducted on twolane, twoway roadway work zones. Such work zone configurations consist of a single lane that accommodates both directions of flow, in an alternating pattern. These work zones typically employ a flagging control person (i.e., someone who operates a sign that gives motorists instructions to stop or proceed) at both ends to regulate the flow of traffic through the work zone. In some situations (usually where the lane closure is long or there are a large number of driveways), a lead vehicle, called a pilot car, may be required to lead the platoon of vehicles through the work zone. Problem Statement Previous to this research project, there was not a single accepted national standard for analyzing work zone operations and estimating performance measures, particularly for twolane, twoway roadways. As a result, transportation agencies were required to develop their own method or adopt/adapt one from existing methods. However, there were a limited number of methods available. The Highway Capacity Manual (HCM) (2000) provides some guidance on work zone analysis, but only for freeway facilities. A software product, called QuickZone, is publicly available, but the level of support and lack of technical documentation (particularly with respect to twolane, twoway work zone configurations) has diminished its widespread acceptance. The Florida Department of Transportation (FDOT) opted to develop their own methodology because of these issues. The FDOT method currently used is a relatively simple deterministic procedure, with rough approximations for work zone capacity and other important parameter values. With everstricter guidelines on acceptable levels of traveler delay from construction activities, it is essential that an analysis method be as accurate as possible. One of the major limitations with most of the existing methods is the assumption of a fixed capacity value, or a very narrow range of capacity values, for a variety of work zone scenarios. However, for twolane, twoway roadways, capacity is a function of saturation flow rate, work zone length, travel time through the work zone, and green time given to each direction of flow. Therefore, to achieve the goals of this project, it was necessary to develop a new procedure, or adapt an existing one, which was more accurate, while still allowing for easy implementation. Meeting these requirements will facilitate the traffic engineering community's acceptance and utilization of the developed method. Research Objective and Supporting Tasks The objective of this research was to develop a procedure to analyze twoway, twolane work zones and implement it in an easytouse format. More specifically, the procedure will estimate capacity, delay, and queue length for varying work zone, traffic, and flagging conditions. The tasks that were conducted to support the objective were as follows: Reviewed the literature to identify existing analysis procedures/methods. Reviewed the state of the practice of flagging operations. Identified alternative analysis methods that could be adapted for use in Florida. Developed a simulation program that calculates several measures of effectiveness for a variety of work zone scenarios, and provides visualization of the work zone operations. Developed saturation flow rate, work zone speed, queue delay, and queue length estimation models from the simulation data. Implemented the models in a spreadsheet format for application by practitioners/analysts. Document Organization In the following report, chapter 2 contains a summary of relevant literature and procedures used by other agencies in analyzing twolane work zones. Next, chapter 3 describes the research approach, including simulation program development and experimental design. Chapter 4 contains a description of the model development and data analysis. Finally, chapter 5 summarizes the study, presents the conclusions reached, and topics for future research. CHAPTER 2 LITERATURE REVIEW Introduction This chapter presents a summary of the review of relevant literature, discusses the literature and proposes a methodology to be developed based on the review of the state of the practice. Specifically, this review addresses two areasprevious research and the procedures used in that research. Background In the literature review process, it was discovered that relatively little research had been performed in the area of twolane, twoway work zones with flagging operations. In contrast, there had been significantly more research conducted on analyzing freeway work zones with lane closures. The reason for this disparity may have resulted from federal government's focus on high traffic/congestion facilities. With the new work zone rule requiring all significant work zone projects to have a traffic management plan, there was a need develop analysis methods for twolane, twoway roadways. The Rule on Work Zone Safety and Mobility, developed in 2004, requires state and local transportation agencies to have traffic management plans in place to mediate work zone related congestion problems by October 2007. This rule states that all "Significant Projects" defined by a state must have a plan from the beginning of the planning process. A "Significant Project" is when certain locations where the congestion will create major delays or there are other projects being performed in coordination, these need to be considered as significant. Twolane, twoway roadways do not automatically qualify as significant (FHWA, 2004). However, for a transportation agency to be able to determine if a twolane roadway work zone would create significant congestion, it needed an accurate analysis method. Previous Research In this section, a summary of previous research is presented that pertains to the estimation of traffic operations in twolane, twoway work zones. Cassidy and Son Cassidy and Son (1995) developed a method to estimate the delays generated due to a lane closure on a twolane, twoway roadway. Their method consisted of a series of equations based on stochastic queuing theory. The delays are primarily a function of traffic demand, travel time through the work zone, and green time. They assessed the validity of their method through both Monte Carlo simulation and microscopic simulation. They concluded that the method "adequately predicts the impacts". The series of equations comprising Cassidy and Son's method are largely based on previously developed equations for analyzing operations at signalized intersections. The sources for these previously developed equations included: 1) Webster (1966) for queue delay estimation at a signalized intersection; 2) Newell (1969) for oneway vehicleactuated signalized intersection operations; and 3) Ceder and Regueres (1990) who obtained average work zone delays from simulation and then compared those results to average delay from Webster's equations. The development of their calculation procedure using equations that account for the stochastic nature of traffic operations in these work zones was based on previous efforts that investigated equations based on both deterministic and stochastic processes (Cassidy and Han, 1993; Cassidy, et al., 1994). An overview of the Cassidy and Son calculation procedure is provided below. The outline lists the required parameters; the work zone types that can be evaluated, and how oversaturated conditions are handled. Calculation procedure outline 1. For undersaturated conditions, estimated delay is a function of: a. work zone length b. work zone speed c. queue discharge rate d. traffic demand e. "red" time 2. For oversaturated conditions, delay is a function of the above factors, and calculated with deterministic queuing equations 3. Work zone types a. Asphalt overlays (w/ pilot car) b. ChipSeal (w/ pilot car) c. General construction (w/ pilot car) d. General construction (w/o pilot car) Field data The data for Cassidy and Son's research consisted of using 15 field sites in California. The field data obtained from these sites were used as the basis to develop parameter values for the four different work zone types listed above. Parameters such as the mean and variance of queue discharge rate, the mean and variance of speed through the work zone, lost time, green time extension, and variance to mean ratios of arrivals and departures were estimated for each of the four work zone types. One issue with their field data is that none of the traffic demand rates were large enough for them to determine the actual capacities of these work zone configurations. While capacity can be determined indirectly through the measured saturation flow rates and proportions of "green" time, these values could not be verified against actual fieldmeasured capacity values. Another potential issue is that at 10 of the 15 field sites, a pilot car was used. The purpose of a pilot car is to lead the queued traffic through the work zone area. Certainly, the presence of a pilot car can have additional impacts beyond that of only flagger control. The Manual on Uniform Traffic Control Devices (MUTCD) (2003) does not offer any guidance on when pilot cars should be used in a work zone. If the work zone is complex or the flaggers do not have a clear sight of the work zone, then a pilot car is usually considered. In Florida, at least, the use of pilot cars at twolane, twoway work zones appears to be quite rare. In their proposed calculation procedure, the startup lost time is a constant value, rather than a random variable, for a given work zone type. They hypothesize that since lost time is typically a small percentage of the overall cycle length, treating it, as a constant value will only introduce a negligible amount of error into the delay estimation. This assumption seems reasonable. Although their delay estimation equation accounts for green time extension (i.e., green time provided after the dissipation of the initial queue), they found that the contribution of this term to the delay estimation was negligible due its small percentage of the cycle length. The "gapout" time (i.e., headway threshold) that was utilized to estimate the green time extension was a constant value of 12.2 seconds, estimated, again, from empirical data. In other words, the green time is assumed to extend for as long as vehicle arrival headways are less than 12.2 seconds. Although Cassidy and Son did not find a relationship between extended green times and the arrival rates, they theorized that the values were a function of the arrival rate. This observation may have been a function of the inherent variance in flagger operations. Simulation data Cassidy and Son's initial efforts in developing a calculation procedure utilized deterministic equations that assumed uniform arrival and queue discharge rates. They then tried to extend these equations by employing Monte Carlo simulation to generate key parameter values for the equations from statistical distributions based on empirical data. While the results of this exercise were more plausible for the stochastic nature of these work zone operations, it still had several significant limitations. This ultimately led them to the adaptation of equations previously developed for modeling vehicleactuated signalized intersections. These equations generally account for the stochastic nature of work zone operations. They also wrote a relatively simple microscopic simulation program for testing the validity of the analytical equations. They found that the equations based on vehicleactuated signalized intersection operations provided the best match with the microscopic simulation results, relative to the equations based on constant values or with values determined from Monte Carlo simulation. FDOT Procedure The FDOT developed a lane closure analysis procedure for use with all road type classes. The procedure is in the Plans Preparation Manual (PPM), Volume I, Section 10.14.7 (2006). The procedure can analyze twolane twoway work zones. In order to accommodate flagging operations, the procedure attempts to determine the peak hour volume and the restricted capacity. From these two values, the time during when lane closures can occur without creating excessive delays is determined. This procedure's main limitation is that capacity is an input, and the given capacities were not specific to twolane work zones. With capacity not based on a flagging work zone value, the procedure quite likely will be unable to model the field conditions accurately. Another limitation with modeling flagging operations with this procedure is that it is based on only the ratio of green time to the cycle length. This assumption does not take in to account the differences in delays of flagging operations, such as the lost time due to the traversing the work zone, startup lost time and the variation of extended green time. The capacity is adjusted by the work zone factor (WZF) shown in Table 21. The WZF is used instead of a calculated travel time based on a typical speed. All of the lost time is also incorporated in to the WZF. This is a simplistic adjustment to incorporate these important factors. The travel time through the work zone is an easy calculation, which would make a logical factor. One of the problems is the WZF is not adjusted by speed and is not documented by what speed the factor is based on. This is an important question, as speeds through a work zone can be quite different for an intense construction operation like chip and seal versus a less intense operation such as shoulder work. The FDOT PPM lane closure analysis procedure is as follows: 1. Select the appropriate capacity (c) from the table below: LANE CLOSURE CAPACITY TABLE Capacity (c) of an Existing 2LaneConverted to 2Way, 1Lane=1400 veh/hr Capacity (c) of an Existing 4LaneConverted to 1Way, 1Lane=1800 veh/hr Capacity (c) of an Existing 6LaneConverted to 1Way, 1Lane=3600 veh/hr Therefore, for a twolane highway work zone, the capacity (c) is 1400 veh/hr. 2. The restricted capacity (RC) is then calculated taking into consideration the following factors: TLW = Travel Lane Width LC = Lateral Clearance. This is the distance from the edge of the travel lane to the obstruction (e.g., Jersey barrier) WZF = Work Zone Factor is proportional to the length of the work zone. This factor is only used in the procedure for twolane twoway work zones. OF = Obstruction Factor. This factor reduces the capacity of the travel lane if the one of the following factors violates their constraints: TLW less than 12 ft and LC less than 6 ft. G/C = Ratio of green time to cycle time. This factor is applied when the lane closure is through or within 600 ft of a signalized intersection. ADT = Average Daily trips this value is used to calculate the design hourly volume. The RC for roadways without signals is calculated as follows: RC (Open Road) = c x OF x WZF If the work zone is through or within 600 feet of a signalized intersection, then RC is determined by applying the following additional calculation. RC (Signalized) = RC (Open Road) x G/C If Peak Traffic Volume < RC, there is no restriction on the lane closure. That is, if the peak traffic volume is less than or equal to the restricted capacity, the work zone lane closure can be implemented at any time during the day. If Peak Traffic Volume > RC, calculate the hourly percentage of ADT at which a lane closure will be permitted. RC(OpenRoad) Open Road% = RC(OpenRoad) ATC x Dx PSCF x RTF where ATC = Actual Traffic Counts. The hourly traffic volumes for the roadway during the desired time period. D = Directional Distribution of peak hour traffic on multilane roads. This factor does not apply to a twolane roadway converted to twoway, onelane. PSCF = Peak Season Conversion Factor RTF = Remaining Traffic Factor is the percentage of traffic that will not be diverted onto other facilities during a lane closure. Signalized% = (Open Road %) x (G/C) Plot the 24hour traffic, relative to capacity, to determine when a lane closure is permitted. QuickZone To estimate the work zone congestion impacts, the FHWA developed QuickZone. QuickZone 2.0, which was released in February 2005, is an Excelbased software tool for estimating queues and delays in work zones. The maximum allowable queues and delays are calculated as part of the procedure in optimizing a staging/phasing plan and developing a traffic mitigation strategy. As a result, lane closure schedules are recommended to minimize user costs. This is a quick and easy method, with a userfriendly, concise spreadsheet setup. (Arguea, 2006). The QuickZone method requires the following input data: * Network data Describing the mainline facility under construction as well as adjacent alternatives in the travel corridor, which can be used to calculate the traffic diversion * Link capacity Each link has its own capacity value for vehicles per hour * Project data Describing the plan for work zone strategy and phasing, including capacity reductions resulting from work zones * Travel demand data Describing patterns of preconstruction corridor utilization * Corridor management data Describing various congestion mitigation strategies to be implemented in each phase, including estimates of capacity changes from these mitigation strategies QuickZone has a module for flagging operations. The procedures are similar to other roadway types handled within the program. However, for flagging operations, QuickZone is limited in several areas. One limitation is that if the work zone is over a mile in length, it assumes the use of pilot cars, which adds an additional lost time factor. Another limitation, per se, is that user interface for the twolane work zone analysis is cumbersome at best, making the data input process very difficult. An additional limitation was the lack of control on the flagging operation. QuickZone requires a pilot car with work zones longer than 1.0 miles, and maximum green time cannot be adjustedan important policy decision in work zones near or over capacity. Another limitation was, unfortunately, very limited documentation on the analysis procedure and justification for selected parameter values. A thorough review of QuickZone's internal calculations procedure written in Microsoft Excel VBA was performed, and from this, it was determined that the twolane work zone procedure was inadequate for the needs of this project. Colorado DOT The Colorado DOT "Lane Closure Strategy" (2004) was intended to give guidance on scheduling lane closures on twolane work zones. Capacity values were determined by the probability of a cycle failure (inability to serve all vehicles) based on a Poisson distribution. It was assumed that some cycles would fail, so a 10% failure rate was allowed. For their analysis, it was determined that 60 seconds was an appropriate "green time" for each direction. The capacity determined for a 10% failure rate results in an average of 22.2 vehicles through the work zone in each direction per cycle. The speed limit through the work zone was assumed to be 30 mi/h. The travel time through the work zone was calculated based on a loaded semitruck accelerating to 30 mi/h. This results in 34 oneway cycles per hour for the 0.25mile closure and 18 cycles for the 1.0mile closure. The resulting hourly capacity calculated for a work zone in flat terrain was 755 veh/h for a 0.25mile work zone and 400 veh/h for a 1.0mile work zone. This analysis is a simple approximation of the field conditions. Flagging variations were not taken into account, and the time to traverse the work zone used the acceleration value from a semitruck, which can be the limiting condition in certain scenarios. One critical assumption made was a 60second green time. This green time was most likely used because the model formulation was based on a delay formulation for signalized intersections, with an upper limit of 72 seconds of green time. With these assumptions, the Colorado DOT model estimates lower capacity values than the Cassidy and Son (1994) method. Summary and Conclusions The literature review explored existing methods/models that were used to estimate capacity and delays for twolane work zones with flagging operations. However, only a limited number of research projects on this topic have been conducted to date, and it is evident that additional research is still needed fully understand work zone operations under flagging operations. * All methods/models examined either use a single, or a very limited number of capacity values. o While the Cassidy and Son method calculates capacity from the saturation flow and green time proportion, they still only use four different values of saturation flow rate (and those only range in value from 1018 veh/h to 1090 veh/h). Obviously, capacity is the most influential factor in work zone operational quality, if not all roadway facility types. Ideally, capacity (or possibly saturation flow rate) should be estimated for the specific combination of work zone conditions being analyzed to more accurately estimate delays and queue lengths. For the existing methods/models, there are clearly many combinations of work zone conditions that result in significantly different capacity values than those "builtin" to the method. Even the Cassidy and Son field data found a range of saturation flow rates from 750 to 1450 veh/h. o FDOT PPM uses a capacity value of 1400 veh/h * With QuickZone's limited documentation on development and procedures used for two lane work zone analysis, the program is difficult to implement into a traffic management plan for twolane work zones. The significant weakness with QuickZone is the requirement for the user to input a capacity. With no guidance, the user has to make their best guess, which could potentially be significantly inaccurate. * The Colorado Department of Transportation procedures were overly conservative and did not provide much flexibility to the user to adapt the methods to a particular location. Without much flexibility to be adapted to specific locations, this method was too limited to be further developed to implement in Florida. * Besides the Cassidy and Son research, the available methods generally provide little technical documentation about the method and/or the derivation of parameter values used in the method. Furthermore, other than the Cassidy and Son study, there is a general lack of field data that have been collected to validate any of the developed methods. However, even with the Cassidy and Son data, most of the field data were obtained from sites using a pilot car and operations levels were generally well below capacity. Table 21. FDOT work zone factor. WZL (ft.) WZF WZL (ft.) WZF WZL (ft.) WZF 200 0.98 2200 0.81 4200 0.64 400 0.97 2400 0.8 4400 0.63 600 0.95 2600 0.78 4600 0.61 800 0.93 2800 0.76 4800 0.59 1000 0.92 3000 0.74 5000 0.57 1200 0.9 3200 0.73 5200 0.56 1400 0.88 3400 0.71 5400 0.54 1600 0.86 3600 0.69 5600 0.53 1800 0.85 3800 0.68 5800 0.51 2000 0.83 4000 0.66 6000 0.5 CHAPTER 3 RESEARCH APPROACH Introduction This chapter describes the research approach adopted to find the capacity, delays, and queue lengths in twolane twoway work zone configurations. More specifically, it discusses the methodological approach, field observations, simulation model development, and the simulation experiments. Also included is description of the sensitivity analysis employed to discover the key variable ranges used in the experimental design. Methodological Approach The typical work zone flagging operation configuration consists of a single lane that accommodates both directions of flow, in an alternating pattern. Figure 31 shows a typical two lane work zone with a lane closure. These work zones predominately use a flag person (i.e., someone who operates a sign that gives motorists instructions on whether to stop or proceed) at both ends to control the flow of traffic into the work zone. Significant delay is incurred by motorists due to the lost time that accrues while the opposing direction has the rightofway. Additionally, both directions incur lost time when there is a change in the rightofway as the last vehicle that received the rightofway must traverse the entire length of the work zone; therefore, all vehicles must wait until the last vehicle has passed the opposite stop bar. The queue discharge is similar to the operation of a signalized intersection, but the lane switch along with the proximity to construction activity would have an affect on the discharge rate. Changing of the rightofway is rarely performed in an optimal manner. Flaggers are not trained on how to switch the rightofway in such a manner as to minimize delay, or otherwise optimize some particular performance measure (Evans, 2006). Generally, flaggers change the flow direction due to queue and cycle length. The queue at the beginning of the "green" period discharges at the saturation flow rate. After the initial queue dissipates, flaggers usually extend the green to allow for vehicles still arriving. This extension time can be lowered if there is a significant queue in the opposite direction. At this point, the flow through the work zone will drop to the arrival rate. The arrival rate can be significantly lower than the queue discharge rate on low volume roadways, thus increasing the overall average delay if vehicles are queuing at the opposite approach (Cassidy and Son, 1994). The standard performance measures for a work zone with flagging operations are: Capacity maximum vehicle throughput Delay time spent not moving, or at a slower speed than desired Queue lengths vehicle arrivals minus vehicle departures for a specified length of time Ideally, the operational impacts of these work zone configurations should be studied at field sites resulting in a dataset that could be used to develop a methodology for estimating two lane work zone capacity. At the field sites, the factors that contribute to the capacity degradation could be extensively examined. These factors could be used to provide additional insight into the results of a simulation study. There would be a large number of different work zone scenarios encountered in the field. Consequently, there are two complications to collecting field data from all of these scenarios: 1) It is not possible to find all such scenarios within a reasonable distance and within the project period, and 2) the project budget does not allow for field data collection at a large number of sites. Therefore, the approach chosen was to use simulation data for the analysis procedure development. However, a limited number of informal field observations were performed to have an understanding of their operations. These sites gave an idea of how the work zones were controlled. Simulation To generate the data for developing the analysis procedure a work zone simulation was used. Using a simulation program provides the ability to test a much larger variety of traffic and work zone configuration conditions than would normally be possible from the amount of field data collected within the normal timeline and resources of a project. Twolane work zones are unique in their operation. In order to estimate the operation a number of factors are required. The following capabilities were necessary to simulate twolane work zones: model a variety of flagging control methods model vehicle arrivals at the work zone model vehicles discharging from the stop line model heavy vehicles, in addition to passenger cars model vehicles traveling through the work zone record various simulation results in order to allow for the following performance measures to be calculated o Lost time due to rightofway change o queue delay o travel time delay due to reduced speeds o queue length o capacity A review of existing commercially available simulation packages was made to determine if any were readily applicable to this situation. VISSIM, CORSIM, AIMSUM, and PARAMICS do not explicitly provide for modeling of work zones on twolane roadways. The key to this research project was the ability to model the flagging control. Each program could be used to change to from green to red, using different detector settings. However, what prevents the implementation of other software packages was the inability for the available programs to track the last vehicle through the work zone. This feature was needed in order to begin the green period for the opposite direction. Additionally, it was required to have more ability to control inputs and outputs. Additional control over the arrangements of inputs and outputs allows for more efficient running of the simulation scenarios and more efficient processing of the results. A lack of technical documentation detailing the underlying methods/models was also problematic for several commercially available simulation models. Program Development The simulation program that was developed, called FlagSim, is a Windowsbased application written with the Visual Basic 2005 language. FlagSim is a microscopic, stochastic simulation program that models the arrival of vehicles to the work zone, the discharge of vehicles into the work zone area, and the travel of these vehicles through the work zone area. From this program, the capacity of the work zone, and delays imparted to the motorists were calculated. The purpose of the program was to realistically model traffic operations in work zone areas using flagging operations and use the results of the data analysis from simulation to develop an analytic computational procedure to estimate pertinent performance measures. Vehicle distribution For each simulation run, a unique set of vehicles was created. This set of vehicles can be defined by the user, given a variety of inputs defined in FlagSim. To choose the vehicle set, a vehicle generator selects from four different vehicle types. The selection was randomly generated, based on userspecified vehicle proportions. Four vehicle types were available within the simulation program: 1) passenger cars, 2) small trucks, 3) medium trucks, and 4) large trucks. For these vehicle types, the user also has the ability to adjust the properties of each vehicle type to fit a particular traffic pattern. Vehicle properties Each vehicle in the program becomes unique based on the vehicle type properties set initially by the user. Each vehicle generated had a number of properties to define the vehicle's characteristics. These characteristics were length, acceleration, freeflow speed, headway, and queue spacing. Some of these properties were treated as random variables according to a normal distribution. Thus, using the user inputted mean and standard deviation for each of these properties, the property values were set according to Eq. 31. Value = sxrorm + [31] where Value = vehicle parameter value, such as desired free flow speed, stop gap distance, time headway, max and min acceleration s = standard deviation input by the user rnorm= random normal number generated by the random normal function1 S= mean value of the property inputted by the user Vehicle arrivals Vehicle arrivals were an important part of the simulation because the distribution of the entering vehicle headways affects how the flagging control algorithms will function. If vehicle headways are generated according to a uniform distribution, then vehicle enter at the same headway, so there arrival at the stop bar will be more uniform than what would be seen in the field. In FlagSim, it was important to have a vehicle arrival process that was realistic. Thus, the vehicle arrival headways, by default, are generated according to a Poisson process. The vehicle arrival headway times are based on the negative exponential probability distribution, as shown in Eq. 32. h = ln(r) x A [32] 1 See Numerical Recipes citation in references section where h = vehicle headway, in seconds r = random number generated from a uniform distribution2 A = average arrival rate, in veh/sec In = natural logarithm Upper and lower bounds were also applied to the generated headway values. Extremely high headway values will lead to significant differences between the input volume and the simulation volume. Extremely low headway values are not realistic due to drivers' general desire to maintain a safe following distance. The lower bound was set to 0.5 seconds. The upper bound was set to a value of four times the average vehicle arrival rate. These values resulted in the simulated volumes reflecting the input traffic volumes. The program has the capability to allow the user to select a uniform arrival rate. The uniform arrival rate was used for calibration to compare procedures that are based on uniform arrivals. Initial speed After a vehicle was generated into the network, the initial speed of the vehicle was set. The desired speed of the vehicle was its free flow speed determined during the setting of the vehicle's properties. A vehicle's speed was initially set to the free flow speed. In some cases, a vehicle that enters at its desired speed could collide with the lead vehicle. A check was performed to determine if the vehicle was too close to its lead vehicle. If the distance between vehicles was too close then the vehicle's speed was set to the current speed of the lead vehicle with an acceleration of zero. 2 This value is generated from the 'Rnd' function within Visual Basic 2005, which generates pseudorandom numbers between 0 and 1 according to a specific algorithm. http://support.microsoft.com/kb/q231847/ Carfollowing model The carfollowing model was an important component of the simulation program. The carfollowing model was the mathematical foundation of the computations that described the movement of vehicles through the specified roadway system. The selection of a carfollowing model for this program was based on specific criteria. The queue discharge aspect of traffic flow in the work zone area was the most critical element to the validity of the simulation results. Therefore, the model selected had to be particularly suitable for modeling the queue discharge phenomenon. After review of various models, the ModifiedPitt carfollowing model (Cohen, 2002) was selected for implementation. The ModifiedPitt carfollowing model was demonstrated by Cohen (2002) and Washburn and CruzCasas (2007) to work well for queue discharge modeling situations. For more discussion on queue discharge models, refer to Washburn and CruzCasas (2007). The Modified Pitt carfollowing equation calculates the acceleration value for a trailing vehicle based on intuitive parameters such as the speed and acceleration of the lead vehicle, the speed of the trailing vehicle, the relative position of the lead and trail vehicles, as well as a desired headway. This equation also incorporates a sensitivity factor, K, which will be discussed later in more detail. This equation allows for relatively easy calibration. Carfollowing models are generally based on a 'driving rule', such as a desired following distance or following headway. The Modified Pitt model is based on the rule of a desired following headway. As indicated before, the acceleration of each vehicle depends of the leading and trailing vehicle and this model takes into consideration the physical and operational characteristics of both. The main form of the model is shown in Eq. 33. a, (t + T) = [33] T(h + ) 2T where af(t+T) = acceleration of follower vehicle at time t+T, in ft/s2 al(t+R) = acceleration of lead vehicle at time t+R, in ft/s2 si(t+R) = position of lead vehicle at time t+R as measured from upstream, in feet sAt+R) = position of follower vehicle at time t+R as measured from upstream, in feet vf(t+R) = speed of follower vehicle at time t+R, in ft/s vl(t+R) = speed of lead vehicle at time t+R, in ft/s L = length of lead vehicle plus a buffer based on jam density, in ft h = time headway parameter (refers to headway between rear bumper plus a buffer of lead vehicle to front bumper of follower), in seconds T= simulation timescan interval, in seconds t = current simulation time step, in seconds R = perceptionreaction time, in seconds K = sensitivity parameter (unitless) For application to this project, the value of the L parameter varied based on one of the four different vehicle types. The time headway parameter (h) was set as a random variable, rather than a constant value, to introduce an additional stochastic element to the model. The value of the vehicle headway was based on a normal distribution to represent the more realistic scenario that desired headways vary by driver. The mean and standard deviation for this distribution can be specified for each of the four vehicle types. Thus, desired headways can vary by driver, as well as by vehicle category. The perceptionreaction time, R, and the simulation timescan interval, T, are important parameters. Considerable time was spent experimenting with different values for each. Ultimately, both values were set to 0.1 seconds. This value for the timescan interval provided for very detailed vehicle trajectory data, which enabled very accurate measurements to be made of the measures of effectiveness, and enabled smooth vehicle animation in the work zone visualization screen. While a perceptionreaction time of 0.1 seconds may seem intuitively low, it was found that this led to the most realistic traffic flow representation. Individual perception reaction times are undoubtedly higher than this for any isolated event. However, the fact is that reallife traffic flow happens on a continuous time scale, and reallife drivers make continuous incremental acceleration and deceleration (as well as steering) inputs, withstanding sudden events/panic maneuvers. Thus, these constant incremental changes by both leading and following vehicles generally results in smooth traffic flow. Again, this value of 0.1 seconds for the timescan interval and perceptionreaction time resulted in this type of realistic traffic flow. Queue arrival and discharge The sensitivity parameter, K, has two separate values in the carfollowing modelone for the queue arrival and discharge and for the travel through the work zone. Cohen stated that a larger K value should be used in interrupted flow conditions due to overdamping effects (Cohen, 2002a). This assumption was tested in the carfollowing model and yielded the best results. Vehicles had a smoother interaction in the work zone (uninterrupted flow) with K = 0.75 and for the queue arrival and queue discharge processes performed well with K = 1.1. The definition of the queue arrival area was 300 feet upstream of the last vehicle in queue, and the definition of the queue discharge area was 300 feet downstream of the entering work zone stop bar. Another key parameter, for queue discharge, was the heavy vehicle acceleration rate. The truck acceleration rate was based on work by Rakha and Lucic (2002), from which a constant value of 1.5 ft/sec2 was selected for implementation in FlagSim. From a visual inspection of the animation, and review of vehicle trajectory data, this value resulted in reasonable truck headways. Flagging operations A significant feature of FlagSim was the ability to specify several different methods by which the rightofway could be controlled. Changing of the rightofway can be a complex operation. A decision to change the rightofway is generally based on several factors, such as the amount of traffic that needs to be served in each direction of travel, the time it takes to travel the work zone, and policy considerations such as maximum queue length or maximum green time. A flag change, much like a phase change at a signalized intersection, has a lost time associated with it. For the work zone to operate efficiently, the rightofway must not be switched too often such that the lost time becomes a significant portion of the cycle length. Additionally, the flagging method employed at a work zone site is almost guaranteed not to result in optimal condition; for example, minimizing vehicle delay. This nonoptimal condition is a direct result of the flag operators allocating nonoptimal amounts of green time. Cassidy and Son (1994) stated that the green time was most often extended past the optimal time that should be given to each direction. Startup lost time Startup lost time begins when the front bumper of the platoon's last vehicle crosses the stop bar exiting the work zone and ends when the front bumper of the vehicle entering work zone crosses the stop bar. This lost time is caused by several factors. The first delay occurs as the last vehicle exiting the work zone travels from the work zone exit point to a safe distance in order to allow the next direction of vehicles to proceed. The exiting vehicle must maneuver the lane switch area and pass the first few vehicles queued. Second, an additional time is needed for the flagger to perform the flag change, such as the time it takes the flagger to determine when the work zone is clear. Finally, there is lost time for the first vehicle reacting to the change of the sign, similar to vehicles' startup lost time at a signalized intersection. In addition, since this lost time is random in the field, the program accounted for this randomness by modeling it with a normal distribution, using a mean of 10 seconds and a standard deviation of (+/) 2 seconds. The randomness accounts for variation with the flaggers and variation in drivers' reaction to the changing of the flag. The first vehicle was delayed the calculated amount of time before beginning to proceed into the work zone. Flagging methods FlagSim contains a variety of flagging methods to try to encapsulate the various methods operators might use to control twolane work zones. The flagging control methods are generally based on control strategies used in traffic signal operations. The following flagging methods are implemented in FlagSim. Distance GapOut: Rightofway change is based on specified distance gap between approaching vehicles. Queue Length: Rightofway change is based on a maximum queue length of vehicles on the opposing approach. Fixed Green Time: Rightofway is changed after the specified fixed green time is reached. This flagging method can also be used in combination with the distance gap out, and queue length methods, subject to a maximum green time. User Interface The user interface was designed to allow the user to quickly and easily use the program. To accomplish this, multiple input forms were incorporated. The main user form is shown in Figure 33. In this form, the user is able to select the most common program inputs. The main form gives the user the ability to quickly edit a single run and generate the results and animation. More detailed user inputs are contained in the 'Vehicle Parameter Settings' form (Figure 34); however, it is not intended that these values be changed unless the analyst has specific data for a site contrary to these values. To facilitate multiple runs of a given scenario, the 'Multiple Run Simulation Control' input form (Figure 35) is provided. Animation FlagSim incorporates a 2D postprocessor animation viewer, shown in Figure 36. The animation allows the user to view the computations previously performed. Viewing the animation gives the user an opportunity to review the simulation scenario visually. Items that can be easily checked are vehicle generation, carfollowing interaction, and the flagging variations. At the top of the screen are the controls, which allow the user to control the animation play, pause, stop and speed control. One feature of the animation is the vehicletracking window, shown in Figure 36. A small popup window appears if the user leftmouse clicks on a vehicle. This window displays all of the timestep by timestep vehicle trajectory information for the selected vehicle. Outputs of the simulation Since FlagSim is a microscopic simulation program, detailed vehicle trajectory data (i.e., acceleration, velocity, and position values) are generated at each time step. These data can be saved to a time step data (TSD) file if the user so desires, in which case one TSD file per travel direction is created. From the detailed time step data, several performance measures can be calculated for the desired analysis period. These include: Total delay The queue delay and the travel time delay accumulate for the entire simulation period. Average delay per vehicle The total delay divided by the number of vehicles exiting the work zone during the simulation period. Average queue delay The average delay of vehicles spent in a queue at the entrance to the lane closure area. For this project, queue delay was accumulated for any vehicle traveling less than 10 mi/h. Thus, this measure represents a hybrid queue delay between the traditional measures of stop delay (where delay is only accumulated when vehicle velocity equals zero) and control delay (where delay is accumulated for a vehicle any time its velocity is less than the average running speed). The value of 10 mi/h was a compromise value to try to capture delay for those vehicles that were decelerating or stopped due to queuing, and not slowing just due to regular traffic flow conditions. Average cycle maximum back of queue (veh/cycle) The average of the all the maximum back of queue lengths for each cycle. It should be noted that this queue length is in terms of number of vehicles, and is the absolute maximum back of queue (which accounts for vehicles arriving on green at the back of the initial queue at the start of green). Maximum back of queue (veh/simulation period) The maximum back of queue length that occurs during the entire simulation period; that is, across all cycles. Average travel time delay through the work zone Travel time delay was calculated based on the time the vehicle enters the work zone and the time it exits the work zone at the opposite crossbar compared to the time the vehicle would have traveled through the work zone if no work zone were present. Average time spent in the system The total time a vehicle spends in the entire system from start of the warm up segment to a position 2000 feet passed the opposite stop bar. Only vehicles that have entered and completely exited the system are included in this measure. Maximum vehicle throughput (i.e., capacity) The number of vehicles exiting the work zone. This is a function of the saturation flow rate, the green time, and the cycle length (which is a function of green time, startup lost time, and travel time through the work zone). Average Cycle Length Cycle length was measured from the beginning of green for one direction to the next beginning of green for the same direction. The average cycle length is calculated simply as the sum of all cycle lengths divided by the number of cycles in the simulation period. Average Green Time The sum of all green periods, by direction, divided by the total number of green periods during the simulation period. Average g/C The average g/C was the average of all g/C ratios for all cycles during the simulation period. A summary file containing all these performance measures can be generated by FlagSim. This file provided the input and output data that were used in the development of the calculations/models for this project. Simulation Calibration For a simulation program's output to be considered valid, it should be calibrated to match real world situations. However, for this project, the resources were not available to perform field data collection. To supplement this lack of field data, a quasicalibration procedure was utilized, which consisted of evaluating the reasonableness of traffic flow in three different modes: 1) queue buildup, queue discharge, and uninterrupted flow through the work zone. The queue buildup component of traffic flow was the most challenging to implement. To have realistic vehicle movement, logic had to be implemented to ensure that a vehicle would decelerate in time to avoid a rearend collision, yet would not decelerate at an unreasonably high rate (i.e., wait until the "last second" to slam on the brakes). Thus, the logic employed was such that a vehicle would decelerate at a reasonable value (on the order of 10 ft/s2) when approaching the stop bar or the back end of a queue. This assumption seems reasonable since drivers would have an appropriate warning of the work zone ahead and would take enough precaution to slow as directed by the work zone signage. Another assumption was that all vehicles, no matter how far back in the queue, have enough warning to begin deceleration. For the queue discharge component of traffic flow, results from an earlier research project performed by Washburn and CruzCasas (2007) were utilized. For this project, an extensive database of queue discharge headways was created. Fortyone hours of video data were collected from six signalized intersections around central Florida. From the video data, queue discharge headways were measured for the same four vehicle types as used in FlagSim. These data provided a reasonable comparison data set because the queue discharge phenomenon at the work zone stop bar is similar to the queue discharge phenomenon at a signalized intersection. However, there can certainly be some differences, particularly for the traffic flow in the direction of the closed lane (i.e., for the vehicles that have to perform a lane shift). To extract the headway values from FlagSim, the program exported the first 10 vehicle headways from the beginning of the green time. These data were compared to the data of Washburn and Cruz. FlagSim had an average headway value of 2.01 seconds, which was reasonably consistent with the results from Washburn and Cruz (2007). For the uninterrupted flow of traffic through the work zone, visual inspection of the simulation animation was performed. For this component of traffic flow, vehicle spacing was the key factor analyzed. The initial platoon would eventually dissipate during travel. Each vehicle has a different desired freeflow speed; therefore, slower vehicles would separate from the leader and fall out of the carfollowing mode. This would happen to several vehicles; thus result in a number of smaller platoons of vehicles. This phenomenon was also observed during informal field site visits. In addition, proper implementation of the flagging control methods was confirmed by visual inspection of the simulation animation. Sensitivity Analysis To determine the most appropriate variables to include in the experimental designs, which were used to generate the data for model development, a sensitivity analysis was performed. The objective was to identify variables that significantly affected capacity, delay, and queuing, as well as the form of their relationship. Due to the computational time required for large experimental designs, variables that did not have a considerable effect on work zone performance were excluded from further consideration. Each analysis scenario had the same base input values. From this base set of inputs, one variable would then be varied over a given range. The base input values were as follows: Work zone length 1 mile Work zone speed 40 mi/h Posted speed 40 mi/h Heavy vehicles 5 percent Max green time 120 seconds Traffic demand greater than capacity Input traffic volumes were selected to insure that the traffic demand was greater than the capacity. The results from the sensitivity analysis are provided in the following figures. The thick line (with diamonds) represents the total traffic throughput (i.e., both directions) of the work zone. The directional traffic flows are represented by the dashed line (with squares) and thin solid (with triangles) lines. Figure 37 shows the relationship of the work zone travel speed to capacity. This relationship indicates that the slower the speed, the lower the capacity. This trend results from the longer time it takes for a vehicle to traverse the work zone, and the additional lost time incurred during the rightofway change. Figure 38 shows the relationship of green time to capacity. The green time value varied from 30 seconds to 360 seconds. The capacity of the work zone increased with increased green time given to each direction. The cycle length increases as the green time increases, which is consistent with signalized intersection operations, and the longer the cycle length, the more vehicles that can be served. This increase in capacity occurs because the percentage of lost time for the cycle length is reduced. Travel time through the work zone during the rightofway change is the largest component of the lost time. While increasing the green time does generally increase the capacity and lower the average delay, it must be noted that a practical maximum green time should be implemented. While one direction has the "green" indication, the other direction obviously has a "red" indication. The longer the green for one direction, the more the queue length builds in the other direction during red. Thus, the individual wait time will eventually reach an intolerable level, from a driver's perspective, as well as the queue length. At this point, the rightofway must be switched, even if it means less than optimal performance measure values. The assumption used in this project was that 5 minutes was reasonable practical maximum green time. Shorter than optimal green times may also be necessary when there are queue storage constraints, such as when the work zone is close to an upstream intersection. The relationship of work zone length to capacity is shown in Figure 39. It can be seen that work zone capacity decreases as the length of the work zone increases. This decrease in capacity can be explained by the increase in the time it takes the last vehicle to enter the work zone on "green" to traverse the work zone, which results in additional lost time. The relationship of heavy vehicle percentage to capacity is shown in Figure 310. An increase in heavy vehicle percentage results in a decrease in capacity. Trucks decrease the queue discharge rate, as well as lower the average speed of vehicles traveling through the work zone, with both factors contributing to a decrease in work zone capacity. Experimental Design Arguably, the two most important measures of effectiveness at twolane work zone sites are delay (particularly queue delay) and queue length. The simulation program was used to generate the data set upon which regression models for estimating these measures were based. These models were incorporated into an analysis procedure for twoway, twolane work zones. Capacity, which is a function of several variables, is the single most influential parameter on values of delay and queue length. The simulation program was also used to generate values of capacity that would later be used to verify the saturation flow rate model and capacity calculations based upon the modelestimated saturation flow rates. Variable Selection Two experimental designs were developed; one for generating capacity values and one for generating queue delay and queue length data. For the development of the experimental designs, the first step was to identify the variables that were expected to have significant influence on the values of the performance measures. The following variables were selected for the capacity experimental design based on the results from the sensitively analysis: * Work zone length: Work zone length affects the travel time through the work zone, which in turn affects lost time and cycle length. * Travel speed through the work zone: Travel speed affects the travel time through the work zone, which in turn affects lost time and cycle length. The speed downstream of a traffic "signal" stop bar has also been shown to affect the queue discharge rate at the stop bar. * Percentage of heavy vehicles: Heavy vehicles affect two components of the traffic flow the queue discharge rate and the travel time through the work zone. The queue discharge rate is affected because large trucks have a slower acceleration rate and consume more space in the queue. For travel through the work zone, trucks again consume more space on the roadway and have slower acceleration rates. Furthermore, truck drivers generally have lower desired travel speeds than passenger cars, presumably particularly so in a work zone area where lateral clearances are more constrained. * Green time: Higher green times result in higher capacities. However, higher green times also result in longer cycle lengths and longer red times. As the red time increases with the green time, the resulting queue delays and queue lengths quickly reach intolerable levels from a driver's perspective. Thus, as previously mentioned, it is usually necessary to implement a maximum acceptable green time. Traffic volume was not a variable in the experimental design. To obtain capacity values, it was necessary to specify a traffic demand that would exceed the expected capacity for the specific combination of input variable values. The same experimental design was used to generate data for both delay and queue length, as the same variables affect both measures. Work zone length, work zone travel speed, and percentage of heavy vehicles were also used in the queue delay/length experimental design. Traffic volume was added to this experimental design, in the form of a total twoway volume and a directionalsplit (D) factor, as traffic volume obviously has a very significant effect on queue delay and queue length. The other variable added was a distance gapout flagging method, as explained in more detail as follows. Several options were possible for the selection of green time values. One option is the maximum green time, as was used for the capacity experimental design. This option is not very realistic, as this maximum green time would only be used for capacity conditions. For situations where the traffic demand is less than capacity, it is likely that smaller green times would be used. Another option is to determine what cycle length is appropriate for each specific combination of variables, and then proportion fixed green times for this cycle length according to the traffic demands in each direction. This option, however, is not realistic for implementation in the field, as flaggers cannot be expected to implement different fixed green times for the varying traffic demands that occur throughout the lane closure period. Another option is to have the flagger allocate just enough green time to serve the initial standing queue at the beginning of the green period. This could also be combined with adding a fixed amount of extended green time to serve vehicles that arrive at the back of the queue during the green period. One challenge with this from a field implementation standpoint is that the flagger may not always be able to see the back of the initial standing queue at the beginning of green. In addition, implementing a fixed green time extension period would probably be difficult for flaggers to implement given that it would be relatively short in duration and they would have to continuously look at a watch or other timing device. Although the maximum green time method employed for the capacity experimental design would also require a flagger to use a timing device, they would not have to check it nearly as often due to the much longer timing period. Furthermore, small errors (on an absolute basis rather than percentage basis) in the actual timing used would not have as significant of an impact on the maximum green time method as the short duration green time extension method. Another option, and the one selected for the experimental design, is a distance gapout method with a maximum green time. With this method, green time is allocated until a specific distance between arriving vehicles is exceeded at the entrance to the work zone, or the maximum green time is reached. The distance gapout method was implemented rather than a time gapout method (as often used in actuated signal control) because it was assumed that implementation of a time gapout method is very difficult to do with human flag operators. With the distance gap out method, a mark or cone can be placed at the appropriate distance and the flagger would be instructed to change the rightofway if there are no vehicles between that mark/cone and the stop bar. This method also offers the potential to reduce vehicle delays relative to fixed timing, as it is responsive to actual traffic demands, such as at vehicle actuated signalized intersections. There is one disadvantage to this method for model development purposes, and that is that the green time is not fixed from one cycle to the next. Therefore, the green time and cycle length were recorded for each cycle during the simulation period to allow for calculating average g/C ratios for each scenario. The values chosen for the gapout distance were based on a number of criteria. The first being stopping sight distance values for the corresponding roadway speed approaching the lane closure area, as given by Eq. 34. The second was the gap had to be long enough not to allow a premature switch in rightofway due to a gap forming in the queue. Gaps tended to form if the first truck in queue was following a number of passenger cars. The third was that the value could not be greater than the average arrival rate or the maximum green time would frequently control. SSD= ~ +Vxt [34] where SSD = stopping sight distance (ft) a = deceleration rate (ft/s2) V1 = initial vehicle speed (ft/s) g = gravitational constant (ft/s2) t, = perception/reaction time (sec) G = roadway grade (+ for uphill and for downhill) in percent/100 In this equation, a value of 1.0 second was used for the perceptionreaction time and a value of 10.0 ft/s2 was used for the deceleration rate. These values are the same as those typically used for yellowinterval timing (ITE, 1999). Although AASHTO (2001) recommends values of 2.5 seconds for perceptionreaction time and 11.2 ft/s2 for deceleration rate for this equation, it was felt that the yellowinterval timing values were more appropriate for this situation where drivers are expecting to have to possibly come to a stop, whereas the AASHTO values are more appropriate for unexpected stopping situations. The grade was assumed to be level, which is generally appropriate for Florida conditions. Even with this gapout method, it should be noted that the maximum green time of five minutes was also applied. Setting Variable Levels The second step in developing the experimental design was to determine the values that will be used for the chosen variables. Two levels (i.e., values) for each variable are typical for situations in which the relationships are linear in nature. If certain relationships are nonlinear in nature, then it is necessary to use three levels for each variable. If the relationship is not predetermined to be linear, then it is usually prudent to use three levels. However, the size of the experimental design (i.e., number of runs) will increase substantially in this case. This can be illustrated with Eq. 35. R = LF where R = Number of unique variable combinations (or simulation runs) L = Number of levels F = Number of factors So for example, an experimental design with seven variables, each run at two levels, would yield 32 (25) unique variable combinations, whereas an experimental design with seven variables, each run at three levels would yield 243 (35) combinations. Thus, if it is known that the relationships of interest are linear, there will be a substantial savings in computational time versus the calculation time of a nonlinear relationship. The selected variables, and their setting levels, for the capacity and queue delay/length experimental designs are shown in Table 31 and Table 32, respectively. Number of Replications The final step of the experimental design is to determine an appropriate number of replications (i.e., runs of the simulation program) for each combination of variables in the experimental design, to account for the stochastic nature of each simulation run. The number of replications required is a function of the desired statistical confidence level, the variance of the data, and the acceptable error tolerance. Eq. 36 can be used to calculate the necessary sample size. n = s a2 [36] where n = minimum number of replications s = estimated sample standard deviation z/2 = constant corresponding to the desired confidence level S= permitted error [35] To determine an appropriate number of iterations, numerous test simulation runs were made. The runtorun variance was calculated for capacity, delay, and queue length. These variance values were used in Eq. 35 with a 90% confidence level (za/2 = 1.645) and error tolerance of 5% of the variable of interest. From this exercise, it was determined that five iterations were sufficient. Therefore, after choosing three levels for each of 5 variables, for a 35 experimental design, with 5 replications, a total of 1215 (243 x 5) simulation runs were required. The next step in the project was to execute the experimental design with the simulation program. The following chapter will describe the data analysis, model development, and development of the calculations procedure based on the resulting simulation data. Length of Queue Stop Bar Arriving vehicle SBack of r Traversing Lane Shift Queue work zone Figure 31: Twolane work zone operated with flagging control. Kvalue= 0.75 1.1 1.1 300 ft Figure 32. K value location used in simulation. Discharge 0.75 300 ft .... Main InputUVar iab a i t rn s Project Titte Direction 1 Direction 2 North v South Directory to Save Resiuts Fe U:\Traffic\Tom Hiles\FlagSim Data\ Traffic Variables Vehicle Arrival Rate (vehth) Direction 1 (Peak) 50 Direction 2 (OffPeak) 50 Pet. Small Trucks Pet. Medium Trucks Pct. Large Trucks Pct. Passenger Cars 97 Vehicle Arrivals Dist. Negative Exponential v, Results Calculation Parameters Delay Threshold Speed (mih) 40.0 Queue Threshold Speed (mith) 10. I Brwse... Simulation Options Simulation Duration (min) Number of Warm Up Cycles R Display Animation ] Display Summary Results O Create TSD File Roadway Variables Work Zone Length (mi) .50 Posted Speed (mih) 40.0 Work Zone Speed (mith) 4.0 OK Figure 33. Screen shot of the program main user interface VehicleDriver Characteristics Passenger Cars Small Trucks Medium Trucks Large Trucks Free Lead Lead Free Flow React React Stop Veh Max. Max. Veh Accl Desired Desired Flow Spd. Hdwy Hdwy Time Time Gap Stop Length Accel. Decel. AccI Std. Decel. Decel. Spd. Std Mean Std. Mean Std. Mean Gap Std (ft) (fflsec2) (ftlec2) (fec2) Dev (fsec2) Std (%) Dev. (sec) Dev. (sec) Dev. (ft) Dev. S16 10 11 25 75 625 15 1 1 2 30 35 10 35 5 .5 9 .25  2 255 2.0 2 1 1 0 14 2  45 ] F25 ] 9 25 ] .25 ] 8  .25 1 32511 2.5 1 25 1  II  16  2.5 S65 15 11 9 15 .25 11 7 .25 3 225 2.75 25 1 1 20 2.5 Pitt Damping Factor (K) Vehicle Generation During Run Time v Q ArrivaQ Discharge 1.10 Work Zone Flow F , Iote: This screen is for advanced users. Changing certain values on this screen can significant affect the results. OK Figure 34. Screen shot of vehicle parameter setting window Select the name of the MultiRun File. This file must be in the correct format. Browse Beginning Scenario 0 Number of Simulation Periods0 Ending Scenario # Calculate Figure 35. Screen shot of the multiple run input form '" EIEI El E S 254 57 . I Figure 36. Screen shot of animation window tua *i ar .sn i 1 81.dix dan@aimmw.w.balm J M .. ,l" .... . 1 1400 0 1200 0 1000 0 800 0 600 0 400 0 200 0 00 25 30 35 40 45 50 55 60 65 Work Zone Speed (mph) m Pk Dir Off Pk Dir Total Cap Figure 37. Relationship of work zone speed to capacity 0 30 60 90 120 150 180 210 240 270 300 330 360 Green Time (sec) w Pk Dir Off Pk Dir Total Cap Figure 38. Relationship of green time to capacity e9  1600.0 1400.0 1200.0 I 1000.0 800.0 8 600.0 400.0 200.0 0.0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 Work Zone Length (mile)  PkDir Off Pk Dir Total Cap Figure 39. Relationship of work zone length to capacity 1200 0 10000  S800 0 S6000 00 4000 0  200 0 0 25 5 75 10 125 15 175 20 Heavy Vehicle (%)  Pk Dir A Off Pk Dir Total Cap Figure 310. Relationship of heavy vehicle percentage to capacity Table 31. Experimental design variables and values for capacity data Settings Factor Units Low Med High Work Zone Length (mi) 0.25 1.0 3.25 Work Zone Speed (mi/h) 20 35 50 Heavy Vehicles (%) 0 10 20 Green Time (sec) 60 180 300 Table 32. Experimental design variables and values for queue delay and queue length estimation models Settings Factor Units Low Med High Work Zone Length (mi) 0.25 1.0 3.25 Work Zone Speed (mi/h) 25 37.5 50 Heavy Vehicles (%) 0 10 20 Total Volume (veh/h) 400 700 1000 Dfactor 0.5 0.6 0.7 Distance GapOut (ft) 325 450 550 CHAPTER 4 CALCULATION PROCEDURE DEVELOPMENT Introduction This chapter describes the development of models and calculations for work zone capacity, delay and queue length. This is followed by a sample application of the calculation procedure. Finally, a comparison of the results from this calculation procedure to those based on simple deterministic equations and those based on the Cassidy and Son calculation procedure. Work Zone Speed Model The first model that was estimated was one for average work zone speed. With impact to the overall cycle length due to the lost time caused by traversing the work zone, and impact on the saturation flow rate, the estimation of the work zone speed must be as accurate as possible. The work zone speed model captures the impact of trucks on the work zone speed along with the work zone length. The posted speed for a work zone is inputted and the model adjusts this speed to account for additional heavy vehicles and the work zone length. The model formulation is shown below in Eq. 41. Table 41 summarizes the coefficient and tstatistic values for each variable. The model has a good fit with an R2 of 0.896. Note that for a perfect model fit, the R2 would be 1.0. The included model variables are all statistically significant at well above the 99% confidence level (z/2 = 2.58). WorkZoneSpd, = 4.608474 + 0.706381 x PostedSpd, + 0.000601 xMin((L x 5280),10560) 0.1063336 x HV where WorkZoneSpd, = estimated average travel speed of vehicles through the work zone for direction i (mi/h) PostedSpd, = the posted speed, or maximum desirable travel speed of vehicles, through the work zone for direction i (mi/h) L = work zone length (mi) HV, = percentage of heavy vehicles in the traffic stream for direction i As the model indicates, a higher posted speed in the work zone logically results in a higher travel speed through the work zone. Shorter work zones decrease the speed due to vehicles not achieving their free flow speed for the majority of the travel through the work zone. However, note that the length value is constrained. That is, for lengths greater than 2 miles, a value of 10560 ft should be used because longer lengths do not provide an additional increase in the work zone speed. Higher truck percentages decrease the work zone speed because of their lower performance capabilities and resultant impacts on following vehicles. Saturation Flow Rate Model One of the key parameters to all of the calculations in the analysis procedure is saturation flow rate. This measure refers to the departure rate of vehicles from a standing queue when the traffic signal (or flagger paddle in this case) turns green. It is typically reported in units of veh/h, assuming the signal/paddle is green for the full hour. Typically, there is base saturation flow rate, which reflects the saturation flow rate under "ideal" or base conditions, such as 100% passenger cars. This saturation flow rate then gets adjusted if there are site conditions that are less than "ideal". The approach used in this work follows the same framework as that specified in Chapter 16 (signalized intersections) of the HCM 2000. That is, a base saturation flow rate value is adjusted downward for various non ideal roadway, traffic, and/or control factors, resulting in an adjusted saturation flow rate3. This calculation framework for adjusted saturation flow rate can be expressed generically as shown in Eq. 42. s = so x flxf2 ... fN [42] 3 Technically, it is also possible to have adjustment factors that adjust the base saturation flow rate upward (see Bonneson et al. [2005] for example). After deciding on the model form for the adjusted saturation flow rate, the next step was to determine the appropriate adjustment factors to include in the model. For this, past research was relied upon, such as Washburn and CruzCasas (2007) and Bonneson et al. (2005). Factors shown to significantly affect saturation flow rate include downstream travel speed, percentage of heavy vehicles, and length of green time. Other factors, such as lane width and grade, can also be significant, but these factors were either not modeled within the simulation program or were not relevant to the situation of twolane work zones. The general model specification for adjusted saturation flow rate is given in Eq. 43. Green time was not found to be significant in this situation since the green times are generally much longer than at signalized intersections. hs = b x (1+ b,(Min(speed,,45)45))x 1+ H x (b, 1) [43] where hst i= saturation headway for direction i (sec/veh) bo = base saturation headway (sec/veh) bl, b2, b3 = model coefficients for adjustment terms speed, = average travel speed downstream of stop bar for direction i (veh/h) HV, = percentage of heavy vehicles in the traffic stream for direction i The model with the estimated parameter values, based on the FlagSim data, is shown in Eq. 44. The model has a reasonable R2 of 0.721. The included model variables are all statistically significant at well above the 99% confidence level (Za2 = 2.58). hs =1.92 x (0.00516(Min(speed,,45)45))x 1+ (2.37 [44] Equation 45 converts the adjusted saturation headway into the adjusted saturation flow rate. 3600 (sec/h) s, (veh/h) = 3 (sec/h) [45] hl, (sec/veh) Note that the base saturation headway of 1.92 seconds (from Eq. 44) translates to a base saturation flow rate of 1875 veh/h. This value, and the truck passenger car equivalent value (b2 = 2.37), are reasonably consistent with the results from Washburn and CruzCasas (2007). Also, note that the speed value is constrained. That is, for speeds above 45 mi/h, a value of 45 should be used because higher speeds do not provide an additional increase in the saturation flow rate. The use of this maximum value results in an adjustment factor value of 1.0. It should be noted that the experimental design for this study used a truck type distribution of 40%/40%/20% for small, medium and large trucks, respectively, as opposed to the Washburn and CruzCasas study (2007), which assumed an equal percentage of each truck type. The proportion was assumed to differ because of the relatively higher number of small and mediumsized construction trucks that would be servicing the construction activities. Capacity Calculation Another key parameter in the assessment of work zone operations is capacity. The capacity indicates the number of vehicles that can be processed through the work zone during a specified period of time. Ideally, a work zone should be set up such that capacity exceeds the traffic demand; otherwise, delays and queue lengths will become excessive. Capacity can be calculated with the standard equation used for signalized intersection analysis (TRB, 2000), as shown in Eq. 46. c =s x x [46] where c, = capacity of the work zone in direction i (veh/h) s, = adjusted saturation flow rate for direction i (veh/h) (g, /C) = effective green time to cycle length ratio for direction i For this equation, the adjusted saturation flow rate is determined from equations 44 and 45. In order to maximize capacity, the green time needs to be maximized. As previously mentioned, a maximum green time of 300 seconds (5 min) was assumed. The other component to this equation is the cycle length. The cycle length is calculated with Eq. 47. wzlen wzlen C = x +g, +g +SLTx2 [47] speed, speed2 where C = cycle length (sec) wzlen = length of the work zone (ft) speed, = average travel speed through the work zone calculated from the work zone speed model for direction i (ft/s) g, = green time for direction i (sec) SLT= startup lost timeelapsed time between last vehicle to exit work zone and time when flagger turns paddle to "green" for other direction Work zone speed should be calculated from the work zone speed model if field data is not available. Lost time is dependent upon the guidance provided to the flaggers about when it is appropriate to change the paddle to "green" after the work zone has been cleared of vehicles traveling in the opposite direction. As previously mentioned, a mean value of 10 seconds was used in this study. Using Equations 44 and 45 to get the saturation flow rate, Eq. 47 to get the cycle length (with the maximum green time), and then plugging these values into Eq. 46 will yield the capacity. The calculated capacity can then be compared to the input volume (by direction) to determine if none, either, or both directions are under or over capacity. If one or both directions are over capacity, an alternative work zone configuration should be considered; otherwise, delays and queue lengths will quickly become intolerable to motorists. If the work zone is under capacity, the standard formula for calculating the minimum cycle length can be applied (TRB, 2000), shown in Eq. 48. LxX Cmn Lx [48] X [v + V where Cm, = minimum necessary cycle length (sec) L = total lost time for cycle (sec) X, = critical v/c ratio for the work zone (v/s), = flow ratio for direction i Here it assumed the critical v/c ratio, Xc, is 1.0. Eq. 410 (TRB, 2000) can be applied to proportion the green times to the two directions of travel. g = [49] where g, = effective green time for phase (direction) i (v/s), = flow ratio for direction i C = cycle length in seconds X, = v/c ratio for direction i (again, assumed to be 1.0) It should be noted that the use of minimum cycle length, and corresponding green times, calculated from equations 48 and 49 do not necessarily lead to minimum delay values. These values just ensure that all the vehicles queued during the red period for a direction are served during the subsequent green period. It was beyond the scope of this project to develop optimal timing strategies, that is, timing guidelines that would minimize the value of specific performance measures, such as vehicle delay. Thus, for an undercapacity situation, the calculation procedure outlined in this report uses equations 48 and 49 to determine the minimum cycle length and minimum green times to apply for the queue delay and queue length estimation models, as outlined in the next section. Queue Delay and Queue Length Models The experimental design for queue delay and queue length did result in some scenarios that were over capacity for some individual cycles during the simulation period, or even for the whole simulation period, due to randomness of the arrivals. Generally, for overcapacity conditions, simple deterministic queuing equations can be applied to estimate queue delay and queue length. For the development of queue delay and queue length models described in this section, scenarios with volumetocapacity ratios up to 1.2 were retained, while anything higher was removed from the data set. The final data set contained 940 out of the original 1215 scenarios. Queue Delay Model A regression analysis of the resulting simulation data resulted in the following model for total queue delay (i.e., units of vehhr) for a 1hour time period, shown in Table 43. The included model variables are all statistically significant at well above the 99% confidence level (z/2 = 2.58). The variable signs are all consistent with expectations; for example, as the g/C ratio increases, the delay decreases. This model, in equation form, is shown in Eq. 410. TotalDelay, = 0.276980 x (g, /C)(%)+ 0.242061 x (v/s) (%)+ 0.003387 x C [410] + 0.148503 x g, 0.001376 x HV x g, where TotalDelhi = total queue delay for a 1hr time period for direction i (vehhr) (g, /C) = effective green time to cycle length ratio for direction i (expressed as a percentage) (v/s), = volume to saturation flow rate ratio for direction i (expressed as a percentage) C = cycle length (sec) HV, = percentage of heavy vehicles in the traffic stream for direction i g, = average green time given to the direction of travel The g/C ratio used in this model should be an average, or expected, glC ratio for the entire simulation period. Under the gapout flagging method, the green time, and consequently the cycle length can vary every cycle (as in actuated signalized intersection control). For the development of the model, the average of the g/C ratios for each cycle within the entire simulation period was used (as opposed to the average green divided by the average cycle length). The model fit, as indicated by the R2 value of 0.958, is excellent. This means that the model describes 95.8% of the variance in the delay data. The model fit is also illustrated in Figure 41. Note that for a perfect model fit (i.e., R2 = 1.0), all the data points would fall directly on the line. For lower delays, the model prediction is better. The larger variance occurs with predictions over 35 vehiclehours of delay. As the volume approaches capacity, any cycle failure will cause a significant increase in the delay. Queue Length Model A regression analysis of the resulting simulation data resulted in the following model for queue length, shown in Table 44. This model estimates the expected maximum back of queue length to occur per cycle (i.e., units of veh/cycle), per direction. The included model variables are all statistically significant at well above the 99% confidence level (Za/2 = 2.58). The variable signs are all consistent with expectations. These same variables were used in the queue delay model. Queue length model, in equation form, is shown in Eq. 411. QueueLength, = 0.616983 x (g, /C)(%)+ 0.598965 x (v/s),(%)+ 0.0006855 x C 0.299197x[411 0.003199 + 0.299197 x g, 0.003199 x H, x g, where QueueLeiigth = maximum queue length per cycle for direction i (veh/cycle) (g, C) = effective green time to cycle length ratio for direction i (expressed as a percentage) (v s), = volume to saturation flow rate ratio for direction i (expressed as a percentage) C = cycle length (sec) HV, = percentage of heavy vehicles in the traffic stream for direction i g, = average green time given to the direction of travel The model fit, as indicated by the R2 value of 0.984, is again excellent. The model fit is also illustrated in Figure 42. Again, for the development of this model, the average of the g/C ratios for each cycle within the simulation period was used. Model Validation All new models or methods developed should have some validation, to other work or relevant data. With the lack of field data, other procedures were used for comparison purposes. The two procedures that were chosen to compare to were Cassidy and Son's procedure and the HCM uniform delay and queue length formulations. While all three methods have their unique elements, they also have several similarities given that they are all founded on signalized intersection operational characteristics. Cassidy and Son Comparison Queue delay and queue length values were compared between Cassidy and Son's method, FlagSim, and the analytical procedure based on FlagSim results, as shown in Table 46. Two different sets of results are provided for the Cassidy and Son method: 1) results based on the default set of parameter values recommended by Cassidy and Son, except for adjusting the work zone speed, and 2) results based on revised parameter values consistent with the results obtained from FlagSim modeling. Some of the default parameter values for the Cassidy and Son method were significantly different from those obtained from FlagSim. Thus, revising the parameter values to be consistent with FlagSim provides a more accurate comparison of the methods. The parameters revised in the Cassidy and Son method are summarized in Table 45. The Cassidy and Son method with revised parameter values consistent with the analytical procedure produced results reasonably consistent with those of the analytical procedure. The Cassidy and Son method using revised parameters for most scenarios estimates higher delays than FlagSim does. This is expected since FlagSim's "actuated" rightofway control responds to the actual arrival rates each cycle, rather than providing the same amount of green time each phase based on an the average arrival rate (similar to a pretimed signal control strategy). The analytical procedure results are lower than Cassidy and Son's method as well, because the analytical procedure results are more consistent with the FlagSim results (e.g., the estimated models used in the analytical procedure are based on FlagSim data). The results of the Cassidy and Son method, based on the default parameter values, have higher delay values than the analytical procedure. This is primarily due to lower saturation flow rates and higher lost times (both startup time and work zone travel time). Uniform Delay and Queue Length A comparison was also made between the uniform signal delay equation (Eq. 1611) of the HCM (TRB, 2000) and FlagSim results based on uniform arrivals, fixed green, and uniform vehicle parameters (i.e., the variance was set equal to zero for the various vehicle performance parameters such as speed, etc.). These results from the HCM and FlagSim were also compared to the Cassidy and Son method, the analytical procedure, and FlagSim (using the default input scheme). Performing a comparison of the HCM uniform delay equation results with FlagSim under uniform/fixed input conditions provides a baseline comparison, and provides one measure of validation for the operation of the simulation program. The results are shown in Table 47. The comparisons in Table 47 have some scenarios with higher than minimum green times to represent flaggers operating the work zone in a relatively nonoptimal manner. The saturation flow rate used in the other methods was calculated according to Eq. 45. The HCM and FlagSim queue delay and queue length values were generally similar. The analytical procedure produced higher delays and longer queue lengths when using a green time much higher than the minimum green time. This confirms that using the minimum green time (i.e., the green time necessary to serve the average number of arrivals on red and the vehicles that arrive while this initial queue is being served) will generally provide lower delays and queue lengths. A comparison was also performed between FlagSim (using random arrivals and a distance gapout flagging method) and the analytical procedure and the HCM uniform delay equation. In order to formulate the input green time and speed values, FlagSim was run first and then these values were input into the analytical procedure and HCM equation. Again, the saturation flow rate was calculated from Eq. 45 for use in the analytical procedure and HCM equation. The analytical procedure and FlagSim have lower delays than the HCM method due to the regression equations developed from FlagSim, which were influenced by the random arrivals and "actuated" control strategy. The green times used for the HCM uniform delay comparison to FlagSim (using distance gapout flagging control) were the average green times obtained from the FlagSim simulation. The Cassidy and Son method yielded similar, but slightly higher delay values than FlagSim (using distance gapout flagging control) and the analytical procedure (using the minimum green time). This is generally because the Cassidy and Son method also factors in red time variance into its cycle delay calculation. Overall, the Cassidy and Son results were fairly consistent with the HCM uniform delay results. Analytical Procedure Compared to FlagSim Tables 46 and 47 both provide a summary of comparisons between FlagSim and the analytical procedure. FlagSim typically had slightly lower queue delay and queue length values. The lower values result from the difference in green times. The green time in the analytical procedure was generally estimated to be a little higher than the resulting FlagSim green times for the same input conditions. The analytical procedure is based on a minimum cycle estimation method similar to signalized intersections, with the green time proportion based on the volume to saturation flow rate ratios. The resulting green times in FlagSim tended to be a little lower than the estimated minimum green times from the analytical procedure because of the "actuated" control operation as discussed previously. The reader may note that the delay in Direction 2 is often higher than the delay in Direction 1. In some cases, where the total delay is higher (vehhr), the pervehicle delay (sec/veh) can be higher due to the lower volume in Direction 2. In other cases, where both delay values are higher for Direction 2 and/or the volumes are equal in both directions, the results may be reflecting a cycle truncation issue (i.e., the simulation period ends midcycle). The FlagSim simulation results represent an average of all the percycle results during the simulation period. For simulation scenarios that result in six or more cycles per simulation period, the effect of the cycle truncation on the calculation results is generally negligible. However, for scenarios that result in very long cycle lengths (e.g., long work zone, slow speed, etc.), only a few cycles may be completed within the simulation period. Thus, calculating the averages based on only a few cycles, and with one direction containing only a partial phase, significant differences can results between the two directions. Due to the setup of the simulation program, the number of phases for Direction 1 was equal to or higher than Direction 2. Consequently, the results for Direction 1 are more reliable for long cycle scenarios. It is anticipated that this issue will be addressed in a future update to the simulation program. 60 o 50 o o S4 oo o a o a) 40 o o I o "? o w 30 0o o0 0 30 0 0 S20 10 0 0 10 10 0 10 20 30 40 50 60 Model Estimated Queue Delay (vehhr) Figure 41. Modelestimated queue delay versus simulation queue delay. 120 000 R 2 = 0 .9 8 4 o . 100 0o 0 80 oP 20 0 20 40 60 80 100 120 40 20 c0 20 0 20 40 60 80 100 120 Model Estimated Queue Length (veh) Figure 42. Modelestimated queue length versus simulation queue length. Table 41. Work Zone Speed Model Factor Coeff. tStat Constant 4.608474 24.78 Posted Speed (mi/h) 0.706381 156.29 HV% 0.106336 25.42 Work Zone Length (mi) 0.000601 53.34 RSquared 0.896 Table 42. Saturation Flow Rate Model Factor Coeff. tStat Base Sat Headway 1.921924 329.23 Work Zone Speed (mi/h) 0.00516 24.76 HV% 2.37013 133.34 Work Zone Length (mi) 1.921924 329.23 RSquared 0.721 Table 43. Queue Delay Model Factor Coeff. tStat g/C(%) 0.276980 8.2305 v/s (%) 0.242061 6.6899 Cycle Length (sec) 0.003387 7.5329 Green Time (sec) 0.148503 58.3398 HV% x Green Time (sec) 0.001376 18.8804 RSquared 0.958 Table 44. Queue Length Model Factor Coeff. tStat g/C(%) 0.616983 14.9374 v/s (%) 0.598965 13.4875 Cycle Length 0.006855 12.4224 Green Time (sec) 0.299197 95.7674 HV% x Green Time (sec) 0.003199 35.7656 RSquared 0.984 Table 45. Parameter revisions made to Cassidy and Son method to facilitate a more direct comparison to the Analytical Procedure. Parameter Saturation Flow Rate Saturation Flow Rate Variance How Revised Calculated according to Eqs. 44 and 45 Value set to zero Work Zone Value set to zero Travel Time Variance Green Time Extension Lost Time Rightof Way Gap Out Work zone speed Value set to zero Changed from 23.32 sec to 10 sec (the value used in FlagSim) Changed the gap out time from 12.4 seconds to 9.4 seconds (the value used in FlagSim, based on a stopping sight distance of 400 ft) Calculated according to Eq. 41 General Effect on Results The saturation flow rate was increased, thus increasing capacity and reducing delays and queue lengths. The Cassidy and Son method accounts for variation in the saturation flow rate with higher values producing higher delays. The analytical procedure does not include an adjustment for saturation flow rate variance, but does include an adjustment to the saturation flow rate for heavy vehicles. The Cassidy and Son method does not adjust the saturation flow rate due to heavy vehicles. Setting the Cassidy and Son method saturation flow rate variance to zero, while using Eq. 45 to calculate the saturation flow rate provides a more direct comparison with results from the analytical procedure. Work zone travel time variance was removed because the analytical procedure does not have a travel time variance term, but does adjust the travel time based on the percentage of heavy vehicles. Including the variance would increase the travel time, which would increase the delay and queue length. Removing the green time extension lowers the green time for each direction by a small amount. This will result in slight reductions to delay and queue length as the provided green time will be largely utilized by vehicles departing at the saturation flow rate. Decreasing lost time decreases the cycle length, which results in a lower queue delay and a shorter queue length. Decreasing the gap out time decreases the green time because smaller gaps are accepted between vehicles on which to base changing the rightofway, which maintains a higher flow rate through the work zone. A lower gap out time will also decrease the green time, which will result in a shorter cycle and reduced delays and queue lengths. The work zone speeds in the Cassidy and Son method are based on the work zone activity type, rather than a posted work zone speed limit. Work zone speed is the most significant factor affecting total lost time. Table 46. Comparison of Cassidy and Son with FlagSim and generated models Work Avg. Zone Posted Traffic Sat Queue Length Speed Volume Flow Total Delay Queue Delay Queue Delay Length (mi) (mi/h) (veh/h) (veh/h) Model (vehhr) (vehhr) (sec/veh) (veh) 1 2 1 2 1 2 1 2 1 2 3.25 45 170 140 FlagSim (gapout)a 125 130 120 126 2502 3160 249 220 Analytical Procedure 103 89 106 91 2248 2347 218 187 Cassidy/Son (default)b 168 143 168 143 3549 3679 1666 Cassidy/Son (revised)c 143 121 143 120 3038 3098 1.25 35 440 355 FlagSim (gapout)a 221 191 214 186 1816 1900 441 375 Analytical Procedure 236 194 225 185 1841 1879 464 382 Cassidy/Son (default)b 55 8 51 8 55 8 51 8 456 2 525 7 1616 Cassidy/Son (revised)c 259 225 259 225 2117 2280 0.75 30 600 300 FlagSim (gapout)a 227 157 219 155 1315 1842 490 294 Analytical Procedure 274 145 262 139 1570 1669 543 288 Cassidy/Son (default)b 83 6 728 83 6 72 8 501 5 873 0 1604 Cassidy/Son (revised)c 265 176 265 176 1589 2117 0.5 25 600 600 FlagSim (gapout)a 312 353 305 347 1929 2122 628 677 Analytical Procedure 41 3 41 3 40 5 40 5 242 9 242 9 83 0 830 Cassidy/Son (default)b over capacity 1598 Cassidy/Son (revised)c 432 432 432 432 2591 259 1 Variables that are the same: Truck Percent = 5%; Maximum Green Time = 5 min; Green Extension time = 9.4 sec, work zone speeds match FlagSim's output a (gapout) Uses a gapout distance of 400 ft, max green of 5 minutes, and random arrivals b (default) Uses all of the default input parameters except the work zone speed. The work zone speed is set equal to the value used in the other comparisons. 0 (revised) The parameters revised consistent with Analytical Procedure results, including saturation flow rate, work zone speed, lost time, gap out headway. Table 47. Comparison of uniform delay and queue length equations Work Zone Green Queue Queue Length Speed Volume Time Sat Flow Delay Delay Avg. Queue (mi) (mi/h) (veh/h) (sec) (veh/h) Model (vehhr) (sec/veh) Length (veh) 1 2 1 2 1 2 1 2 1 2 1.75 35 250 250 FlagSim (gapout)a 127 126 184 182 248 247 Analytical Procedure (min green)b 13 1 131 189 189 27 1 27 1 1558 Cassidy/Son (revised)c 171 171 246 246 100 90 1558 HCM Uniform Delayd 162 162 233 233 31 4 31 4 180 180 Analytical Procedure (fixed green)e 235 235 338 338 469 469 180 180 FlagSim (uniform)f 136 162 196 233 31 8 31 8 180 180 1558 HCM Uniform Delayc 176 176 253 253 390 390 1 25 400 300 FlagSim (gapout)a 207 188 193 221 440 367 Analytical Procedure (min green)b 207 160 186 192 42 7 33 0 1489 Cassidy/Son (revised)c 253 208 228 250 160 125 1489 HCM Uniform Delayd 246 194 222 232 478 383 180 120 Analytical Procedure (fixed green)e 190 199 171 239 435 365 180 120 FlagSim (uniform)f 190 199 171 238 435 365 180 120 1489 HCM Uniform Delayc 237 210 213 252 489 417 0.5 30 200 100 FlagSim (gapout)a 37 21 683 749 73 35 Analytical Procedure (min green)b 36 21 64 76 78 45 1528 Cassidy/Son (revised)c 48 26 86 93 30 15 HCM Uniform Delayd 42 23 76 82 85 46 120 60 Analytical Procedure (fixed green)e 102 54 183 195 194 104 120 60 FlagSim (uniform)f 31 26 565 953 84 55 120 60 1528 HCM Uniform Delayc 40 31 72 113 111 72 0.5 45 400 400 FlagSim (gapout)a 77 84 738 759 158 172 Analytical Procedure (min green)b 73 73 66 66 159 159 1528 Cassidy/Son (revised)c 105 105 95 95 70 70 1528 HCM Uniform Delayd 85 85 77 77 172 172 180 180 Analytical Procedure (fixed green)e 207 207 187 187 41 6 41 6 180 180 FlagSim (uniform)f 104 115 94 104 276 276 180 180 1528 HCM Uniform Delayc 127 127 114 114 31 1 31 1 Variables that are the same: Truck Percent = 10%, work zone speeds match FlagSim's output a (gapout) Uses a gapout distance of 400 ft, maximum green time of 5 minutes, and random arrivals b (min green) Uses models based on FlagSim data generated with gapout control strategy (with 5 minute maximum green time) and normal stochastic variations S(revised) The parameters revised consistent with Analytical Procedure results, including saturation flow rate, work zone speed, lost time, gap out headway. d Delay was calculated using Equationl6 1, and the queue length calculated according to Appendix G, of Chapter 16 in the Highway Capacity Manual 2000 e (fixed green) Analytical procedure uses a fixed green time higher than the necessary minimum green time (uniform) Uses the fixed green time given for the scenario and uniform arrivals and vehicles types with identical vehicle characteristics CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS Summary Twolane twoway roadways with a lane closure under flagging control are frequent fixtures on the roadway construction landscape. This type of work zone can be one of the most frustrating to motorists due to the need to alternate traffic flow directions and the lengthy time that can be spent sitting in a queue. It is essential that the impacts of this type of work zone on traffic flow operations be accurately quantified in order to assist engineers with setting up work zone traffic control plans that balance the competing issues of maximizing construction productivity and minimizing impacts/frustration to motorists. Conceptually, this type of work zone has many similarities to a twophase signalized intersection. As such, many of the equations applicable to signalized intersection analysis can be applied to this type of work zone. However, some of the equations are not directly applicable due to some significant differences in the calculation of the green time and the significant lost time due to traversing the work zone and the laneswitch at the beginning of the work zone. This thesis has provided a calculation procedure for estimating the capacity, delays, and queue lengths of twolane, twoway work zones with flagging control. This calculation procedure utilizes a combination of standard signalized intersection analysis equations as well as some custom models developed from simulation data. Conclusions From the literature review, there was a general lack of available resources on twolane work zones under flagging operations. Additional research was, and still is, warranted on this topic. The analytical procedure, implemented in a spreadsheet format, allows for a quick, yet fairly comprehensive comparison of different work zone configurations and traffic conditions. It is robust with the regard to the inputs and outputs, and still easy to use. The analytical procedure yields results reasonably consistent with those generated from the simulation program. These results are generally slightly lower than the values calculated by the HCM uniform delay and queue length equations, which is largely due to the regression equations reflecting the efficient "actuated" operation of flagging control used in FlagSim. The analytical procedure, in most scenarios, had lower delays than did Cassidy and Son's method with revised parameters. This is generally because the Cassidy and Son method also factors in red time variance into its cycle delay calculation. The microscopic simulation program, FlagSim, produced for this project can be utilized to investigate issues that are not within the scope of the basic analysis spreadsheet. For example, it can also be used to test the effect of a variety of different vehicle performance characteristics, or some different flagging methods or parameter values beyond what was used for the development of the models/calculations contained in the analytical procedure. Additionally, FlagSim can be used to analyze oversaturated work zone conditions. Recommendations for Further Research While it is felt that the results of this project offer significant improvements over the existing FDOT PPM procedure, there are still areas that could benefit from additional research. These areas are as follows: *One obvious limitation to the results of this project is the lack of field data for verification/validation of several aspects of the simulation program. Although certain parameter values used in the simulation program were compared for consistency to field data values obtained from the Cassidy and Son research (1994), most of their field sites utilized a pilot car; thus, their parameter values may not be directly comparable to sites that do not use a pilot car. Field data should be collected at several sites, under only flagging control, to confirm the following factors: o Saturation flow rates and/or capacities What are typical values, and how do they differ due to traffic stream composition? Are they different by direction, e.g., due to the required lane shift in one direction? o Travel speeds through the work zone Are they related to, or independent of, posted speed limits? Are they different by direction due to the lane crossover at the beginning of the work zone? Son (1994) states from their literature review that vehicles in the blocked travel direction usually have lower speeds than the opposite direction. o Startup lost time What are typical values? Are they different by direction? o Flagging methods Is a gapout strategy ever applied, and if so, how? Is a maximum green time used, and if so, what value? Is a green time extension used, and if so, what value? * The calculation procedure and models in this thesis assume a constant speed through the work zone. It is not uncommon, however, for there to be localized reductions in speed within the lane closure area, such as where a paving machine may be working. Currently, there is a basic capability for examining this within the simulation program, but field data and potentially input from construction contractors would help to make this feature more robust and accurate. With an improvement to this feature within the simulation program, the simulation program can then be used to enhance the analytical procedure. * Development of an "optimal" flagging strategy o While there may be some structure to the rightofway changing methods employed by flaggers, informal observation suggests that there is a considerable amount of randomness that gets introduced into the cycleby cycle timings. Thus, it would appear that there is room for improvement in the timing guidance that is offered to flaggers, which would ultimately lead to more consistent and efficient rightofway changes. o As mentioned previously, it was beyond the scope of this project to explore a flagging strategy, or strategies, that would lead to minimal levels of delay and queuing for a given work zone configuration. While there are certainly improvements that could be made under an automated control situation, the challenge, of course, is finding an improved method that can actually be implemented with a manual flagging method. Nonetheless, it is believed that there are strategies that could be developed that could be reasonably employed by human flaggers that will reduce delays and queue lengths. APPENDIX SUMMARY OUTPUT FILE Output from FLagSIH 9/3/2007 9:05:55 PH Peak (EB) OffPeak (WB) Detector Output System Output System Entry Volume (veh per time period) Work Zone Entry Volume (veh per time period) Work Zone Exit Volume (veh per time period) Avg Speed in Workzone (mi/h) Avg Delay in Workzone (sec/veh) Avg Delay in Queue (sec/veh) Total Delay in Workzone (vehhr) Total Delay in Queue (vehhr) Total Delay per Direction (vehhr) Total System Delay (vehhr) Max Back of Queue (veh) Max Queue Length (veh/cycle) Avg Green per Cycle per Direction (sec) Avg Cycle Length per Direction (sec) Avg g/C per Cycle per Direction 377 391 365 29.06 33.88 143.81 3.44 15.62 19.05 33.87 45.00 32.56 107.44 439.51 0.245 277 259 259 29.04 33.95 171.99 2.44 12.37 14.82 37.00 24.22 74.06 447.03 0.166 Figure Al: Sample of the Summary Output File REFERENCES AASHTO (American Association of State Highway and Transportation Officials). A Policy on Geometric Design ofHighways and Streets. 4th ed., Washington, D.C., 2001. Arguea, D.F. (2006). A Simulation Based Approach to Estimate Capacity of a Temporary Freeway Work Zone Lane Closure. Masters Thesis, University of Florida. Cassidy, M. J and Han, L. D. (1993). A Proposed model for Prediction Motorist Delays at Two Lane Highway Work Zones. ASCE Journal of Transportation Engineering. Vol. 119., No 1 Jan/Feb. 2742. Cassidy, M. J. and Son, Y. T. (1994). Predicting Traffic Impacts at TwoLane Highway Work Zones. Final Report. Indiana Department of Transportation. Cassidy, M.J., Son, Y.T. and Rosowsky, D. V. (1993) Prediction Vehicle Delay During Maintenance or Reconstruction Activity on TwoLane Highways. Final Report No. CE TRA931, Purdue University, West Lafayette, Indiana. Ceder, A. and Regueros, A. (1993). Traffic Control (at Alternate OneWay Sections) during Lane Closure Periods of a TwoWay highway. Proc., 11th International Symposium on Transportation and Traffic Theory, Elsevier Publishing, Cohen, Stephen, L. (2002). Application of CarFollowing Systems in Microscopic TimeScan Simulation Models. Journal of the Transportation Research Board, TRR 1802, 239247. Cohen, Stephen, L. (2002). Application of CarFollowing Systems to Queue Discharge Problem at Signalized Intersections. Journal of the Transportation Research Board, TRR 1802, 205213. DeGuzman W.C., et al. (2004) Lane Closure Analysis. Colorado Dept of Transportation., Denver, CO. Evans, A. (2006). Personal Email. Florida Transportation Technology Transfer Center. Florida Dept of Transportation. (2006). Plans Preparation Manual, Volume I. Institute of Transportation Engineers (ITE). Traffic Engineering Handbook. 5th Edition. Washington, D.C., 1999. Mannering, F.L., Kilareski, W.P., Washburn, S.S. (2005). Principles ofHighway Engineering and Traffic Analysis, 3rd ed. John Wiley & Sons, Inc, New York, NY. Microsoft Language Library, March 25, 2007. http://msdn2.microsoft.com/en us/librarv/f7s023d2(VS.80).asox. Newell, G.F. (1969). Properties of VehicleActuated Signals: I. Oneway Street. Transportation Science, Vol. #3, 3051. Press W.H., et al. (1994). Numerical Recipes in C, the Art of Scientific Computing, Second Edition. Cambridge University Press, New York, NY. 288290 QuickZone Delay Estimation Program, Version 2.0, USER GUIDE, prepared for FHWA Rakha H. and Lucic I. (2002). Variable Power Vehicle Dynamics Model for Estimating Maximum Truck Acceleration Levels. Journal of Transportation Engineering, Vol. 128(5), Sept/Oct. pp. 412419 Son, Y. T. (1994). Stochastic Modeling of Vehicle Delay at twolane highway work zones. Doctoral Dissertation, Purdue University. Transportation Research Board (TRB), Highway Capacity Manual, National Research Council, Washington, D.C., 2000. U.S. Federal Highway Administration, Manual on Uniform Traffic Control Devices for Streets and Highways. U.S. Government Printing Office., Washington, DC, 2003. Washburn, S.S. and CruzCasas, C. (2007). Impact of Trucks on Arterial LOS and Freeway Work Zone Capacity. Final Report BD54551. Florida Department of Transportation. Tallahassee, FL. BIOGRAPHICAL SKETCH Thomas Hiles was born November 22, 1983, in Independence, Missouri. The younger of two children grew up in Odessa, Missouri, which is about 30 miles east of Kansas City, Missouri. He graduated from Odessa High School in 2002. Hiles earned his B.S. in civil and environmental engineering from the University of Missouri in 2006. Hiles enrolled in the master's program to further his knowledge in traffic engineering. Before joining the program, he received a Young Member position on the Access Management Committee of the Transportation Research Board. Upon graduation, he will assume a position with HDR Inc, in Kansas City, Missouri. Soon after graduation, he will be wed to Catherine Shelley. PAGE 1 1 ANALYSIS OF TWOLANE ROADWAY LANE CLOSURE OPERATIONS UNDER FLAGGING CONTROL By THOMAS HILES A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2008 PAGE 2 2 2008 Thomas Hiles PAGE 3 3 To My Parents PAGE 4 4 ACKNOWLEDGMENTS I thank Dr. Scott Washburn (my supervisory committee chair) and the other committee members (Dr. Lily Elefteriadou a nd Dr. Kevin Heaslip) for their mentoring and support. I would like to thank Catherine for helping me through my graduate work. I would finally like to thank my parents and grandmother for their loving support. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS...............................................................................................................4 LIST OF TABLES................................................................................................................. ..........7 LIST OF FIGURES.........................................................................................................................8 ABSTRACT.....................................................................................................................................9 CHAP TER 1 INTRODUCTION..................................................................................................................11 Background.........................................................................................................................11 Problem Statement.............................................................................................................. 11 Research Objective and Supporting Tasks......................................................................... 12 Document Organization...................................................................................................... 13 2 LITERATURE REVIEW.......................................................................................................14 Introduction................................................................................................................... .....14 Background........................................................................................................................14 Previous Research.............................................................................................................. 15 Cassidy and Son........................................................................................................ 15 Calculation procedure outline.......................................................................... 16 Field data..........................................................................................................16 Simulation data................................................................................................ 17 FDOT Procedure.......................................................................................................18 QuickZone.................................................................................................................20 Colorado DOT..........................................................................................................22 Summary and Conclusions................................................................................................22 3 RESEARCH APPROACH.....................................................................................................25 Introduction................................................................................................................... .....25 Methodological Approach.................................................................................................25 Simulation..................................................................................................................... .....27 Program Development..............................................................................................28 Vehicle distribution.......................................................................................... 28 Vehicle properties............................................................................................29 Vehicle arrivals................................................................................................29 Initial speed...................................................................................................... 30 Carfollowing model........................................................................................31 Queue arrival and discharge.............................................................................33 Flagging operations..........................................................................................34 Startup lost time............................................................................................... 34 Flagging methods............................................................................................. 35 User Interface............................................................................................................35 PAGE 6 6 Animation........................................................................................................36 Outputs of the simulation................................................................................. 36 Simulation Calibration.............................................................................................. 38 Sensitivity Analysis ........................................................................................................... 39 Experimental Design.......................................................................................................... 41 Variable Selection..................................................................................................... 41 Setting Variable Levels.............................................................................................45 Number of Replications............................................................................................ 46 4 CALCULATION PROCEDURE DEVELOPMENT............................................................. 53 Introduction................................................................................................................... .....53 Work Zone Speed Model...................................................................................................53 Saturation Flow Rate Model..............................................................................................54 Capacity Calculation.......................................................................................................... 56 Queue Delay and Queue Length Models...........................................................................59 Queue Delay Model..................................................................................................59 Queue Length Model................................................................................................ 60 Model Validation...............................................................................................................61 Cassidy and Son Comparison................................................................................... 61 Uniform Delay and Queue Length............................................................................62 Analytical Procedure Compared to FlagSim............................................................ 64 5 CONCLUSIONS AND RECOMME NDATIONS................................................................. 72 Summary............................................................................................................................72 Conclusions........................................................................................................................72 Recommendations for Further Research............................................................................ 73 APPENDIX Summary Output File................................................................................................ 75 REFERENCES..............................................................................................................................76 BIOGRAPHICAL SKETCH.........................................................................................................78 PAGE 7 7 LIST OF TABLES Table Page 21 FDOT work zone factor.................................................................................................... 24 41 Work Zone Speed Model...................................................................................................68 42 Saturation Flow Model...................................................................................................... 68 43 Queue Delay Model...........................................................................................................68 44 Queue Length Model......................................................................................................... 68 45 Parameter revisions made to Cassidy and Son m ethod to facilitate more direct comparison to the Analytical Procedure............................................................................ 69 46 Comparison of Cassidy and Son w ith FlagSim and generated models............................. 70 47 Comparison of uniform dela y and queue length equations ...............................................71 PAGE 8 8 LIST OF FIGURES Figure page 31 Twolane work zone operated with flagging control......................................................... 47 32 K value location used in simulation................................................................................... 47 33 Screen shot of the program main user interface................................................................. 48 34 Screen shot of vehicl e param eter setting window.............................................................. 48 35 Screen shot of the multiple run input form........................................................................ 49 36 Screen shot of animation window...................................................................................... 49 37 Relationship of work zone speed to capacity..................................................................... 50 39 Relationship of green time to capacity............................................................................... 50 310 Relationship of work zone length to capacity.................................................................... 51 311 Relationship of heavy vehi cle percentage to capacity ....................................................... 51 41 Modelestimated queue delay versus sim ulation queue delay........................................... 66 42 Modelestimated queue length ve rsus sim ulation queue length........................................ 67 A1 Sample of the Summary Output File................................................................................. 75 PAGE 9 9 Abstract of Thesis Presen ted to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering ANALYSIS OF TWOLANE ROADWAY LANE CLOSURE OPERATIONS UNDER FLAGGING CONTROL By Thomas Hiles December 2008 Chair: Dr. Scott Washburn Major: Civil Engineering With an aging roadway infrastructure and c ontinual urban development, construction work zones are a common fixture on our roadway system. Work zone delays have a negative effect on not only the transportatio n network, but also on the national economy as well. While there have been a number of studies conducted on roadway wo rk zone operations, very few of them have focused on twolane roadway work zones, where one lane is closed a nd traffic flow must alternate on one lane. These types of work zone s usually rely on the use of flagging personnel to alternate the flow of traffic on the single open lane. Thus, the analysis of this type of work zone is quite different from that of multilane roadwa ys. While a couple of analysis methods do exist for this type of work zone, there is no commonly accepted or nationally adopted method. The Florida Department of Transportation (F DOT) developed their own method, which is included in their Plans Preparation Manual (PPM). This method is fairly simple and considers a limited number of factors. Conse quently, there is a very limited range of field conditions for which this method will yield reasonably accurate results. Furthermore, the only output from method is work zone capacity. The objective of this project was to develop an analysis procedure for twolane roadway work zones (with a lane closure) that was more robust, both in PAGE 10 10 terms of inputs and outputs, than the FDOTs current PPM method. The FDOT also had the requirement that this new pro cedure still be easy to use. A custom microscopic simulation program was de veloped to generate the data used in the development of the models contained in the new an alysis procedure. Specifically, models were developed to estimate saturation flow rate/capacit y, queue delay, and queue length. The analysis procedure also employs calculation elements c onsistent with the an alysis of signalized intersections. The analysis procedure has been implemented into an easy to use spreadsheet format. This procedure is much more robust th an the current PPM procedure, and the results match well with the simulation data. For situations that are not handled by the analytical procedure, such as oversaturated conditions, the simulation program can be used instead. PAGE 11 11 CHAPTER 1 INTRODUCTION Background With an aging roadway infrastructure and increase in city sprawl, construction work zones are a common fixture on our roadway system. Work zone delays have a negative effect on not only the transportation network, but also on the national econom y, as well. On September 9, 2004, the Federal Highway Administration (FHW A) updated its Work Zone Safety and Mobility rule. This rule manda tes that states develop an agencylevel work zone safety and mobility policy. The states policies must include plans to mi nimize the congestion impacts to the public, and address all types of roadway facilities and co nstruction operations on a corridor, and network level. From freeways to rural twolane roads, each construction project must develop a plan to lower the cost of congestion. Over the past 20 years, there have been numerous research projects on estimating motorist delays for freeway work z ones. However, few research projects have been conducted on twolane, twoway roadway work zones. Such work zone configurations consist of a single lane that accommodates both di rections of flow, in an alternating pattern. These work zones typically employ a flagging co ntrol person (i.e., someone who operates a sign that gives motorists instructions to stop or proceed) at both ends to regulate the flow of traffic through the work zone. In some situations (usual ly where the lane closur e is long or there are a large number of driveways), a lead vehicle, called a pilot car, may be required to lead the platoon of vehicles through the work zone. Problem Statement Previous to this research project, there was not a single accepted national standard for analyzing work zone operations and estimating pe rformance measures, particularly for twolane, PAGE 12 12 twoway roadways. As a result, transportation agencies were required to develop their own method or adopt/adapt one from existing methods However, there were a limited number of methods available. The Highway Capacity Manual (HCM) (2000) provides some guidance on work zone analysis, but only for freeway facilit ies. A software product, called QuickZone, is publicly available, but th e level of support and lack of techni cal documentation (particularly with respect to twolane, twoway work zone conf igurations) has diminished its widespread acceptance. The Florida Department of Tran sportation (FDOT) opted to develop their own methodology because of these issues. The FDOT method currently used is a relatively simple deterministic procedure, with rough approximations for work zone capacity and other important parameter values. With everstricter guideline s on acceptable levels of traveler delay from construction activities, it is essential that an anal ysis method be as accurate as possible. One of the major limitations with most of the existing methods is the assumption of a fixed capacity value, or a very narrow range of capacity values, for a variety of work zone scenarios. However, for twolane, twoway roadways, cap acity is a function of saturation flow rate, work zone length, travel time through the work zone, and green time given to each direction of flow. Therefore, to achieve the goals of this project, it was neces sary to develop a new procedure, or adapt an existing one, which was more accurate, while st ill allowing for easy implementation. Meeting these requirements will facilitate the traffic e ngineering communitys acceptance and utilization of the developed method. Research Objective and Supporting Tasks The objective of this research was to develop a procedure to analyze twoway, twolane work zones and implement it in an easytouse format. More specifically, the procedure will estimate capacity, delay, and queue length for va rying work zone, tra ffic, and flagging conditions. The tasks that were conducted to support the objective were as follows: PAGE 13 13 Reviewed the literature to identify existing analysis procedures/methods. Reviewed the state of the practice of flagging operations. Identified alternative analysis methods th at could be adapted for use in Florida. Developed a simulation program that calculate s several measures of effectiveness for a variety of work zone scenarios, and provide s visualization of the work zone operations. Developed saturation flow rate, work zone speed, queue delay, and queue length estimation models from the simulation data. Implemented the models in a spreadsheet form at for application by practitioners/analysts. Document Organization In the following report, chapter 2 contains a summary of releva nt literature and procedures used by other agencies in analyzing twolane work zones. Next, chapter 3 describes the research approach, including simulation program devel opment and experimental design. Chapter 4 contains a description of the model developm ent and data analysis. Finally, chapter 5 summarizes the study, presents the conclusions reached, and topics for future research. PAGE 14 14 CHAPTER 2 LITERATURE REVIEW Introduction This chapter presents a summary of the revi ew of relevant literature, discusses the literature and proposes a methodolog y to be developed based on the review of the state of the practice. Specifically, this review addresses two areasprevious resear ch and the procedures used in that research. Background In the literature review proce ss, it was discovered that relatively little research had been performed in the area of twolane, twoway work zones with flagging oper ations. In contrast, there had been significantly more research conduc ted on analyzing freeway work zones with lane closures. The reason for this disparity may ha ve resulted from federal governments focus on high traffic/congestion facilities. With the new work zone rule requiring all significant work zone projects to have a traffic management pla n, there was a need develop analysis methods for twolane, twoway roadways. The Rule on Work Zone Safety and Mobilit y, developed in 2004, requires state and local transportation agencies to have traffic management plans in place to mediate work zone related congestion problems by October 2007. This rule stat es that all Significant Projects defined by a state must have a plan from the beginning of the planning process. A Significant Project is when certain locations where the congestion will create major delays or there are other projects being performed in coordination, these need to be considered as significant. Twolane, twoway roadways do not automatically qualify as significant (FHWA, 2004). However, for a transportation agency to be able to determine if a twolane roadway work zone would create significant congestion, it needed an accurate analysis method. PAGE 15 15 Previous Research In this section, a summary of previous research is presented that pertains to the estimation of traffic operations in twolane, twoway work zones. Cassidy and Son Cassidy and Son (1995) developed a method to estimate the delays generated due to a lane closure on a twolane, twoway ro adway. Their method consisted of a series of equations based on stochastic queuing theory. The delays are pr imarily a function of traffic demand, travel time through the work zone, and green time. They assessed the validity of their method through both Monte Carlo simulation and microscopic simu lation. They concluded that the method adequately predicts the impacts. The series of equations comprising Cassi dy and Sons method are largely based on previously developed equations for analyzing oper ations at signalized intersections. The sources for these previously developed equations includ ed: 1) Webster (1966) for queue delay estimation at a signalized intersection; 2) Newell (1969 ) for oneway vehicleactuated signalized intersection operations; and 3) Ceder and Regue res (1990) who obtained average work zone delays from simulation and then compared t hose results to average delay from Websters equations. The development of their calculation proce dure using equations that account for the stochastic nature of traffic operations in thes e work zones was based on previous efforts that investigated equations based on both determinis tic and stochastic processes (Cassidy and Han, 1993; Cassidy, et al., 1994). An overview of the Cassidy and Son calculation procedure is provided below. The outline lists the required parameters; the work zone t ypes that can be evaluate d, and how oversaturated conditions are handled. PAGE 16 16 Calculation procedure outline 1. For undersaturated conditions, estimated delay is a function of: a. work zone length b. work zone speed c. queue discharge rate d. traffic demand e. red time 2. For oversaturated conditions, dela y is a function of the above factors, and calculated with deterministic queuing equations 3. Work zone types a. Asphalt overlays (w/ pilot car) b. ChipSeal (w/ pilot car) c. General construction (w/ pilot car) d. General construction (w/o pilot car) Field data The data for Cassidy and Sons research consiste d of using 15 field sites in California. The field data obtained from these sites were used as the basis to develop parameter values for the four different work zone types li sted above. Parameters such as the mean and variance of queue discharge rate, the mean and va riance of speed through the work zone, lost time, green time extension, and variance to mean rati os of arrivals and departures were estimated for each of the four work zone types. One issue with their fi eld data is that none of the traffic demand rates were large enough for them to determine the actual capacities of these work zone configurations. While capacity can be determined indirectly th rough the measured satu ration flow rates and proportions of green time, these values could not be verified against actual fieldmeasured capacity values. Another potential issue is that at 10 of the 15 field sites, a pilot car was used. The purpose of a pilot car is to lead the queued traffic through the work zone area. Certainly, the presence of a pilot car can have additional impacts beyond th at of only flagger control. The Manual on Uniform Traffic Control Devices (MUTCD) (20 03) does not offer any guidance on when pilot cars should be used in a work zone. If the work zone is complex or the flaggers do not have a PAGE 17 17 clear sight of the work zone, then a pilot car is usually considered. In Florida, at least, the use of pilot cars at twolane, twoway work zones appears to be quite rare. In their proposed calculation procedure, the star tup lost time is a constant value, rather than a random variable, for a given work zone ty pe. They hypothesize that since lost time is typically a small percentage of the overall cycl e length, treating it, as a constant value will only introduce a negligible amount of error into the delay estimation. This assumption seems reasonable. Although their delay estimation equation accounts for green time extension (i.e., green time provided after the dissipation of the initial queue), they found that the contribution of this term to the delay estimation was negligible due its small percentage of the cycle length. The gapout time (i.e., headway threshold) that wa s utilized to estimate the green time extension was a constant value of 12.2 seconds, estimated, ag ain, from empirical data. In other words, the green time is assumed to extend for as long as vehicle arrival headways are less than 12.2 seconds. Although Cassidy and Son did not find a relationship between extended green times and the arrival rates, they theorized that the values were a function of the arrival rate. This observation may have been a function of the inherent variance in flagger operations. Simulation data Cassidy and Sons initial effo rts in developing a calcul ation procedure utilized deterministic equations that assumed uniform arriva l and queue discharge rates. They then tried to extend these equations by employing Monte Carlo simulation to generate key parameter values for the equations from statistical distribu tions based on empirical data. While the results of this exercise were more plausible for the stoc hastic nature of these work zone operations, it still had several significant limitations. PAGE 18 18 This ultimately led them to the adaptation of equations previously developed for modeling vehicleactuated signalized intersections. Thes e equations generally account for the stochastic nature of work zone operations. They also wrote a relatively simple microscopic simulation program for testing the validity of the analytical equations. They found that the equations based on vehicleactuated signalized intersection operations provid ed the best match with the microscopic simulation results, relative to the equa tions based on constant values or with values determined from Monte Carlo simulation. FDOT Procedure The FDOT developed a lane closur e analysis procedure for use w ith all road type classes. The procedure is in the Plans Preparation Manu al (PPM), Volume I, Section 10.14.7 (2006). The procedure can analyze twolane twoway work zones. In order to accommodate flagging operations, the procedure attempts to determine th e peak hour volume and the restricted capacity. From these two values, the time during when lane closures can occur w ithout creating excessive delays is determined. This procedures main limitation is that capac ity is an input, and the given capacities were not specific to twolane work z ones. With capacity not based on a flagging work zone value, the procedure quite likely will be unable to model th e field conditions accurately. Another limitation with modeling flagging operations with this procedure is that it is based on only the ratio of green time to the cycle length. This assumption does not take in to account the differences in delays of flagging operations, such as the lost ti me due to the traversing the work zone, startup lost time and the variation of extended green time. The capacity is adjusted by the work zone f actor (WZF) shown in Table 21. The WZF is used instead of a calculated travel time based on a typical speed. All of the lost time is also incorporated in to the WZF. This is a simp listic adjustment to incorporate these important PAGE 19 19 factors. The travel time through the work z one is an easy calculation, which would make a logical factor. One of the problems is the WZF is not adjusted by speed and is not documented by what speed the factor is based on. This is an important question, as speeds through a work zone can be quite different for an intense constr uction operation like chip and seal versus a less intense operation such as shoulder work. The FDOT PPM lane closure analysis procedure is as follows: 1. Select the appropriate capacity (c) from the table below: LANE CLOSURE CAPACITY TABLE Capacity (c) of an Existing 2LaneC onverted to 2Way, 1Lane=1400 veh/hr Capacity (c) of an Existing 4LaneC onverted to 1Way, 1Lane=1800 veh/hr Capacity (c) of an Existing 6LaneC onverted to 1Way, 1Lane=3600 veh/hr Therefore, for a twolane highway work zone, the capacity (c) is 1400 veh/hr. 2. The restricted capacity (RC) is then calcula ted taking into consideration the following factors: TLW = Travel Lane Width LC = Lateral Clearance. This is the distance from the edge of the travel lane to the obstruction (e.g., Jersey barrier) WZF = Work Zone Factor is pr oportional to the length of the work zone. This factor is only used in the procedure for twolane twoway work zones. OF = Obstruction Factor. This factor reduces the capacity of the travel lane if the one of the following factors violates their constraint s: TLW less than 12 ft and LC less than 6 ft. G/C = Ratio of green time to cycle time. This factor is applied when the lane closure is through or within 600 ft of a signalized intersection. ADT = Average Daily trips this value is us ed to calculate the design hourly volume. The RC for roadways without sign als is calculated as follows: RC (Open Road) = c OF WZF PAGE 20 20 If the work zone is through or within 600 f eet of a signalized inte rsection, then RC is determined by applying the fo llowing additional calculation. RC (Signalized) = RC (Open Road) G/C If Peak Traffic Volume RC, there is no restriction on the lane closure. That is, if the peak traffic volume is less than or equal to the restricted capacity, the work zone lane closure can be implemented at any time during the day. If Peak Traffic Volume > RC, calculate the hourly percentage of ADT at which a lane closure will be permitted. Open Road% = RTF PSCFDATC OpenRoad RC ) ( where ATC = Actual Traffic Counts. The hourly traffic volumes for the roadway during the desired time period. D = Directional Distribution of peak hour tra ffic on multilane roads. This factor does not apply to a twolane roadway conve rted to twoway, onelane. PSCF = Peak Season Conversion Factor RTF = Remaining Traffic Factor is the percentage of traffic th at will not be diverted onto other facilities during a lane closure. Signalized% = (Open Road %) (G/C) Plot the 24hour traffic, re lative to capacity, to determine when a lane closure is permitted. QuickZone To estimate the work zone congestion im pacts, the FHWA developed QuickZone. QuickZone 2.0, which was released in February 2005, is an Excelbased software tool for PAGE 21 21 estimating queues and delays in work zones. The maximum allowable queues and delays are calculated as part of the proce dure in optimizing a st aging/phasing plan and developing a traffic mitigation strategy. As a result, lane closure schedules are recommended to minimize user costs. This is a quick and easy method, with a userfri endly, concise spreadsh eet setup. (Arguea, 2006). The QuickZone method require s the following input data: Network data Describing the mainline facil ity under construction as well as adjacent alternatives in the travel co rridor, which can be used to calculate the traffic diversion Link capacity Each link has its own capacity value for vehicles per hour Project data Describing the plan for work zone strategy and phasing, including capacity reductions resulting from work zones Travel demand data Describing patterns of preconstruction corridor utilization Corridor management data Describing various congestion mitigation strategies to be implemented in each phase, including estimates of capacity changes from these mitigation strategies QuickZone has a module for flagging operations The procedures are similar to other roadway types handled within the program. Ho wever, for flagging operations, QuickZone is limited in several areas. One limitation is that if the work zone is over a mile in length, it assumes the use of pilot cars, which adds an addi tional lost time factor. Another limitation, per se, is that user interface for the twolane work zone analysis is cumbersome at best, making the data input process very difficult. An additional limitation was the lack of control on the flagging operation. QuickZone requires a pilot car with work zones longer than 1.0 miles, and maximum green time cannot be adjustedan important po licy decision in work zones near or over capacity. Another limitation was, unfortunately very limited documentation on the analysis procedure and justification for selected parame ter values. A thorough review of QuickZones internal calculations procedure written in Microsoft Excel VBA was performed, and from this, PAGE 22 22 it was determined that the twolane work zone procedure was inadequate for the needs of this project. Colorado DOT The Colorado DOT Lane Closure Strategy (2004) was intended to give guidance on scheduling lane closures on twolane work zone s. Capacity values were determined by the probability of a cycle failure (inability to serve a ll vehicles) based on a Poisson distribution. It was assumed that some cycles would fail, so a 10% failure rate was allowed. For their analysis, it was determined that 60 seconds was an appr opriate green time for each direction. The capacity determined for a 10% failure rate resu lts in an average of 22.2 vehicles through the work zone in each direction per cycle. The spee d limit through the work zone was assumed to be 30 mi/h. The travel time through the work zone was calculated based on a loaded semitruck accelerating to 30 mi/h. This results in 34 oneway cycles per hour for the 0.25mile closure and 18 cycles for the 1.0mile closure. The resulti ng hourly capacity calculated for a work zone in flat terrain was 755 veh/h for a 0.25mile work z one and 400 veh/h for a 1.0mile work zone. This analysis is a simple approximation of th e field conditions. Flagging variations were not taken into account, and the time to traverse th e work zone used the acceleration value from a semitruck, which can be the limiting condition in certain scenarios. One critical assumption made was a 60second green time. This green time was most likely used because the model formulation was based on a delay formulation for signalized intersec tions, with an upper limit of 72 seconds of green time. With these assump tions, the Colorado DOT model estimates lower capacity values than the Cassidy and Son (1994) method. Summary and Conclusions The literature review explored existing methods/models that we re used to estimate capacity and delays for twolane work zones with flaggi ng operations. However, only a limited number PAGE 23 23 of research projects on this topic have been c onducted to date, and it is evident that additional research is still needed fully understand work zone operations under flagging operations. All methods/models examined either use a sing le, or a very limited number of capacity values. o While the Cassidy and Son method calculate s capacity from th e saturation flow and green time proportion, they still only use four different values of saturation flow rate (and those only range in va lue from 1018 veh/h to 1090 veh/h). Obviously, capacity is the most influe ntial factor in work zone operational quality, if not all roadway facility types. Ideally, capacity (or possibly saturation flow rate) should be estimated for th e specific combination of work zone conditions being analyzed to more accurately estimate delays and queue lengths. For the existing methods/models, there ar e clearly many combinations of work zone conditions that result in significantly different capacity values than those builtin to the method. Even the Ca ssidy and Son field data found a range of saturation flow rates from 750 to 1450 veh/h. o FDOT PPM uses a capac ity value of 1400 veh/h With QuickZones limited documentation on development and procedures used for twolane work zone analysis, the program is difficult to implement into a traffic management plan for twolane work zones. The si gnificant weakness with QuickZone is the requirement for the user to input a capacity. With no guidance, the user has to make their best guess, which could potentially be significantly inaccurate. The Colorado Department of Transportation pr ocedures were overly conservative and did not provide much flexibility to the user to adapt the methods to a particular location. Without much flexibility to be adapted to sp ecific locations, this method was too limited to be further developed to implement in Florida. Besides the Cassidy and Son research, the av ailable methods genera lly provide little technical documentation about the method and/or the derivation of parameter values used in the method. Furthermore, other than the Cassidy and Son study, th ere is a general lack of field data that have been collected to validate any of th e developed methods. However, even with the Cassidy and Son da ta, most of the field data we re obtained from sites using a pilot car and operations levels were generally well below capacity. PAGE 24 24 Table 21. FDOT work zone factor. WZL (ft.)WZFWZL (ft.)WZFWZL (ft.)WZF 2000.9822000.8142000.64 4000.9724000.844000.63 6000.9526000.7846000.61 8000.9328000.7648000.59 10000.9230000.7450000.57 12000.932000.7352000.56 14000.8834000.7154000.54 16000.8636000.6956000.53 18000.8538000.6858000.51 20000.8340000.6660000.5 PAGE 25 25 CHAPTER 3 RESEARCH APPROACH Introduction This chapter describes the research approach adopted to find the capacity, delays, and queue lengths in twolane twoway work zone conf igurations. More specifically, it discusses the methodological approach, field observations, simulation model deve lopment, and the simulation experiments. Also included is description of the sensitivity analysis employed to discover the key variable ranges used in the experimental design. Methodological Approach The typical work zone flagging operation config uration consists of a single lane that accommodates both directions of flow in an alternating pattern. Figure 31 shows a typical twolane work zone with a lane closu re. These wo rk zones predominately use a flag person (i.e., someone who operates a sign that gives motorists instructions on whether to stop or proceed) at both ends to control the flow of traffic into the work zone. Significant delay is incurred by motorists due to the lost time that accrues while the opposing di rection has the rightofway. Additionally, both directions incur lost time when there is a cha nge in the rightofway as the last vehicle that received the rightofway must traverse the entire length of the work zone; therefore, all vehicles must wait until the last vehicle has passed the opposite stop bar. The queue discharge is similar to the opera tion of a signalized in tersection, but the la ne switch along with the proximity to construction activity would ha ve an affect on the discharge rate. Changing of the rightofway is rarely performe d in an optimal manner. Flaggers are not trained on how to switch the rightofway in such a manner as to minimize delay, or otherwise optimize some particular performance measure (Evans, 2006). Generally, flaggers change the flow direction due to queue and cycle length. The queue at the beginni ng of the green period PAGE 26 26 discharges at the saturation flow rate. After th e initial queue dissipates, flaggers usually extend the green to allow for vehicles still arriving. Th is extension time can be lowered if there is a significant queue in the opposite direction. At this point, the flow through the work zone will drop to the arrival rate. The arrival rate can be significantly lower than the queue discharge rate on low volume roadways, thus increasing the overall average delay if vehicles are queuing at the opposite approach (Cassidy and Son, 1994). The standard performance measures for a wo rk zone with flagging operations are: Capacity maximum vehicle throughput Delay time spent not moving, or at a slower speed than desired Queue lengths vehicle arrivals minus vehicle departures for a specified length of time Ideally, the operational impacts of these work zone configura tions should be studied at field sites resulting in a datase t that could be used to develop a methodology for estimating twolane work zone capacity. At the field sites, the factors that contribute to the capacity degradation could be extensively examined. These factors could be used to provide additional insight into the results of a simulation study. There would be a large number of different work zone scenarios encountered in the fiel d. Consequently, there are two complications to collecting field data from all of these scenarios: 1) It is not pos sible to find all such scen arios within a reasonable distance and within the project period, and 2) the project budget does not allow for field data collection at a larg e number of sites. Therefore, the approach chosen was to use simulation data for the analysis procedure development. However, a limited number of info rmal field observations were performed to have an understanding of their operations. These site s gave an idea of how the work zones were controlled. PAGE 27 27 Simulation To generate the data for developing the anal ysis procedure a work zone simulation was used. Using a simulation program provides the ability to test a much larger variety of traffic and work zone configuration conditions than would normally be possible from the amount of field data collected within the normal timeline and resources of a project. Twolane work zones are unique in their opera tion. In order to estimate the operation a number of factors are required. The following capabilities were necessary to simulate twolane work zones: model a variety of flagging control methods model vehicle arrivals at the work zone model vehicles discharging from the stop line model heavy vehicles, in addition to passenger cars model vehicles traveling through the work zone record various simulation results in order to allow for the following performance measures to be calculated o Lost time due to rightofway change o queue delay o travel time delay due to reduced speeds o queue length o capacity A review of existing commercially available si mulation packages was made to determine if any were readily applicable to this situat ion. VISSIM, CORSIM, AIMSUM, and PARAMICS do not explicitly provide for modeling of work zones on twolane roadways. The key to this research project was the ability to model the flag ging control. Each program could be used to change to from green to red, us ing different detector settings. However, what prevents the implementation of other software packages was th e inability for the available programs to track the last vehicle through the work zone. This f eature was needed in or der to begin the green period for the opposite direction. PAGE 28 28 Additionally, it was required to have more abil ity to control inputs a nd outputs. Additional control over the arrangeme nts of inputs and outputs allows for more efficient running of the simulation scenarios and more efficient proces sing of the results. A lack of technical documentation detailing the underlying methods/m odels was also problematic for several commercially available simulation models. Program Development The simulation program that was develope d, called FlagSim, is a Windowsbased application written with the Vi sual Basic 2005 language. FlagSim is a microscopic, stochastic simulation program that models the arrival of vehicles to th e work zone, the discharge of vehicles into the work zone area, and the travel of these vehicl es through the work zone area. From this program, the capacity of the work zone and delays imparted to the motorists were calculated. The purpose of the program was to realistically model traffic operations in work zone areas using flagging operati ons and use the results of the da ta analysis from simulation to develop an analytic computational procedure to estimate pertinent performance measures. Vehicle distribution For each simulation run, a unique set of vehicles was created. This set of vehicles can be defined by the user, given a variety of inputs define d in FlagSim. To choose the vehicle set, a vehicle generator selects from four different vehicle types. The selection was randomly generated, based on userspecified vehicle proporti ons. Four vehicle types were available within the simulation program: 1) passenger cars, 2) small tr ucks, 3) medium trucks, and 4) large trucks. For these vehicle types, the user also has the abil ity to adjust the proper ties of each vehicle type to fit a particular traffic pattern. PAGE 29 29 Vehicle properties Each vehicle in the program becomes unique based on the vehicle type properties set initially by the user. Each vehicle generated ha d a number of properties to define the vehicles characteristics. These characteristics were length, acceleration, freeflow speed, headway, and queue spacing. Some of these properties were treated as random variables according to a normal distribution. Thus, using the user inputted m ean and standard deviation for each of these properties, the property values we re set according to Eq. 31. normValuesrx [31] where Value = vehicle parameter value, such as desired free flow speed, stop gap distance, time headway, max and min acceleration s = standard deviation input by the user rnorm = random normal number generated by the random normal function1 x = mean value of the property inputted by the user Vehicle arrivals Vehicle arrivals were an impor tant part of the simulation be cause the distribution of the entering vehicle headways affects how the flagging control algorithms will function. If vehicle headways are generated according to a uniform di stribution, then vehicle enter at the same headway, so there arrival at the stop bar will be more uniform th an what would be seen in the field. In FlagSim, it was important to have a vehicle arrival process that wa s realistic. Thus, the vehicle arrival headways, by default, are generate d according to a Poisson process. The vehicle arrival headway times are based on the negative exponential probability dist ribution, as shown in Eq. 32. ln() hr [32] 1 See Numerical Recipes citation in references section PAGE 30 30 where h = vehicle headway, in seconds r = random number generated from a uniform distribution2 = average arrival rate, in veh/sec ln = natural logarithm Upper and lower bounds were also applied to the generated headway values. Extremely high headway values will lead to significant differences be tween the input volume and the simulation volume. Extremely low headway values are not realistic due to drivers general desire to maintain a safe following distance. The lower bound was set to 0.5 seconds. The upper bound was set to a value of four times the average vehicle arrival rate. Th ese values resulted in the simulated volumes reflecting the input traffic volumes. The program has the capability to allow the user to select a uniform arrival rate. The uniform arrival rate was used for calibration to compare procedures that are based on uniform arrivals. Initial speed After a vehicle was generated in to the network, the initial speed of the vehicle was set. The desired speed of the vehicle was its free fl ow speed determined during the setting of the vehicles properties. A vehicles speed was initially set to the free flow speed. In some cases, a vehicle that enters at its desi red speed could collide with th e lead vehicle. A check was performed to determine if the vehicle was too close to its lead vehicle. If the distance between vehicles was too close then the vehicles speed wa s set to the current speed of the lead vehicle with an acceleration of zero. 2 This value is generated from the Rnd function within Visual Basic 2005, which generates pseudorandom numbers between 0 and 1 according to a specific algorithm. http://support. microsoft.com/kb/q231847/ PAGE 31 31 Carfollowing model The carfollowing model was an important co mponent of the simulation program. The carfollowing model was the mathematical founda tion of the computations that described the movement of vehicles through the specified roadway system. Th e selection of a carfollowing model for this program was based on specific criteri a. The queue discharge aspect of traffic flow in the work zone area was the most critical el ement to the validity of the simulation results. Therefore, the model selected had to be partic ularly suitable for modeling the queue discharge phenomenon. After review of various models, the ModifiedPitt carfollowing model (Cohen, 2002) was selected for implementation. Th e ModifiedPitt carfollowing model was demonstrated by Cohen (2002) and Washburn and CruzCasas (2007) to work well for queue discharge modeling situations. For more discussion on queue discharge models, refer to Washburn and CruzCasas (2007). The Modified Pitt carfollowing equation calcul ates the acceleration value for a trailing vehicle based on intuitive paramete rs such as the speed and acceler ation of the lead vehicle, the speed of the trailing vehicle, the relative positi on of the lead and trail vehicles, as well as a desired headway. This equation also incorporates a sensitivity factor, K which will be discussed later in more detail. This equation allows for relatively easy calibration. Carfollowing models are generally based on a driving rule, such as a desired followi ng distance or following headway. The Modified Pitt model is based on the rule of a desired following headway. As indicated before, the acceleration of each vehicle depends of the leading and trailing vehicle and this model takes into considerati on the physical and operational characteristics of both. The main form of the model is shown in Eq. 33. PAGE 32 32 2()()() 1 [()()] 2() () 1 () 2lflf fl l fstRstRLhvtR K vtRvtRT atTT atT Th T [33] where af( t +T) = acceleration of fo llower vehicle at time t +T in ft/s2 al( t +R ) = acceleration of lead vehicle at time t +R in ft/s2 sl( t +R ) = position of lead vehicle at time t +R as measured from upstream, in feet sf( t +R ) = position of follow er vehicle at time t +R as measured from upstream, in feet vf( t +R ) = speed of follower vehicle at time t +R in ft/s vl( t +R ) = speed of lead vehicle at time t +R in ft/s Ll = length of lead vehicle plus a buffer based on jam density, in ft h = time headway parameter (refers to headway between rear bumper plus a buffer of lead vehicle to front bumper of follower), in seconds T = simulation timescan interval, in seconds t = current simulation time step, in seconds R = perceptionreaction time, in seconds K = sensitivity parameter (unitless) For application to this project, the value of the L parameter varied based on one of the four different vehicle types. The time headway parameter ( h ) was set as a random variable, rather than a constant value, to introdu ce an additional stochastic elemen t to the model. The value of the vehicle headway was based on a normal distribu tion to represent the mo re realistic scenario that desired headways vary by driver. The mean and standard deviation for this distribution can be specified for each of the four vehicle types. Thus, desired headways can vary by driver, as well as by vehicle category. The perceptionreaction time, R, and the simulation timescan interval, T are important parameters. Considerable time was spent expe rimenting with different values for each. Ultimately, both values were set to 0.1 seconds. This value for the timescan interval provided for very detailed vehicle trajectory data, which en abled very accurate measurements to be made of the measures of effectiveness, and enable d smooth vehicle animation in the work zone PAGE 33 33 visualization screen. While a perceptionreaction time of 0.1 seconds may seem intuitively low, it was found that this led to the most realistic tr affic flow representation. Individual perceptionreaction times are undoubtedly higher th an this for any isolated event. However, the fact is that reallife traffic flow happens on a continuous time scale, and reallife drivers make continuous incremental acceleration and decel eration (as well as steering ) inputs, withstanding sudden events/panic maneuvers. Thus, these consta nt incremental changes by both leading and following vehicles generally result s in smooth traffic flow. Again, this value of 0.1 seconds for the timescan interval and perceptionreaction time resulted in this type of realistic traffic flow. Queue arrival and discharge The sensitivity parameter, K has two separate values in the carfollowing modelone for the queue arrival and discharge and for the travel through the work zone. Cohen stated that a larger K value should be used in interrupted flow conditions due to overdamping effects (Cohen, 2002a). This assumption was tested in the carf ollowing model and yielded the best results. Vehicles had a smoother interaction in th e work zone (uninterrupted flow) with K = 0.75 and for the queue arrival and queue discha rge processes performed well with K = 1.1. The definition of the queue arrival area was 300 feet upstream of th e last vehicle in queue, and the definition of the queue discharge area was 300 feet downstream of the entering work zone stop bar. Another key parameter, for queue discharge, was the heavy vehicle acceleration rate. The truck acceleration rate was based on work by Rakha and Lucic (2002), from which a constant value of 1.5 ft/sec2 was selected for implementation in FlagSim. From a visual inspection of the animation, and review of vehicle trajectory data, this value resulted in reasonable truck headways. PAGE 34 34 Flagging operations A significant feature of FlagSi m was the ability to specify several different methods by which the rightofway could be controlled. Changing of the rightofway can be a complex operation. A decision to change the rightofway is generally based on several factors, such as the amount of traffic that needs to be served in ea ch direction of travel, th e time it takes to travel the work zone, and policy considerations such as maximum queue length or maximum green time. A flag change, much like a phase change at a signalized intersection, has a lost time associated with it. For the work zone to operate efficiently, the rightofway must not be switched too often such that the lost time beco mes a significant portion of the cycle length. Additionally, the flagging method employed at a work zone site is almost guaranteed not to result in optimal condition; for example, minimi zing vehicle delay. This nonoptimal condition is a direct result of the flag operators allocating nonoptimal am ounts of green time. Cassidy and Son (1994) stated that the green time was most often extended past the optimal time that should be given to each direction. Startup lost time Startup lost time begins when the front bumper of the platoons last vehicle crosses the stop bar exiting the work zone and ends when th e front bumper of the vehi cle entering work zone crosses the stop bar. This lost time is caused by seve ral factors. The first de lay occurs as the last vehicle exiting the work zone trav els from the work zone exit point to a safe distance in order to allow the next direction of vehi cles to proceed. The exiting vehicle must maneuver the lane switch area and pass the first few vehicles queued. Second, an additional time is needed for the flagger to perform the flag change, such as th e time it takes the flagger to determine when the work zone is clear. Finally, there is lost time for the first vehicle reacti ng to the change of the sign, similar to vehicles startup lost time at a sign alized intersection. In addition, since this lost PAGE 35 35 time is random in the field, the program account ed for this randomness by modeling it with a normal distribution, using a mean of 10 seconds a nd a standard deviation of (+/) 2 seconds. The randomness accounts for variation with the flaggers and variation in drivers reaction to the changing of the flag. The first vehicle was delayed the calculated amount of time before beginning to proceed into the work zone. Flagging methods FlagSim contains a variety of flagging methods to try to en capsulate the various methods operators might use to control tw olane work zones. The flagging control methods are generally based on control strategies used in traffic si gnal operations. The follo wing flagging methods are implemented in FlagSim. Distance GapOut: Rightofway change is based on specified distance gap between approaching vehicles. Queue Length: Rightofway change is based on a maximum queue length of vehicles on the opposing approach. Fixed Green Time: Rightofway is changed after the specified fixed green time is reached. This flagging method can also be used in combination with the distance gapout, and queue length methods, subject to a maximum green time. User Interface The user interface was designed to allow the us er to quickly and easily use the program. To accomplish this, multiple input forms were inco rporated. The main user form is shown in Figure 33. In this form, the user is able to select the m ost common program inputs. The main form gives the user the ability to quickly edit a single run and generate the results and animation. More detailed user inputs are contained in the Vehicle Parameter Settings form ( Figure 34); however, it is not intended that these values be changed unless the analyst has specific data for a site contr ary to these values. To facilitate mu ltiple runs of a given scenario, the Multiple Run Simulation Control input form ( Figure 35) is provided. PAGE 36 36 Animation FlagSim incorporates a 2D postprocessor animation viewer, shown in Figure 36. The anim ation allows the user to view the computations previously performed. Viewing the animation gives the user an opportunity to review the simulation scenario visually. Items that can be easily checked are vehicle generation, carfollowing interaction, and the flagging variations. At the top of the screen are the controls, wh ich allow the user to control the animation play, pause, stop and speed control. One feat ure of the animation is the vehicletracking window, shown in Figure 36. A small popup window appears if the user leftmouse clicks on a vehicle. This window displays all of the tim e step by timestep vehicle trajectory information for the selected vehicle. Outputs of the simulation Since FlagSim is a microscopic simulation progr am, detailed vehicle trajectory data (i.e., acceleration, velocity, and position values) are gene rated at each time step. These data can be saved to a time step data (TSD) file if the user so desires, in which case one TSD file per travel direction is created. From the detailed time st ep data, several performance measures can be calculated for the desired analysis period. These include: Total delay The queue delay and the travel time delay accumulate for the entire simulation period. Average delay per vehicle The total delay divided by the number of vehicles exiting the work zone during the simulation period. Average queue delay The average delay of ve hicles spent in a queue at the entrance to the lane closure area. For this project, queue delay was accumulated for any vehicle traveling less than 10 mi/h. Thus, this meas ure represents a hybrid queue delay between the traditional measures of stop delay (where delay is only accumulated when vehicle velocity equals zero) and control delay (whe re delay is accumulated for a vehicle any time its velocity is less than the average running speed). The value of 10 mi/h was a PAGE 37 37 compromise value to try to capture delay fo r those vehicles that were decelerating or stopped due to queuing, and not slowing just due to regular traffic flow conditions. Average cycle maximum back of queue (veh/cycle) The average of the all the maximum back of queue lengths for each cycle. It should be noted that this queue length is in terms of number of vehicles, and is the absolute maximum back of queue (which accounts for vehicles arriving on green at the ba ck of the initial queue at the start of green). Maximum back of queue (veh/simulation peri od) The maximum back of queue length that occurs during the entire simulation period; that is, across all cycles. Average travel time delay through the work zone Travel time delay was calculated based on the time the vehicle enters the work z one and the time it exits the work zone at the opposite crossbar compared to the time th e vehicle would have traveled through the work zone if no work zone were present. Average time spent in the system The total time a vehicle spends in the entire system from start of the warm up segment to a posit ion 2000 feet passed th e opposite stop bar. Only vehicles that have entered and completely exited the system are included in this measure. Maximum vehicle throughput (i.e., capacity) The number of vehicles exiting the work zone. This is a function of the saturation flow rate, the green time, and the cycle length (which is a function of green time, startup lost time, and travel time through the work zone). Average Cycle Length Cycle length was meas ured from the beginning of green for one direction to the next beginning of green for th e same direction. The average cycle length is calculated simply as the sum of all cycle lengths divided by the number of cycles in the simulation period. Average Green Time The sum of all green periods, by direction, divided by the total number of green periods during the simulation period. Average g/C The average g/C was the average of all g/C ratios for all cycles during the simulation period. A summary file containing all these performance measures ca n be generated by FlagSim. This file provided the input and output data that were used in the development of the calculations/models for this project. PAGE 38 38 Simulation Calibration For a simulation programs output to be consider ed valid, it should be calibrated to match real world situations. However, for this project, the resources were not available to perform field data collection. To supplement this lack of fi eld data, a quasicalibrati on procedure was utilized, which consisted of evaluating the reasonableness of traffic flow in three different modes: 1) queue buildup, queue discharge, and uni nterrupted flow through the work zone. The queue buildup component of traffic flow was the most challenging to implement. To have realistic vehicle movement, logic had to be implemented to ensure that a vehicle would decelerate in time to avoid a rea rend collision, yet would not d ecelerate at an unreasonably high rate (i.e., wait until the last second to slam on the brakes). Thus, the logic employed was such that a vehicle would decelerate at a reasonable value (on the order of 10 ft/s2) when approaching the stop bar or the back end of a queue. This assumption seems reasonable since drivers would have an appropriate warning of the work zone ahead and would take enough precaution to slow as directed by the work zone signage. Another assumption was that all vehicles, no matter how far back in the queue, have enough wa rning to begin deceleration. For the queue discharge component of traffic fl ow, results from an earlier research project performed by Washburn and CruzCasas (2007) were utilized. For this project, an extensive database of queue discharge headways was created. Fortyone hours of video data were collected from six signalized intersections around central Florida. From the video data, queue discharge headways were measured for the same f our vehicle types as used in FlagSim. These data provided a reasonable comparison data set because the queue discharge phenomenon at the work zone stop bar is similar to the queue di scharge phenomenon at a signalized intersection. However, there can certainly be some differences, pa rticularly for the traffic flow in the direction of the closed lane (i.e., for the vehicles that have to perform a lane shift). To extract the headway PAGE 39 39 values from FlagSim, the program exported the first 10 vehicle headways from the beginning of the green time. These data were compared to the data of Washburn and Cruz. FlagSim had an average headway value of 2.01 seconds, which was reasonably consistent w ith the results from Washburn and Cruz (2007). For the uninterrupted flow of traffic thr ough the work zone, visual inspection of the simulation animation was performed. For this component of traffic fl ow, vehicle spacing was the key factor analyzed. The initial platoon wo uld eventually dissipate during travel. Each vehicle has a different desired fr eeflow speed; therefore, slower vehicles would separate from the leader and fall out of the ca rfollowing mode. This would happen to several vehicles; thus result in a number of smaller platoons of vehicles. This phenomenon was also observed during informal field site visits. In addition, proper implementation of the flagging control methods was confirmed by visual inspection of the simulation animation. Sensitivity Analysis To determine the most appropriate variables to include in the experi mental designs, which were used to generate the data for model development, a sensitivity analysis was performed. The objective was to identify variables that significan tly affected capacity, delay, and queuing, as well as the form of their relationship. Due to the computational time required for large experimental designs, variables that did not have a consider able effect on work zone performance were excluded fr om further consideration. Each analysis scenario had the same base inpu t values. From this base set of inputs, one variable would then be varied over a given range. The base input values were as follows: Work zone length 1 mile Work zone speed 40 mi/h Posted speed 40 mi/h Heavy vehicles 5 percent PAGE 40 40 Max green time 120 seconds Traffic demand greater than capacity Input traffic volumes were selected to insure that the traffic dema nd was greater than the capacity. The results from the sensitivity analys is are provided in the following figures. The thick line (with diamonds) repres ents the total traffic throughput (i.e., both directions) of the work zone. The directional traffic flows are re presented by the dashed line (with squares) and thin solid (with triangles) lines. Figure 37 shows the relationship of the work zo ne travel speed to capacity. This relationship indicates that the slower the speed, the lower the capacity. This trend results from the longer time it takes for a vehicle to traverse the work zone, and the additional lost time incurred during the rightofway change. Figure 38 shows the relationship of green time to capacity. The green time value varied from 30 seconds to 360 seconds. The capacity of the work zone increased with increased green time given to each direction. The cycle length in creases as the green time increases, which is consistent with signalized intersection operati ons, and the longer the cycle length, the more vehicles that can be served. This increase in cap acity occurs because the percentage of lost time for the cycle length is reduced. Travel time through the work zone during the rightofway change is the largest component of the lost time. While increasing the green time does generally increase the capacity and lower the average delay, it must be noted that a practical maximu m green time should be implemented. While one direction has the green indica tion, the other direction obviously has a red indication. The longer the green for one direction, the more the queue length build s in the other direction during red. Thus, the individual wait time will eventually reach an intolerable level, from a drivers perspective, as well as the queue length. At this point, the rightofway must be switched, even PAGE 41 41 if it means less than optimal performance measure values. The assumption used in this project was that 5 minutes was reasonable practical maxi mum green time. Shorter than optimal green times may also be necessary when there are queue storage constraints, such as when the work zone is close to an upstream intersection. The relationship of work zone length to capacity is shown in Figure 39. It can be seen that work zo ne capacity decreases as the length of the work zone increases. This decrease in capacity can be explained by the increase in the tim e it takes the last vehicle to enter the work zone on green to traverse the work zone which results in additional lost time. The relationship of heavy vehicle per centage to capacity is shown in Figure 310. An increase in heavy vehicle percenta ge results in a d ecrease in capac ity. Trucks decrease the queue discharge rate, as well as lowe r the average speed of vehicles traveling through the work zone, with both factors contributing to a decrease in work zone capacity. Experimental Design Arguably, the two most important measures of effectiveness at twolane work zone sites are delay (particularly queue de lay) and queue length. The simulation program was used to generate the data set upon which regression models for estimating these measures were based. These models were incorporated into an analysis procedure for twoway, twolane work zones. Capacity, which is a function of several variables, is the single most influential parameter on values of delay and queue length. The simulation program was also used to generate values of capacity that would later be used to verify the saturation flow rate model and capacity calculations based upon the modeles timated saturation flow rates. Variable Selection Two experimental designs were developed; on e for generating capacity values and one for generating queue delay and queue length data. Fo r the development of the experimental designs, PAGE 42 42 the first step was to identify the variables that were expected to have significant influence on the values of the performance measures. The follo wing variables were selected for the capacity experimental design based on the resu lts from the sensitively analysis: Work zone length: Work zone length affect s the travel time through the work zone, which in turn affects lost time and cycle length. Travel speed through the work zone: Travel speed affects the travel time through the work zone, which in turn affects lost time and cycle length. The speed downstream of a traffic signal stop bar has also been shown to affect the queue discharge rate at the stop bar. Percentage of heavy vehicles: Heavy vehicles affect two co mponents of the traffic flow the queue discharge rate and the travel time through the work zone. The queue discharge rate is affected because large trucks have a slower acceleration rate and consume more space in the queue. For travel through the work zone, trucks again consume more space on the roadway and have slower acceleration rates. Furthermore, truck drivers generally have lower desired travel speeds than passenger cars, presumably particularly so in a work zone area where lateral clearances are more constrained. Green time: Higher green times result in high er capacities. However, higher green times also result in longer cycle lengt hs and longer red times. As th e red time increases with the green time, the resulting queue delays and que ue lengths quickly reac h intolerable levels from a drivers perspective. Thus, as prev iously mentioned, it is usually necessary to implement a maximum acceptable green time. Traffic volume was not a variable in the experi mental design. To obtain capacity values, it was necessary to specify a traffic demand that would exceed the expected capacity for the specific combination of input variable values. The same experimental design was used to ge nerate data for both de lay and queue length, as the same variables affect both measures. Work zone length, work zone travel speed, and percentage of heavy vehicles were also used in the queue delay/length experimental design. Traffic volume was added to this experimental design, in the form of a total twoway volume and a directionalsplit (D) factor, as traffic volume obviously has a ve ry significant effect on queue delay and queue length. The ot her variable added was a distan ce gapout flagging method, as explained in more detail as follows. PAGE 43 43 Several options were possible for the selection of green time values. One option is the maximum green time, as was used for the capacity experimental design. Th is option is not very realistic, as this maximum green time would only be used for capacity cond itions. For situations where the traffic demand is less than capacity, it is likely that smaller green times would be used. Another option is to determine wh at cycle length is appropriate for each specific combination of variables, and then proportion fixed green times for this cycle length according to the traffic demands in each direction. This option, however, is not realistic for implementation in the field, as flaggers cannot be expected to implement di fferent fixed green times for the varying traffic demands that occur throughout the lane closure period. Another option is to have the flagger alloca te just enough green time to serve the initial standing queue at the beginning of the green period. This could al so be combined with adding a fixed amount of extended green time to serve vehicl es that arrive at the back of the queue during the green period. One challenge with this from a field implementation standpoint is that the flagger may not always be able to see the back of the initial standing que ue at the beginning of green. In addition, implementing a fixed green time extension period would probably be difficult for flaggers to implement given th at it would be relati vely short in duration and they would have to continuously look at a watc h or other timing device. Although the maximum green time method employed for the capacity experimental de sign would also requir e a flagger to use a timing device, they would not have to check it nearly as often due to the much longer timing period. Furthermore, small errors (on an absolu te basis rather than percentage basis) in the actual timing used would not have as significa nt of an impact on the maximum green time method as the short duration green time extension method. PAGE 44 44 Another option, and the one se lected for the experimental design, is a distance gapout method with a maximum green time. With this method, green time is allocated until a specific distance between arriving vehicles is exceeded at the entrance to the work zone, or the maximum green time is reached. The distance gapout met hod was implemented rather than a time gapout method (as often used in actuated signal control) because it was assumed that implementation of a time gapout method is very difficult to do with human flag operators. With the distance gapout method, a mark or cone can be placed at th e appropriate distance and the flagger would be instructed to change the rightofway if there are no vehicles between that mark/cone and the stop bar. This method also offers the potential to reduce vehicle delays relative to fixed timing, as it is responsive to actual traffic demands, such as at vehicle actuated signalized intersections. There is one disadvantage to this method for model development purposes and that is that the green time is not fixed from one cycle to th e next. Therefore, the green time and cycle length were recorded for each cycle during the simula tion period to allow for calculating average g/C ratios for each scenario. The values chosen for the gapout distance were based on a number of criteria. The first being stopping sight distance va lues for the corresponding roadwa y speed approaching the lane closure area, as given by Eq. 34. The second was the gap had to be long enough not to allow a premature switch in rightofway due to a gap forming in the queue. Gaps tended to form if the first truck in queue was following a number of passenger cars. The third was that the value could not be greater than the average arrival ra te or the maximum green time would frequently control. rtV G g a g V 1 2 1+ 2 = SSD [34] PAGE 45 45 where SSD = stopping sight distance (ft) a = deceleration rate (ft/s2) V1 = initial vehicle speed (ft/s) g = gravitational constant (ft/s2) tr = perception/reaction time (sec) G = roadway grade (+ for uphill and for downhill) in percent/100 In this equation, a value of 1.0 second wa s used for the perceptionreaction time and a value of 10.0 ft/s2 was used for the deceleration rate. These values are the same as those typically used for yellowinterval timing (I TE, 1999). Although AAS HTO (2001) recommends values of 2.5 seconds for perc eptionreaction time and 11.2 ft/s2 for deceleration rate for this equation, it was felt that the ye llowinterval timing values were more appropriate for this situation where drivers are expecting to have to possibly come to a stop, whereas the AASHTO values are more appropriate for unexpected stopping situations. The grade was assumed to be level, which is generally appr opriate for Florida conditions. Even with this gapout method, it should be noted that the maximum green time of five minutes was also applied. Setting Variable Levels The second step in developing the experimental design was to determine the values that will be used for the chosen variables. Two leve ls (i.e., values) for each variable are typical for situations in which the relationships are linear in nature. If certain relationships are nonlinear in nature, then it is necessary to use three levels for each variable If the relationship is not predetermined to be linear, then it is usually prudent to use three levels. However, the size of the experimental design (i.e., number of runs) will increase substantially in this case. This can be illustrated with Eq. 35. PAGE 46 46 FL R [35] where R = Number of unique variable co mbinations (or simulation runs) L = Number of levels F = Number of factors So for example, an experimental design with seven variables, each run at two levels, would yield 32 (25) unique variable combinations, whereas an experimental design with seven variables, each run at thr ee levels would yield 243 (35) combinations. Thus, if it is known that the relationships of interest are linear, there will be a substantial savings in computational time versus the calculation time of a nonlinear relationship. The selected variables, and their setting le vels, for the capacity and queue delay/length experimental designs are shown in Table 31 and Table 32, respectively. Number of Replications The final step of the experimental design is to determine an appropriate number of replications (i.e., runs of the simulation progr am) for each combination of variables in the experimental design, to account for the st ochastic nature of each simulation run. The number of replications requi red is a function of the desire d statistical confidence level, the variance of the data, and the ac ceptable error tolerance. Eq. 36 can be used to calculate the necessary sample size. 2 2 z sn/ [36] where n = minimum number of replications s = estimated sample standard deviation z/2 = constant corresponding to the desired confidence level = permitted error PAGE 47 47 To determine an appropriate number of itera tions, numerous test simulation runs were made. The runtorun variance was calculated for capacity, delay, and queue length. These variance values were used in Eq. 35 with a 90% confidence level ( z/2 = 1.645) and error tolerance of 5% of the variable of interest. From this exercise, it was determined that five iterations were sufficient. Therefore, after choos ing three levels for each of 5 variables, for a 35 experimental design, with 5 replications, a tota l of 1215 (243 5) simulation runs were required. The next step in the project was to execute the experimental design with the simulation program. The following chapter will describe the data analysis, model development, and development of the calculations procedur e based on the resulting simulation data. Work Zone Stop Bar Stop Bar Lane Shift Back of Queue Traversing work zone Arriving vehicle Length of Queue Figure 31: Twolane work zone op erated with flagging control. Figure 32. K value locati on used in simulation. PAGE 48 48 Figure 33. Screen shot of the program main user interface Figure 34. Screen shot of vehicle parameter setting window PAGE 49 49 Figure 35. Screen shot of the multiple run input form Figure 36. Screen s hot of animation window PAGE 50 50 0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 253035404550556065 Work Zone Speed (mph)Capacity (veh/hr) Pk Dir Off Pk Dir Total Cap Figure 37. Relationship of wo rk zone speed to capacity 0 200 400 600 800 1000 1200 1400 1600 1800 0306090120150180210240270300330360 Green Time (sec) Pk Dir Off Pk Dir Total Cap Figure 38. Relationship of green time to capacity PAGE 51 51 Capacity (veh/hr) Figure 39. Relationship of wo rk zone length to capacity 0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 02.557.51012.51517.520 Heavy Vehicle (%) Capacity (veh/hr) Pk Dir Off Pk Dir Total Cap Figure 310. Relationship of hea vy vehicle percentage to capacity PAGE 52 52 Table 31. Experimental design vari ables and values for capacity data Settings Factor Units Low Med High Work Zone Length (mi) 0.25 1.0 3.25 Work Zone Speed (mi/h) 20 35 50 Heavy Vehicles (%) 0 10 20 Green Time (sec) 60 180 300 Table 32. Experimental design variables and values for queue delay and queue length estimation models Settings Factor Units Low Med High Work Zone Length (mi) 0.25 1.0 3.25 Work Zone Speed (mi/h) 25 37.5 50 Heavy Vehicles (%) 0 10 20 Total Volume (veh/h) 400 700 1000 Dfactor 0.5 0.6 0.7 Distance GapOut (ft) 325 450 550 PAGE 53 53 CHAPTER 4 CALCULATION PROCEDURE DEVELOPMENT Introduction This chapter describes the development of m odels and calculations for work zone capacity, delay and queue length. This is followed by a sample application of the calculation procedure. Finally, a comparison of the results from this calculation procedure to those based on simple deterministic equations and those based on the Cassidy and Son calculation procedure. Work Zone Speed Model The first model that was estimated was one for average work zone speed. With impact to the overall cycle length due to the lost time cau sed by traversing the work zone, and impact on the saturation flow rate, the estimation of the work zone speed must be as accurate as possible. The work zone speed model captures the impact of trucks on the work zone speed along with the work zone length. The posted speed for a work z one is inputted and the m odel adjusts this speed to account for additional heavy vehicles and the work zone length. The model formulation is shown below in Eq. 41. Table 41 summarizes the coefficient and tstatistic v alues for each variable. The model has a good fit with an R2 of 0.896. Note that for a perfect model fit, the R2 would be 1.0. The included model variables are all statistically significant at well above the 99% confidence level ( z/2 = 2.58). i i iHV LMin PostedSpd d WorkZoneSp 1063336.0)10560),5280(( 000601.0 706381.0608474.4 [41] where WorkZoneSpdi = estimated average travel speed of vehicles through the work zone for direction i (mi/h) PostedSpdi = the posted speed, or maximum desirable travel speed of vehicles, through the work zone for direction i (mi/h) L = work zone length (mi) HVi = percentage of heavy vehicles in the traffic stream for direction i PAGE 54 54 As the model indicates, a higher posted speed in the work zone logically results in a higher travel speed through the work zone. Shorter work zones decrease the speed due to vehicles not achieving their free flow speed for the majority of the travel through the work zone. However, note that the length value is constrained. That is, for lengths greater th an 2 miles, a value of 10560 ft should be used because longer lengths do not provide an additional increase in the work zone speed. Higher truck percentages decrease the work zone speed because of their lower performance capabilities and result ant impacts on following vehicles. Saturation Flow Rate Model One of the key parameters to all of the calculations in the analysis procedure is saturation flow rate. This measure refers to the departure rate of vehicles from a standing queue when the traffic signal (or flagger paddle in th is case) turns green. It is typica lly reported in units of veh/h, assuming the signal/paddle is green for the full hour. Typically, there is base saturation flow rate, which reflects the satura tion flow rate under ideal or base conditions, such as 100% passenger cars. This saturation flow rate then gets adjusted if there are site conditions that are less than ideal. The approach used in this work follows the same framework as that specified in Chapter 16 (signalized intersections) of the HCM 2000. That is, a base satu ration flow rate value is adjusted downward for various nonideal roadway, traffic, and/or control factors, resulting in an adjusted saturation flow rate3. This calculation framework for adjusted saturation flow rate can be expressed generically as shown in Eq. 42. Nfffss 210 [42] 3 Technically, it is also possible to have adjustment factors that adjust the base saturation flow rate upward (see Bonneson et al. [2005] for example). PAGE 55 55 After deciding on the model form for the adjusted saturation flow rate, the next step was to determine the appropriate adjustment factors to incl ude in the model. For this, past research was relied upon, such as Washburn and CruzCasas (2007) and Bonneson et al. (2005). Factors shown to significantly affect saturation flow rate include downstream travel speed, percentage of heavy vehicles, and length of green time. Other f actors, such as lane width and grade, can also be significant, but these factors were either not modeled within the simulation program or were not relevant to the situation of twolane work zones. The general model specification for adjusted saturation flow rate is given in Eq. 43. Green time was not found to be significant in this situation since the green times are generally much longer than at signalized intersections. 1 100 145)45, (12 1 0_b HV speedMinbbhi i isat [43] where isath_= saturation headway for direction i (sec/veh) b0 = base saturation headway (sec/veh) b1, b2, b3 = model coefficients for adjustment terms speedi = average travel speed downstr eam of stop bar for direction i (veh/h) HVi = percentage of heavy vehicles in the traffic stream for direction i The model with the estimated parameter valu es, based on the FlagSim data, is shown in Eq. 44. The model has a reasonable R2 of 0.721. The included model variables are all statistically significant at well above the 99% confidence level (z/2 = 2.58). 137.2 100 145)45, (00516.0192.1_ i i isatHV speedMin h [44] Equation 45 converts the adjusted saturation headway into the adju sted saturation flow rate. (sec/veh) (sec/h) 3600 (veh/h) isat ih s [45] PAGE 56 56 Note that the base saturation headway of 1.92 seconds (from Eq. 44) translates to a base saturation flow rate of 1875 veh/h. This value, and the truck passenger car equivalent value (b2 = 2.37), are reasonably consistent w ith the results from Washburn and CruzCasas (2007). Also, note that the speed value is constrained. That is, for speeds above 45 mi/h, a value of 45 should be used because higher speeds do not provide an a dditional increase in the saturation flow rate. The use of this maximum value results in an adjust ment factor value of 1.0. It should be noted that the experimental design for this study used a truck type distribu tion of 40%/40%/20% for small, medium and large trucks, respectively, as opposed to the Washburn and CruzCasas study (2007), which assumed an equal percentage of ea ch truck type. The proportion was assumed to differ because of the relatively higher number of smalland mediumsized construction trucks that would be servicing th e construction activities. Capacity Calculation Another key parameter in the assessment of work zone operations is capacity. The capacity indicates the number of vehicles that can be processe d through the work zone during a specified period of time. Ideally, a work zone should be set up such th at capacity exceeds the traffic demand; otherwise, delays and queue lengths will become excessive. Capacity can be calculated with the standard equation used for signalized intersection analysis (TRB, 2000), as shown in Eq. 46. C g sci ii [46] where ci = capacity of the work zone in direction i (veh/h) si = adjusted saturation flow rate for direction i (veh/h) (g i /C) = effective green time to cy cle length ratio for direction i PAGE 57 57 For this equation, the adjusted saturation flow rate is determined from equations 44 and 45. In order to maximize capacity, the green time needs to be maximized. As previously mentioned, a maximum green time of 300 seconds (5 min) was assumed. The other component to this equation is the cycle length. The cycle length is calculated with Eq. 47. 221 2 1 SLTgg speed wzlen speed wzlen C [47] where C = cycle length (sec) wzlen = length of the work zone (ft) speedi = average travel speed through the work zone calculated from the work zone speed model for direction i (ft/s) gi = green time for direction i (sec) SLT = startup lost timeelapsed time between last vehicle to exit work zone and time when flagger turns paddle to green for other direction Work zone speed should be calculated from the work zone speed model if field data is not available. Lost time is dependent upon the guida nce provided to the flaggers about when it is appropriate to change the paddle to green after the work zone has been cleared of vehicles traveling in the opposite direction. As previously mentioned, a mean value of 10 seconds was used in this study. Using Equations 44 and 45 to get the saturati on flow rate, Eq. 47 to get the cycle length (with the maximum green time), and then plugging these values into Eq. 46 will yield the capacity. The calculated capacity can then be comp ared to the input volume (by direction) to determine if none, either, or both di rections are under or over capaci ty. If one or both directions are over capacity, an altern ative work zone configuration should be consider ed; otherwise, delays and queue lengths will quickly be come intolerable to motorists. If the work zone is under capacity, the standa rd formula for calculating the minimum cycle length can be applied (TRB, 2000), shown in Eq. 48. PAGE 58 58 2 1 s v s v X XL = Cc c min [48] where Cmin = minimum necessary cycle length (sec) L = total lost time for cycle (sec) Xc = critical v / c ratio for the work zone ( v/s )i = flow ratio for direction i Here it assumed the critical v/c ratio, Xc, is 1.0. Eq. 410 (TRB, 2000) can be applied to proportion the green times to th e two directions of travel. i i iX C s v g [49] where gi = effective green time for phase (direction) i ( v/s )i = flow ratio for direction i C = cycle length in seconds Xi = v / c ratio for direction i (again, assumed to be 1.0) It should be noted that the use of minimum cycle length, and corresponding green times, calculated from equations 48 and 49 do not necessa rily lead to minimum delay values. These values just ensure that all the vehicles queue d during the red period for a direction are served during the subsequent green period. It was beyond the scope of th is project to develop optimal timing strategies, that is, timing guidelines that would minimize the value of specific performance measures, such as vehicle delay. Thus, for an undercap acity situation, the calculation procedure outlined in this report uses equations 48 and 49 to determine the minimum cycle length and minimu m green times to apply for the queue delay and queue length estimation models, as outlined in the next section. PAGE 59 59 Queue Delay and Queue Length Models The experimental design for queue delay and queue length did result in some scenarios that were over capacity for some individual cycles during the simulation period, or even for the whole simulation period, due to randomness of the arrivals. Generally, for overcapacity conditions, simple deterministic queuing equation s can be applied to estimate queue delay and queue length. For the development of queue de lay and queue length models described in this section, scenarios with volumetocapacity ratios up to 1.2 were retained, while anything higher was removed from the data set. The final da ta set contained 940 out of the original 1215 scenarios. Queue Delay Model A regression analysis of the resulting simulation data resulted in the following model for total queue delay (i.e., units of vehhr) for a 1hour time period, shown in Table 43. The included model variables are all statis tically significant at well above the 99% confidence level ( z/2 = 2.58). The variable signs are all consistent with expectations; for example, as the g/ C ratio increases, the delay decreases. This model, in equa tion form, is shown in Eq. 410. ii i i i igHV g C sv Cg TotalDelay 001376.0 148503.0 003387.0(%)/242061.0(%)/ 276980.0 [410] where TotalDelayi = total queue delay for a 1hr time period for direction i (vehhr) ( gi /C ) = effective green time to cy cle length ratio for direction i (expressed as a percentage) ( v/s )i = volume to saturation flow rate ratio for direction i (expressed as a percentage) C = cycle length (sec) HVi = percentage of heavy vehicles in the traffic stream for direction i ig = average green time given to the direction of travel PAGE 60 60 The g/ C ratio used in this model should be an average, or expected, g / C ratio for the entire simulation period. Under the gapout flagging method, the green time, and consequently the cycle length can vary every cycle (as in actua ted signalized intersection control). For the development of the model, the average of the g/ C ratios for each cycle within the entire simulation period was used (as opposed to the average green divided by the average cycle length). The model fit, as indicated by the R2 value of 0.958, is excellent. This means that the model describes 95.8% of the variance in the delay data. The model fit is also illustrated in Figure 41. Note that for a perfect model fit (i.e., R2 = 1.0), all the data points would fall directly on the line. For lower delays, the model prediction is better. The larger variance occurs with predictions over 35 vehiclehours of delay. As the volume approaches capacity, any cycle failure will cause a significant increase in the delay. Queue Length Model A regression analysis of the resulting simulation data resulted in the following model for queue length, shown in Table 44. This model estimates th e expected m aximum back of queue length to occur per cycl e (i.e., units of veh/cycle), per direction. The included model variables are all statis tically significant at well above the 99% confidence level ( z/2 = 2.58). The variable signs are all consistent with expectations. These same variables were used in the queue delay model. Queue length model, in equation form, is shown in Eq. 411. ii i i i igHV g C sv Cg h QueueLengt 003199.0 299197.0 0006855.0(%)/598965.0(%)/ 616983.0 [411] PAGE 61 61 where QueueLengthi = maximum queue length per cycle for direction i (veh/cycle) (gi /C ) = effective green time to cycle length ratio for direction i (expressed as a percentage) ( v/s )i = volume to saturation flow rate ratio for direction i (expressed as a percentage) C = cycle length (sec) HVi = percentage of heavy vehicles in the traffic stream for direction i ig = average green time given to the direction of travel The model fit, as indicated by the R2 value of 0.984, is again excellent. The model fit is also illustrated in Figure 42. Again, for the developmen t of this model, the average of the g/ C ratios for each cycle within the simulation period was used. Model Validation All new models or methods developed should have some validation, to other work or relevant data. With the lack of field data, ot her procedures were used for comparison purposes. The two procedures that were chosen to compare to were Cassidy and Sons procedure and the HCM uniform delay and queue length formulations While all three methods have their unique elements, they also have seve ral similarities given that th ey are all founded on signalized intersection operational characteristics. Cassidy and Son Comparison Queue delay and queue length values were compared between Cassidy and Sons method, FlagSim, and the analytical procedure based on Fl agSim results, as shown in Table 46. Two different sets of results are provided for the Cassidy and Son me thod: 1) results based on the default set of parameter values recommended by Cassidy and Son, except for adjusting the work zone speed, and 2) results based on revised parameter values consis tent with the results obtained from FlagSim modeling. Some of the default parameter values for the Cassidy and Son method were significantly different from those obtained from FlagSim. Thus, revising the parameter PAGE 62 62 values to be consistent with FlagSim provides a more accurate comparison of the methods. The parameters revised in the Cassidy and Son method are summarized in Table 45. The Cassidy and Son method with revised parameter values consistent with the analytical procedure produced results reasonabl y consistent with those of the analytical procedure. The Cassidy and Son method us ing revised parameters for most scenarios estimates higher delays than FlagSim does. This is expected since Fl agSims actuated rightofway control responds to the actual arrival rates each cycle, rather than providing the same amount of green time each phase based on an the average arrival rate (simila r to a pretimed signal control strategy). The analytical procedure results ar e lower than Cassidy and Sons method as well, because the analytical procedure results are more consistent with the FlagSim results (e.g., the estimated models used in the analytical procedure are ba sed on FlagSim data). The results of the Cassidy and Son method, based on the default paramete r values, have higher delay values than the analytical procedure. This is primarily due to lower saturation flow rates and higher lost times (both startup time and work zone travel time). Uniform Delay and Queue Length A comparison was also made between the unifo rm signal delay equation (Eq. 1611) of the HCM (TRB, 2000) and FlagSim results based on uniform arrivals, fixed green, and uniform vehicle parameters (i.e., the variance was set equa l to zero for the various vehicle performance parameters such as speed, etc.). These result s from the HCM and FlagSim were also compared to the Cassidy and Son method, the analytical procedure, and FlagSim (using the default input scheme). Performing a comparison of the HCM uniform delay equation results with FlagSim under uniform/fixed input conditions provides a ba seline comparison, and provides one measure of validation for the operation of the simulation program. The results ar e shown in Table 47. PAGE 63 63 The comparisons in Table 47 have some scenarios with higher than minimum green times to represent flaggers operating the work zone in a relatively nonoptimal manner. The saturation flow rate used in the other methods was calculated according to Eq. 45. The HCM and FlagSim queue delay and queue length values were generally similar. Th e analytical procedure produced higher delays and longer queue lengths when usi ng a green time much higher than the minimum green time. This confirms that using the minimu m green time (i.e., the green time necessary to serve the average number of arrivals on red and the ve hicles that arrive while this initial queue is being served) will generally provide lower delays and queue lengths. A comparison was also performed between Fl agSim (using random arrivals and a distance gapout flagging method) and the analytical procedure and the HCM uniform delay equation. In order to formulate the input green time and speed values, FlagSim was run first and then these values were input into the anal ytical procedure and HCM equation. Again, the saturation flow rate was calculated from Eq. 45 for use in th e analytical procedure and HCM equation. The analytical procedure and FlagSim have lower dela ys than the HCM method due to the regression equations developed from FlagSim, which were influenced by the random arrivals and actuated control strategy. The green times used for the HCM uniform delay comparison to FlagSim (using distance gapout fl agging control) were the average green times obtained from the FlagSim simulation. The Cassidy and Son met hod yielded similar, but slightly higher delay values than FlagSim (using dist ance gapout flagging control) and the analytical procedure (using the minimum green time). This is generally because the Cassidy and Son method also factors in red time variance into its cycle delay ca lculation. Overall, the Cassidy and Son results were fairly consistent with the HCM uniform delay results. PAGE 64 64 Analytical Procedure Compared to FlagSim Tables 46 and 47 both provi de a summary of comparisons between FlagSim and the analytical procedure. FlagSim typically had slig htly lower queue delay and queue length values. The lower values result from the difference in green times. The green time in the analytical procedure was generally estimated to be a little higher than the resulting FlagSim green times for the same input conditions. The analytical pr ocedure is based on a minimum cycle estimation method similar to signalized intersections, with the green time proportion based on the volume to saturation flow rate ratios. The resulting green times in FlagSim tended to be a little lower than the estimated minimum green times from the an alytical procedure because of the actuated control operation as discussed previously. The reader may note that the delay in Dire ction 2 is often higher than the delay in Direction 1. In some cases, where the total delay is higher (vehhr), the pervehicle delay (sec/veh) can be higher due to the lower volume in Direction 2. In other cases, where both delay values are higher for Direction 2 and/or the volumes are equal in both directions, the results may be reflecting a cycle truncation issue (i.e ., the simulation period ends midcycle). The FlagSim simulation results represent an av erage of all the percycle results during the simulation period. For simulation scenarios that result in six or more cycles per simulation period, the effect of the cycle truncation on the calculation results is generally negligible. However, for scenarios that resu lt in very long cycle lengths (e .g., long work zone, slow speed, etc.), only a few cycles may be completed with in the simulation period. Thus, calculating the averages based on only a few cycles, and with on e direction containing on ly a partial phase, significant differences can results between the two directions. Due to the setup of the simulation program, the number of phases for Direction 1 was equal to or higher than Direction 2. PAGE 65 65 Consequently, the results for Direction 1 are more reliable for long cycle scenarios. It is anticipated that this issue will be addressed in a future update to the simulation program. PAGE 66 66 Figure 41. Modelestima ted queue delay versus simulation queue delay. PAGE 67 67 Figure 42. Modelestimated queue length versus simulation queue length. PAGE 68 68 Table 41. Work Zone Speed Model Factor Coeff. tStat Constant 4.608474 24.78 Posted Speed (mi/h) 0.706381 156.29 HV% 0.106336 25.42 Work Zone Length (mi) 0.000601 53.34 RSquared 0.896 Table 42. Saturation Flow Rate Model Factor Coeff. tStat Base Sat Headway 1.921924329.23 Work Zone Speed (mi/h) 0.00516 24.76 HV% 2.37013 133.34 Work Zone Length (mi) 1.921924 329.23 RSquared 0.721 Table 43. Queue Delay Model Factor Coeff. tStat g/C(%) 0.276980 8.2305 v/s (%) 0.2420616.6899 Cycle Length (sec) 0.0033877.5329 Green Time (sec) 0.14850358.3398 HV% x Green Time (sec) 0.00137618.8804 RSquared 0.958 Table 44. Queue Length Model Factor Coeff. tStat g/C(%) 0.61698314.9374 v/s (%) 0.59896513.4875 Cycle Length 0.00685512.4224 Green Time (sec) 0.29919795.7674 HV% x Green Time (sec) 0.00319935.7656 RSquared 0.984 PAGE 69 69 Table 45. Parameter revisions made to Cassidy and Son method to facilitate a more direct comparison to the Analytical Procedure. Parameter How Revised General Effect on Results Saturation Flow Rate Calculated according to Eqs. 44 and 45 The saturation flow rate was increased, thus increasing capacity and reducing delays and queue lengths. Saturation Flow Rate Variance Value set to zero The Cassidy and Son method accounts for variation in the saturation flow rate w ith higher values producing higher delays. The analytical procedure does not include an adjustment for saturation flow rate variance, but does include an adjustment to the saturation flow rate for heavy vehicles. The Cassidy and Son method does not adjust the saturation flow ra te due to heavy vehicles. Setting the Cassidy and Son me thod saturation flow rate variance to zero, while using Eq. 45 to calculate the saturation flow rate provides a more direct comparison with results from the analytical procedure. Work Zone Travel Time Variance Value set to zero Work zone travel time variance was removed because the analytical procedure does not have a travel time variance term, but does adjust the travel time based on the percentage of heavy vehicles. Including the variance would increase the travel time, which would increase the delay and queue length. Green Time Extension Value set to zero Removing the green time extension lowers the green time for each direction by a small amount. This will result in slight reductions to delay and queue length as the provided green time will be largely utilized by vehicles departing at th e saturation flow rate. Lost Time Changed from 23.32 sec to 10 sec (the value used in FlagSim) Decreasing lost time decreases the cycle length, which results in a lower queue delay and a shorter queue length. RightofWay Gap Out Changed the gap out time from 12.4 seconds to 9.4 seconds (the value used in FlagSim, based on a stopping sight distance of 400 ft) Decreasing the gap out time decreases the green time because smaller gaps are accepted between vehicles on which to base changing the rightofway, which maintains a higher flow rate through the work zone. A lower gap out time will also decrease the green time, which will result in a shorte r cycle and reduced delays and queue lengths. Work zone speed Calculated according to Eq. 41 The work zone speeds in the Cassidy and Son method are based on the work zone activity type, rather than a posted work zone speed limit. Work zone speed is the most significant factor affecting total lost time. PAGE 70 70 Table 46. Comparison of Cassidy and S on with FlagSim and generated models Work Zone Length (mi) Posted Speed (mi/h) Traffic Volume (veh/h) Sat Flow (veh/h) Model Total Delay (vehhr) Queue Delay (vehhr) Queue Delay (sec/veh) Avg. Queue Length (veh) 1 2 1 2 1 2 1 2 1 2 3.25 45 170 140 FlagSim (gapout)a 12.5 13.0 12.0 12.6 250.2 316.0 24.9 22.0 Analytical Procedure 10.3 8.9 10.6 9.1 224.8 234.7 21.8 18.7 Cassidy/Son (default)b 16.8 14.3 16.8 14.3 354.9 367.9 1666 Cassidy/Son (revised)c 14.3 12.1 14.3 12.0 303.8 309.8 1.25 35 440 355 FlagSim (gapout)a 22.1 19.1 21.4 18.6 181.6 190.0 44.1 37.5 Analytical Procedure 23.6 19.4 22.5 18.5 184.1 187.9 46.4 38.2 Cassidy/Son (default)b 55.8 51.8 55.8 51.8 456.2 525.7 1616 Cassidy/Son (revised)c 25.9 22.5 25.9 22.5 211.7 228.0 0.75 30 600 300 FlagSim (gapout)a 22.7 15.7 21.9 15.5 131.5 184.2 49.0 29.4 Analytical Procedure 27.4 14.5 26.2 13.9 157.0 166.9 54.3 28.8 Cassidy/Son (default)b 83.6 72.8 83.6 72.8 501.5 873.0 1604 Cassidy/Son (revised)c 26.5 17.6 26.5 17.6 158.9 211.7 0.5 25 600 600 FlagSim (gapout)a 31.2 35.3 30.5 34.7 192.9 212.2 62.8 67.7 Analytical Procedure 41.3 41.3 40.5 40.5 242.9 242.9 83.0 83.0 Cassidy/Son (default)b over capacity 1598 Cassidy/Son (revised)c 43.2 43.2 43.2 43.2 259.1 259.1 Variables that are the same: Truck Percent = 5%; Maximum Green Time = 5 min; Green Extension time = 9.4 sec, work zone speeds match FlagSims output a (gapout) Uses a gapout distance of 400 ft, max green of 5 minutes, and random arrivals b (default) Uses all of the default input parameters exce pt the work zone speed. The work zone speed is set equal to the value used in the other comparisons. c (revised) The parameters revised consistent with Anal ytical Procedure results, including saturation flow rate, work zone speed, lost time, gap out headway. PAGE 71 71 Table 47. Comparison of uniform delay and queue length equations Work Zone Length (mi) Speed (mi/h) Volume (veh/h) Green Time (sec) Sat Flow (veh/h) Model Queue Delay (vehhr) Queue Delay (sec/veh) Avg. Queue Length (veh) 1 2 1 2 1 2 1 2 1 2 1.75 35 250 250 FlagSim (gapout)a 12.7 12.6 184 182 24.8 24.7 Analytical Procedure (min green)b 13.1 13.1 189 189 27.1 27.1 1558 Cassidy/Son (revised)c 17.1 17.1 246 246 100 90 1558 HCM Uniform Delayd 16.2 16.2 233 233 31.4 31.4 180 180 Analytical Procedure (fixed green)e 23.5 23.5 338 338 46.9 46.9 180 180 FlagSim (uniform)f 13.6 16.2 196 233 31.8 31.8 180 180 1558 HCM Uniform Delayc 17.6 17.6 253 253 39.0 39.0 1 25 400 300 FlagSim (gapout)a 20.7 18.8 193 221 44.0 36.7 Analytical Procedure (min green)b 20.7 16.0 186 192 42.7 33.0 1489 Cassidy/Son (revised)c 25.3 20.8 228 250 160 125 1489 HCM Uniform Delayd 24.6 19.4 222 232 47.8 38.3 180 120 Analytical Procedure (fixed green)e 19.0 19.9 171 239 43.5 36.5 180 120 FlagSim (uniform)f 19.0 19.9 171 238 43.5 36.5 180 120 1489 HCM Uniform Delayc 23.7 21.0 213 252 48.9 41.7 0.5 30 200 100 FlagSim (gapout)a 3.7 2.1 68.3 74.9 7.3 3.5 Analytical Procedure (min green)b 3.6 2.1 64 76 7.8 4.5 1528 Cassidy/Son (revised)c 4.8 2.6 86 93 30 15 HCM Uniform Delayd 4.2 2.3 76 82 8.5 4.6 120 60 Analytical Procedure (fixed green)e 10.2 5.4 183 195 19.4 10.4 120 60 FlagSim (uniform)f 3.1 2.6 56.5 95.3 8.4 5.5 120 60 1528 HCM Uniform Delayc 4.0 3.1 72 113 11.1 7.2 0.5 45 400 400 FlagSim (gapout)a 7.7 8.4 73.8 75.9 15.8 17.2 Analytical Procedure (min green)b 7.3 7.3 66 66 15.9 15.9 1528 Cassidy/Son (revised)c 10.5 10.5 95 95 70 70 1528 HCM Uniform Delayd 8.5 8.5 77 77 17.2 17.2 180 180 Analytical Procedure (fixed green)e 20.7 20.7 187 187 41.6 41.6 180 180 FlagSim (uniform)f 10.4 11.5 94 104 27.6 27.6 180 180 1528 HCM Uniform Delayc 12.7 12.7 114 114 31.1 31.1 Variables that are the same: Truck Percent = 10%, work zone speeds match FlagSims output a (gapout) Uses a gapout distance of 400 ft, maximum green time of 5 minutes, and random arrivals b (min green) Uses models based on FlagSim data generated with gapout control strategy (with 5 minute maximum green time) and normal stochastic variations c (revised) The parameters revised consistent with Analytical Procedure results, including saturation flow rate, work zone speed, lost time, gap out headway. d Delay was calculated using Equation1611, and the queue length calculated according to Appendix G, of Chapter 16 in the Highway Capacity Manual 2000 e (fixed green) Analytical procedure uses a fixed green time higher than the necessary minimum green time f (uniform) Uses the fixed green time given for the scenario and uniform arrivals and vehicles types with identical vehicle characteristics PAGE 72 72 CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS Summary Twolane twoway roadways with a lane closure under flagging control are frequent fixtures on the roadway constructio n landscape. This type of work zone can be one of the most frustrating to motorists due to the need to alte rnate traffic flow directions and the lengthy time that can be spent sitting in a queue. It is essent ial that the impacts of this type of work zone on traffic flow operations be accurately quantified in order to assist engineers with setting up work zone traffic control plans that balance the competing issues of maximizing construction productivity and minimizing impacts/ frustration to motorists. Con ceptually, this type of work zone has many similarities to a twophase signa lized intersection. As such, many of the equations applicable to signalized intersection analysis can be applied to this type of work zone. However, some of the equations are not directly applicable due to some significant differences in the calculation of the green time and the significan t lost time due to traversing the work zone and the laneswitch at the beginning of the work zone. This thesis has provided a calculation procedure for estima ting the capacity, delays, and queue lengths of twolane, twoway work zones with flagging control. This calculation procedure utilizes a combination of standard signalized intersection analysis equations as well as some custom models developed from simulation data. Conclusions From the literature review, there was a genera l lack of available resources on twolane work zones under flagging operations. Additiona l research was, and still is, warranted on this topic. The analytical procedure, implemented in a spreadsheet format, allows for a quick, yet fairly comprehensive comparison of different work zone configurations and traffic conditions. It is robust with the regard to the inputs and out puts, and still easy to use. PAGE 73 73 The analytical procedure yields results reas onably consistent with those generated from the simulation program. These results are generally slightly lower than the values calculated by the HCM uniform delay and queue length equations, which is largely due to the regression equations reflecting the effici ent actuated operati on of flagging control used in FlagSim. The analytical procedure, in most scenarios, had lower delays than did Cassidy and Sons method with revised parameters. This is generally because the Cassidy and Son method also factors in red time variance into its cycle delay calculation. The microscopic simulation program, FlagSim, produced for this project can be utilized to investigate issues that are not within the scope of the basic analys is spreadsheet. For example, it can also be used to test the effect of a variety of different vehicle performance characteristics, or some different flagging methods or parameter values beyond what was used for the development of the models/ calculations contained in the analytical procedure. Additionally, FlagSim can be us ed to analyze oversaturated work zone conditions. Recommendations for Further Research While it is felt that the results of this project offer significant improvements over the existing FDOT PPM procedure, there are still areas that could benefit from additional research. These areas are as follows: One obvious limitation to the resu lts of this project is th e lack of field data for verification/validation of se veral aspects of the simula tion program. Although certain parameter values used in the simulation program were compared for consistency to field data values obtained from the Cassi dy and Son research (1994), most of their field sites utilized a pilot car; thus, thei r parameter values may not be directly comparable to sites that do not use a pilot car. Field data should be collected at several sites, under only flagging contro l, to confirm the following factors: o Saturation flow rates and/or capacities What are typical values, and how do they differ due to traffic stream composition? Are they different by direction, e.g ., due to the required lane shift in one direction? o Travel speeds through the work zone Are they related to, or independent of, posted speed limits? PAGE 74 74 Are they different by direction due to the lane crossover at the beginning of the work zone? Son (1 994) states from their literature review that vehicles in the bloc ked travel direction usually have lower speeds than the opposite direction. o Startup lost time What are typical values? Are they different by direction? o Flagging methods Is a gapout strategy ever applied, and if so, how? Is a maximum green time used, and if so, what value? Is a green time extension used, and if so, what value? The calculation procedure and models in this thesis assume a constant speed through the work zone. It is not uncommon, however, for there to be localized reductions in speed within the lane clos ure area, such as where a paving machine may be working. Currently, there is a basic capability fo r examining this within the simulation program, but field data and potentially input from construction contractors would help to make this f eature more robust and accurate. With an improvement to this feature within the simulation program, the simulation program can then be used to enhance the analytical procedure. Development of an optimal flagging strategy o While there may be some structure to the rightofway changing methods employed by flaggers, informal obser vation suggests that there is a considerable amount of randomness that gets introduced into the cyclebycycle timings. Thus, it would appear th at there is room for improvement in the timing guidance that is offered to flaggers, which would ultimately lead to more consistent and efficient rightofway changes. o As mentioned previously, it was beyond the scope of this project to explore a flagging strategy, or strategies, that would lead to minimal levels of delay and queuing for a given work zone conf iguration. While there are certainly improvements that could be made under an automated control situation, the challenge, of course, is finding an im proved method that can actually be implemented with a manual flagging method. Nonetheless, it is believed that there are strategies that could be developed that could be reasonably employed by human flaggers that will reduce delays and queue lengths. PAGE 75 75 APPENDIX SUMMARY OUTPUT FILE Figure A1: Sample of th e Summary Output File PAGE 76 76 REFERENCES AASHTO (American Association of State Highway and Transportation Officials). A Policy on Geometric Design of Highways and Streets. 4th ed., Washington, D.C., 2001. Arguea, D.F. (2006). A Simulation Based Appro ach to Estimate Capacity of a Temporary Freeway Work Zone Lane Closure. Mast ers Thesis, University of Florida. Cassidy, M. J and Han, L. D. (1993). A Proposed model for Prediction Motorist Delays at TwoLane Highway Work Zones. ASCE Journal of Transportation Engineering Vol. 119., No 1 Jan/Feb. 2742. Cassidy, M. J. and Son, Y. T. (1994). Predicting Traffic Impacts at TwoLane Highway Work Zones Final Report. Indiana De partment of Transportation. Cassidy, M.J., Son, Y.T. and Rosowsky, D. V. (1993) Prediction Vehicle Delay During Maintenance or Reconstruction Ac tivity on TwoLane Highways. Final Report No. CETRA931, Purdue University, West Lafayette, Indiana. Ceder, A. and Regueros, A. (1993). Traffic Control (at Alternate On eWay Sections) during Lane Closure Periods of a TwoWay highway. Proc., 11th International Symposium on Transportation and Traffic Theory, Elsevier Publishing, Cohen, Stephen, L. (2002). Application of CarFollowing Systems in Microscopic TimeScan Simulation Models. Journal of the Transportation Research Board TRR 1802, 239247. Cohen, Stephen, L. (2002). Application of CarFollowing Systems to Queue Discharge Problem at Signalized Intersections. Journal of the Transportation Research Board TRR 1802, 205213. DeGuzman W.C., et al. (2004) Lane Closure Analysis. Colorado Dept of Transportation., Denver, CO. Evans, A. (2006). Personal Email. Florida Transportation Technology Transfer Center. Florida Dept of Transportation. (2006) Plans Preparation Manual, Volume I. Institute of Transportation Engineers (ITE). Traffic Engineering Handbook. 5th Edition. Washington, D.C., 1999. Mannering, F.L., Kilareski, W.P., Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis 3rd ed. John Wiley & Sons, Inc, New York, NY. Microsoft Language Library, March 25, 2007. http://msdn2.microsoft.com/enus/library/f7s023d2(VS.80).aspx. PAGE 77 77 Newell, G.F. (1969). Properties of Vehicl eActuated Signals: I. Oneway Street. Transportation Science Vol. #3, 3051. Press W.H., et al. (1994). Numeri cal Recipes in C, the Art of Scientific Computing, Second Edition. Cambridge University Press, New York, NY. 288290 QuickZone Delay Estimation Program, Versi on 2.0, USER GUIDE, prepared for FHWA Rakha H. and Lucic I. (2002). Variable Po wer Vehicle Dynamics Model for Estimating Maximum Truck Acceleration Levels. Journal of Transportation Engineering, Vol. 128(5), Sept /Oct. pp. 412419 Son, Y. T. (1994). Stochastic Modeling of Vehi cle Delay at twolane highway work zones. Doctoral Dissertation, Purdue University. Transportation Research Board (TRB), Highway Capacity Manual, National Research Council, Washington, D.C., 2000. U.S. Federal Highway Administration, Manual on Uniform Traffic Control Devices for Streets and Highways U.S. Government Printing Office., Washington, DC, 2003. Washburn, S.S. and CruzCasas, C. (2007). Im pact of Trucks on Arterial LOS and Freeway Work Zone Capacity. Final Report BD54551. Florida Department of Transportation. Tallahassee, FL. PAGE 78 78 BIOGRAPHICAL SKETCH Thomas Hiles was born November 22, 1983, in Independence, Missouri. The younger of two children grew up in Odessa, Missouri, wh ich is about 30 miles east of Kansas City, Missouri. He graduated from Odessa High School in 2002. Hiles earned his B.S. in civil and environmental engineering from the University of Missouri in 2006. Hiles enrolled in the masters program to further his knowledg e in traffic engineering. Before joining the program, he received a Y oung Member position on the Access Management Committee of the Transportation Research Board. Upon graduation, he will assume a position with HDR Inc, in Kansas City, Missouri. Soon after graduation, he will be wed to Catherine Shelley. 