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PAGE 1 1 IMPACT OF LEFT TURN SPILLOVER ON THROUGH MOVEMENT DISCHARGE AT SIGNALIZED INTERSECTIONS By ABIGAIL OSEI ASAMOAH A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREM ENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2009 PAGE 2 2 2009 Abigail Osei Asamoah PAGE 3 3 To My Family PAGE 4 4 ACKNOWLEDGMENTS I would like to thank my faculty advisors, Dr. Scott Washburn, Dr. Yafeng Yin, and my committee member ; Dr. Lily Elefteriadou for their guidance and direction. I would also like to thank my entire family for their continuous support t h roughout my graduate work. Lastly I would like to express my gratitude to the Ministry of Tran sportation of Ghana for their support. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 ABSTRACT ................................ ................................ ................................ ................................ ..... 9 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 10 Background ................................ ................................ ................................ ............................. 10 Problem Statement ................................ ................................ ................................ .................. 10 Obj ective and Tasks ................................ ................................ ................................ ................ 11 Document Organization ................................ ................................ ................................ .......... 11 2 LITERATURE REVIEW ................................ ................................ ................................ ....... 13 Introduction ................................ ................................ ................................ ............................. 13 Current Analysis Procedures ................................ ................................ ................................ .. 13 Queue Length Model Comparisons ................................ ................................ ........................ 15 Simulation Studies ................................ ................................ ................................ .................. 16 Analytical and Probabilistic Methods ................................ ................................ ..................... 17 Summary of Literature Review ................................ ................................ .............................. 23 3 RESEARCH APPROACH ................................ ................................ ................................ ..... 24 Introduction ................................ ................................ ................................ ............................. 24 Methodological Approach ................................ ................................ ................................ ...... 24 Selection of Simulation Tool ................................ ................................ ................................ .. 25 Testing the Operation of CORSIM ................................ ................................ ......................... 25 Left Tur n Storage Length ................................ ................................ ................................ 26 Left Turn Phasing Sequence ................................ ................................ ............................ 27 Left Turn Percentage ................................ ................................ ................................ ....... 28 Heavy Vehicle Percentage ................................ ................................ ............................... 28 Number of Through Lanes ................................ ................................ .............................. 29 Identification of Significant Factors ................................ ................................ ....................... 29 Experimental Design ................................ ................................ ................................ .............. 31 Selection of Variables ................................ ................................ ................................ ...... 31 Variable Levels ................................ ................................ ................................ ................ 32 Number of Replications ................................ ................................ ................................ ... 32 Network Configuration for Experimental Design ................................ ................................ .. 33 4 MODEL DEVELOPMENT AND ANALYSIS ................................ ................................ ..... 41 Introduction ................................ ................................ ................................ ............................. 41 Model Development ................................ ................................ ................................ ............... 41 PAGE 6 6 Single Through Lane Model ................................ ................................ ............................ 41 Multiple Through Lane Model ................................ ................................ ........................ 42 Model Application and Comparisons with Simulation Results ................................ .............. 43 Sample Calculations for the Single Through Lane Model ................................ .............. 43 Sample Calculation for the Multiple Through Lanes Model ................................ ........... 44 Comparison of Reductions in Through Vehicle Discharge as Predicted By Single Through Lane and Multiple Through Lane Models ................................ ............................ 45 Sample Calculations for Single Through Lane Model Reduction ................................ ... 46 Sample Calculations for Multiple Through Lane Model Reduction ............................... 47 Guidelines for Appl ication of Model ................................ ................................ ...................... 48 5 CONCLUSIONS AND RECOMMENDATIONS ................................ ................................ 54 Summary ................................ ................................ ................................ ................................ 54 Conclusions ................................ ................................ ................................ ............................. 54 Recommendations for Further Research ................................ ................................ ................ 54 APPENDIX A EXPERIMENTAL DESIGN COMBINATIONS ................................ ................................ .. 56 REFERENCES ................................ ................................ ................................ .............................. 62 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ......... 63 PAGE 7 7 LIST OF TABLES Table page 3 1 Settings coded into experimental network ................................ ................................ ......... 39 3 2 Summary of inputs and results for left turn phasing sequence experiment ....................... 40 3 3 Factor levels for experimental design ................................ ................................ ................ 40 3 4 Signal settings used specified in simulation tool for experimental design ........................ 40 4 1 Summary of Single through lane model parameters ................................ .......................... 51 4 2 Summary of Multiple through lane model parameters ................................ ...................... 52 4 3 Values of parameters used in sample calculations for single through lane approach model ................................ ................................ ................................ ................................ .. 52 4 4 Comparison of sample single through lane model predictions with simulation results .... 52 4 5 Values of parameters used in sample calculations for multiple through lanes model ....... 53 4 6 Comparison of sample multiple through lane s model predictions with simulation results ................................ ................................ ................................ ................................ 53 4 7 Summary of inputs used in sample calculations for through discharge reduction model comparisons ................................ ................................ ................................ ............ 53 4 8 Comparison of reduction in through discharge rates for both models ............................... 53 A 1 Experimental design combinations for single through lane experiment ............................ 56 A 2 Experimental design combinations for multiple through lanes experiment ...................... 58 PAGE 8 8 LIST OF FIGURES Figure page 3 1 Relationship between left turn storage and through vehicle discharge rate ....................... 35 3 2 Relationship between left turn percent and through vehicle discharge rate ...................... 36 3 3 Relationship between heavy vehicle percent and through discharge rate .......................... 37 3 4 Relationship of through discharge rate to number of approaching through lanes ............. 38 3 5 Screen shot of CORSIM output processor settings ................................ ............................ 39 4 1 Comparison of simulation and model estimation results for single through lane model ................................ ................................ ................................ ................................ .. 49 4 2 Comparison of simulation and model estimation results for multiple through lanes model ................................ ................................ ................................ ................................ .. 50 PAGE 9 9 Abstract of Thesis Presented to the Gradua te School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science IMPACT OF LEFT TURN SPILLOVER ON THROUGH MOVEMENT DISCHARGE AT SIGNALIZED INTERSECTIONS By Ab igail Osei Asamoah May 2009 Chair: Scott S. Washburn Major: Civil Engineering Signalized intersections are arguably the most critical components of an arterial. One of the major factors that affect the capacity of a signalized intersection is the presence of left turning vehicles. Intersections that allow left turns usually have a left turn bay to accommodate a certain amount of queuing. However, it is common to see the storage of a left turn bay at a busy intersection exc eeded during the peak periods. When this happens, the left t urning vehicles will spill over into the adjacent through lane and potentially reduce the discharge rate of through vehicles. The current Highway Capacity Manual (HCM) analysis procedure for signalized intersection operations does not explicitly account fo r left turn bay spillover; thus, the assumption is that the through movement is unimpeded during the green p hase of the through movement. For situations where left turn spillover is prevalent, this can lead to overly optimistic estimates of signal delay fo r the through movement. This study developed predictive models for through movement discharge that consider the effects of left turn traffic, phasing, and geometry, in addition to the thr ough movement characteristics. Therefore, potential left turn spillov er conditions are explicitly accounted for in the developed models. Simulation was used to generate the data on which the model development was based. PAGE 10 10 CHAPTER 1 INTRODUCTION Background Signalized intersections are arguably the most critical components of an arterial. They can be a major source of delay on the arterial. This Highway Capacity Manual 2000 prescribes intersection delay (also referred to as control delay) as the service measure for signalized intersection s; that is the performance measure upon which level of service is based. Effective traffic operations at a signalized intersection improve delay conditions and ultimately the level of service of the intersection. Left turn operations and their treatment are very important at a signalized inter section. Where left turn demand is very high, a separate phase is usually created for the left turning vehicles in the signal timing plan in addition to an exclusive left turn lane. These left turn lanes are usually shorter than the through lanes and are r eferred to as bays. If the length of the left turn bay and phase timing are appropriate for the traffic conditions, there will be no adverse impact to through traffic operations (disregarding tradeoffs in green time due to adding a phase). A common occurr ence usually during the peak period however is when left turn volumes are significantly high left turning vehicles spillover from the left turn bay to the adjacent through lane as a result of inadequate signal timing and/or storage bay length. This situat ion can result in a reduction of the through vehicle discharge rate. Problem Statement The HCM traffic operations analysis procedure for signalized intersection s assumes that t hr ough traffic is not impeded by turning movements. However, in urban settings, congestion is the norm and the probability of left turning traffic spilling over from turn lanes and into the adjacent t hr ough lanes can occur frequently during the peak period. When the left turn traffic PAGE 11 11 spills over into the t hr ough lane, the discharge ra te of the t hr ough lane is often reduced. If the HCM methodology is used for an analysis under these conditions, the results will be overly optimistic in the estimation of capacity and delay at the signalized intersection. It is therefore necessary to deter mine the factors that significantly affect left turn spillover and how these factors affect the discharge rate of the adjacent through lane(s). Objective and Tasks Our primary objective was to determine the factors that significantly affect left turn lane spillover and develop a model, or models, to predict the expected t hr ough movement discharge rate as a function of this spillover. This objective was accomplished t hr ough the following supporting tasks: Conduct a literature review Perform simple tests in t he selected simulation tool to ensure the results were reliable Develop and execute a simulation experimental design based on the identified significant variables Analyze the simulation data and develop the model(s) Document Organization Chapter 2 presents an overview of relevant studies found in literature. This review looks at the various methods proposed in the literature for identifying factors that significantly affect left turn spillover, determining the probability of a left turn spillover and the ef fect of the spillover on the discharge rate of the adjacent through lane(s). Chapter 3 describes the research approach that was used to accomplish the objectives of this study. This chapter presents the tests of variables that significantly affect left tur n spillover, and the development and execution of an experimental design of these significant variables in a simulation tool. Chapter 4 presents the development of models that predict through vehicle PAGE 12 12 discharge based on roadway, traffic, and control charact eristics of the intersection approach. Chapter 5 presents a summary of this study, conclusions drawn and recommendations for further study PAGE 13 13 CHAPTER 2 LITERATURE REVIEW Introduction This chapter provides an overview of previous studies and methodologies that deal with left turn spillover. While a number of studies have been done on signalized intersections and their operation, only a limited number of them deal explicitly with the effect of left turn spill over on through lane discharge rate. Most previo us studies on left turn spillover focus on the determination of storage lengths of left turn lanes to prevent left turn spillover. A few studies deal with the complimentary issue of left turn lane blockage due to through lane spillback. Some studies also i nvolve determining the probability of the occurrence of left turn lane spillover and determination of capacity of the through lane based on this probability. Current Analysis Procedures The HCM (2000) does provide a separate procedure in appendix G of the signalized intersection analysis methodology to calculate the back of queue. The HCM (2000) defines the vehicles and on the number of vehicles that do not clea r the intersection during the green phase (overflow) The back of queue calculation comprises of two terms; Q 1 ; defined as the first term queued vehicles and Q 2 ; defined as the second termed queued vehicles. This first term queued vehicles Q 1 calcula ted using Equation 2 1 [2 1] Where Q 1 = first term queued vehicles (veh) PAGE 14 14 PF 2 = adjustment factor for effects of progression v L = lane group flow rate per lane (veh/h) C = cycle length (s) g = effective green time (s) X L = ratio of flow rate to capacity (v L / c L ratio) Q 1 is calculated using Equation 2 2 [2 2] Where Q 2 = second term of queued vehicles, estimate for average overflow queue (veh) c L = lane group capacity per lane (veh/h) T = le ngth of analysis period (h) X L = v L / c L ratio k B = second term adjustment f actor related to early arrivals Q bL = initial queue at sta rt of analysis period (veh) C = cycle length (s) From these, the average back of queue can be determined as the sum of the t erms; Q 1 and Q 2 .The back of queue measure is specified as useful for dealing with the blockage of available queue storage distance determined from the queue storage ratio; which is defined as the ratio of estimated queue length to the available storage spa ce. The queue storage ratio uses the back of queue, queued vehicle spacing and available storage to determine if blockage will occur. The queue storage ratio is calculated using Equation 2 3.Blockage is defined to occur when this queue storage ratio equals or exceeds a value of 1. [2 3] Where Q R = average queue storage ratio L H = average queue spa cing in a stationary queue (ft) L a = available queue storage distance (ft) Q = average nu mber of vehicles in queue (veh) PAGE 15 15 Although this proc edure exists to compute the queue storage ratio, the results are not directly incorporated into the HCM signal analysis methodology. Furthermore, even though an analyst can use this calculation procedure to determine if through lane blockage may occur due to spillover, the HCM offers no guidance on how to determine the subsequent quantitative impact to the through movement discharge rate of the adjacent through lane(s). Queue Length Mode l Comparisons Viloria et al. (2000) compared queue length models. Queue length m odels from the following traffic analysis methodologies or programs were included in the study: SIDRA, NETSIM, TRANSYT 7F, SOAP, SIGNAL 97, HCM 2000, NC HR method queuing criteria A classification framework was developed for models from the above programs /methodologies and their behavior compared to that of the HCM 2000 queue model. The scope of analysis was limited to under saturated conditions. A queue reach measure was defined in the study as a measure t o determine adequacy of storage at the intersection. Some models were identified to predict the probability that the maximum queue reach will exceed the maximum storage requirements. Older queue models applied a constant of 2 as a factor of safety to accou nt for the combination of factors that cause the queue to exceed its average length on some cycles causing overflow. M ore complex model s dealt with overflow and assigned an explicit confidence percentile to a stochastic adjustment factor. Of the models co mpared; NETSIM was the only model found to deal explicitly with effects of queue storage spillover on movement of traffic on adjacent lanes. Analytical models /methodologies just computed queue length, whereas NETSIM is a microscopic simulation tool that ac counts for spillover through the vehicle movement modeling. NETSIM unlike the analytical models defined its queue length as queue accumulation and not queue reach. PAGE 16 16 Regression te chniques were used to establish; the type of relation and reliability between p roposed HCM queue models and the other queue models. Queue estimates generated by each model were plotted against the HCM average back of queue, 90th and 98th percentile, queue confidence levels. The HCM 2000 model and SIDRA provided higher queue length v alues than most of the other models because some models reported only the average values and applied no extension factor. Average values from other models before expansion (adjustment to account for the effect of overflow) did not reflect the possibility o f overflow from previous cycles. Simulation Studies Messer and Fambro (1977) investigated the effect of signal phasing and length of left turn bay on signal capacity and delay Traffic operations were simulated on only one intersection approach with a prot ected left turn lane and an adjacent t hr ough lane. For their study of delay, t wo signal phasing arrangements were used in their simulation program; leading and lagging phase sequences Two different cycle lengths of 60 s and 80 s were used in the study. T heir results showed that leading and lagging phase sequences performed better for short bay lengths. Results of their simulation showed that delay increased with increasing volume, nominal saturation ratio (defined as the ratio of the normal demand of the movement to the phase capacity when the left turn storage is enough to prevent blockages) and cycle length. Delay also increased as the length of the bay decreased Lagging left turn operations resulted in a slightly reduced delay for the conditions studi ed. For left turn capacity investigations, two additional phase sequences were added; dual leading lefts and dual lagging lefts. Greater reductions in capacity occurred at higher volumes. Reductions in capacity also varied with the percentage of traffic t urning left and the green splits for the left turn and t hr ough movements. PAGE 17 17 Left turn bay lengths were also determined from a modified P ois s on approach. Design lengths of left turn lanes were provided based on results of the study Oppenlander and Oppenland er (1994) developed a Monte Carlo Simulation model for determining the design lengths of left turn lanes with separate control. This simulation model was designed to model the interaction of vehicles arriving at the signalized intersection the signal oper ation and the movement of vehicle t hr ough the intersection. Queue lengths over commonly observed ranges of left turn volumes (50 to 400 veh/h, 50 veh/h intervals) green times (10 to 30 s, 5 s intervals ) and cycle lengths (60 to 120 s, 15 s intervals) were generated using the model. Vehicle arrivals were modeled according to a Poisson relationship A total of 1000 signal cycles were simulated in the model for a single set of design parameters to produce queue length distributions. D esign tables were develo ped to indicate the 50th, 85th and 95th percentile queue lengths for left turns with separate phases, at intersections with different left turn volumes, cycle lengths and left turn green times. The 85 th and 95 th percentiles were specified to minimize the possibility of traffic demand exceeding storage requirements of the left turn lane. The 50th percentile queue length provide d a median point for the designer. Design storage lengths were to be sized in accordance with local design vehicles. Analytical and Probabilistic Methods Kikuchi et al. (1993) developed a probabilistic model for determination of lengths of left turn lanes at signalized intersections based on left turn overflow into t hr ough lanes and blockage of the entrance into the left turn lane by the queued adjacent through vehicles Left turn o verflow was determined to be dependent on left turn volume, the protected phase duration, cycle length, opposing t hr ough volume and layout of the intersection; factors that affect the PAGE 18 18 arrival and the serv ice rate o f the left turning vehicles. Left turn blockage, problem however was determined to be dependent on the t hr ough vehicle volume and t hr ough red time. Models for computing the probabilities of lane overflow and blockage were developed. A threshold probability defined as the tolerable frequency of occurrence of both problems was specified for both cases Selection of this threshold value depended on a number of factors including economic, capacity, safety, and site specific conditions. This thresho ld affected the necessary length of left turn lanes. Other factors affecting the length of left turn lanes were traffic volumes, vehicle mix, signal timing, time required to make a left turn and the space required for a stationary vehicle. The required le N from the lane overflow perspective were determined by Equation 2 4 [2 4 ] Where N = number of vehicles in left turn lane i = steady state probability of a given queue existing in left turn l ane i = t hr eshold probability Left t N** were determined from Equation 2 5 [2 5] Where P B (N ) = probability of blockage when left turn storage length is suffici ent to store at most N v ehicles i = threshold probability Lane lengths determined from the blockage perspective usually had longer lengths than those determined from Equation 2 6 [2 6] PAGE 19 19 Kikuchi et al. (2004 ) employed a probabilistic approach for determining the lengths of dual left turn lanes (DLTL) Lengths of the left turn lanes were determined based on two main considerations; first, minimizing the probability of ov erflow of left turning vehicles into adjacent t hr ough lanes and second, minimizing the chance of queued t hr ough vehicles blocking the entrance to left turn lanes. T he arrival patterns of left turning vehicles and t hr ough vehicle s were directly related to t he event of overflow and blockage of entrance to the dual left turn lane as determined from surveys on lane selection in dual left turn lanes A t hr eshold probability was specified and defined in their approach as; the minimum value of probability that all the arriving vehicles can enter the dual left turn lanes without spillover or blockage. Other factors considered included, signal timing and vehicle mix Vehicle arrivals The probability of all left turnin g vehicles arriving during the red phase entering the dual left turn lanes without blockage or spillover was determined as a function of the length of left turn lanes and the average arrival rate of the left turning vehicles and through vehicles. T he abov e probability increased with the length of left turn lane. It was also a function of the duration of the red phase for the left turning and t hr ough vehicles. Shorter red left turn phases resulted in an increase in the probability of all left turning vehic les entering the dual left turn lanes without spillover Also the probability of the queued t hr ough vehicles blocking the left turn lanes decreased with an increase in the number of lanes. The required lengths of left turn lanes were determined as the leng th for which this probability that all arriving vehicles can enter the DLTL without blockage or spillover is greater than the t hr eshold value. Adequate lengths of the DLTL was also to take into account volume distribution among the DLTL and adjacent throug h lane and the vehicle mix. PAGE 20 20 Zhang and Tong (2007) developed models for left turn and through movement capacity that account for the effects of left turn bay length and signal tim ing strategy on the intersection capacity and signal operation investigated. T he capacity models incorporate a term that represents the probability of blockage (of t he left turn or through lane(s) The physical length of the left turn bay was denoted N but it was found from field observation that an additional two veh icles could enter the left turn lane before the lane was completely blocked by through vehicles. The blockage by a t hr ough vehicle wa s determined to be equi valent the arrival of the (N+2 ) th vehicle on the adjacent t hr ough lane at the start of the red inte rval. The probability of left turn blockage by through traffic was calculated by Equation 2 7 [2 7] Where P B = probability of blockage X TH = number of through arrivals within the cycle at the intersection (veh) X LT = number of lef t turn vehicle in the bay when blockage occurs (veh) P = Probability N = length of left turn bay (veh) Similarly the probability of Left turn spillover is determined from Equation 2 8 [2 8] Where Ps = probability of spillover and the rest of the terms are defined the same as in Equation 2 7. Left turn capacity determined from the probability of blockage and is calculated using Equation 2 9 [2 9 ] Where c PROTECTED = c apacity of protected left turn(veh/h) n = number of cycles in peak hour at designated intersection C = cycle length (s) PAGE 21 21 S LT = saturation flow rate for protected left turn movement (veh/hg/ln) g LT = effective green interval for protected left turn movement (s) and the rest of the terms are as def ined in Equation 2 7 The adjacent through capacity model was developed assuming a lagging left turn phase operation The probability of left turn spill over was defined to be the event of (N+3) left turn vehicle arrivals with no blockage of left turn vehic les occurring after the start of the t hr ough red interval. Thr ough capacity was estimated from the probability of spillover using Equation 2 10. [2 10 ] Where c T HR OUGH = t hr ough lane capacity (veh/h) N LN = the number of t hr ough lane s on the approach g TH = effective t hr ough green interval (s) S TH = t hr ough movement saturation flow rate (veh/hg/ln) C = cycle Length (s) n = number of cycles in peak hour and the remaining terms are defined as in Equation. 2 9 Kikuchi et al. (200 7 ) used a probabilistic approach to determine the lengths of turn lanes, when a single lane approaches a signalized intersection and splits into a left, right and through lane. Probabilities of lane overflow and lane entrance blockag e are computed. Probabilities o f lane overflow and lane blockage are a function of the arriving volume, sequences of the movements during the red phase and length of turn lanes. Lengths of turn lanes were determined by volumes of vehicles for the turn lanes and vehicles wishing to move to other lanes due to the possibility of lane entrance blockage. The probabilities that vehicles arriving at the intersection toward the end of the red phase will not experience lane overflow or lane entrance blockage (acceptable conditions), were derived based on the pattern of arrivals at the end of the red signal phase. The following conditions were identified as possible outcomes at the end of the red signal phase: PAGE 22 22 The entrance to the desired lane is blocked so that vehicle s cannot enter lane. The entr ance to the desired lane is not blocked and not overflowed. The entrance to the desired lane is overflowed by vehicles having the same destination lanes as the arriving vehicle. The entrance to the desired lane is overflowed by vehicles having different de stin ation lanes as the arriving vehicle. The required length of turn lanes is the length for which th ese probabilit ies are greater than a specified t h reshold value. Charts were provided for lane lengths computed in distance and units of vehicle s for differ ent threshold probabilities. Qi et al. (2007) developed a method for estimating left turn lane storage lengths lanes at signalized intersections. The length of the left turn queue is estimated based on vehicle arrivals during the red phase and residual que ues from previous cycles. Residual queues were analyzed based on discrete time M arkov chains. Factors taken in to account included opposing traffic volume, cycle length, phasing, vehicle mix length of the lef t turn queue during the red phase was determined based on the probability of arrivals during the red phase; using a Poisson approach and is given by Eq uation 2 11 [2 11] Where A R = arrivals in the red phase Q R = maximum queue lengt h during red phase (veh) N = number of left turn arrivals in red phase (veh) t = average arrival rate of left turn vehicle (veh) R = duration of red phase (s) 1 = desired probability level The residual queue at the length of the green phase is given by Equation 2 12 [2 12] PAGE 23 23 Where N O = number of left over veh icles Q L = maximum left over queue length (veh) i 2 = desired probability level The required storage length in units of vehicles is determined as the sum of Q R and Q L Summary o f Literature Review A comprehensive literature search was conducted in an effort to identify previous studies that examined the issue of left turn spillover and its effect on through movement discharge. Nearly all of the studies found are focused only on queue length estimation, the probability of spillover, and/or the determination of appropriate left turn storage lengths. Only one study examined the impact of left turn lane spillover on through movement discharge. This study, however, still had limita tio ns. For example, it only considers the much less common phasing situation of a lagging left turn and estimates just the capacity due to spillover (through movement discharge can still be reduced even if the demand is less than capacity). PAGE 24 24 CHAPTER 3 RESEARC H APPROACH Introduction This chapter describes the approach taken to achieve the objectives of this study. It provides a detailed discussion of the variables identified that significantly affect the likelihood of left turn lane spillover, tests performed in the simulation tool to verify its reliability and the development and execution of a simulation experimental design. Methodolog ical Approach As learned from the literature review, t hree main methodologies have been used in studies of left turn spillove r. The first approach involve s various methods proposed for estimating and adjusting queue length models to account for left turn spillover. The second methodological approach involves the use of simulation to analyze operations at signalized intersections with left turn bays and determining relationships between left turn spillover and elements of the signalized arterial, mainly geometric elements like left turn bay length These studies then, estimate required lengths of left turn bays to prevent left tur n spillover The last approach used involves determining the probability of left turn spillover and determining required storage lengths to prevent spillover based on these probabilities and in one study, determination of the resulting through lane capacit y when left turn spillover happens Ideally, for a study such as this, an extensive amount of field data would be collected to base the model development upon. However, the time and cost requirements for this kind of data collection effort are extremely hi gh. Furthermore, with the capabilities of current simulation tools, it was expected that good results could be obtained using simulation data as a surrogate for field data. Simulation was therefore used to generate the required data for this study. The met hodological approach taken was to develop models for through vehicle discharge rate, as a PAGE 25 25 function of traffic, roadway, and control factors for a signalized intersection approach, using regression analysis. The remainder of this chapter discusses the sele cted simulation tool, the variables selected for inclusion in the experimental design and the development of the experimental design. Selection of Simulation Tool Several publicly available software programs are capable of simulating signalized arterial o perations. For this project, the simulation program needed to be capable of simulating vehicle movements at the microscopic level (due to sensitivities with spillover conditions), allow for modification to a number of traffic flow parameters (such as queue discharge rate), have an animation viewing utility (to allow for visual verification of the simulation operation), and provide for efficient extraction of the pertinent performance measures One simulation tool that met these criteria i s CORSIM (CORridor S IMulation). This tool has previously undergone a tremendous amount of testing and validation and is generally recognized as a reliable simulation program with excellent modeling capabilities. The scripting capability for multiple runs and the comprehensive output processor provide for more efficient simulation runs and data processing th an many other simulation tools. Additionally, the research team had direct access to the individuals that support and maintain CORSIM; thus, if any questions or issues were identified, they could be quickly resolved Testing the Operation of CORSIM Despite all the previous studies that have used CORSIM, some basic tests were still conducted to make sure that it was functioning as expected and that its results could be conside red as reliable. These tests involved identifying the relationships between key variables and left turn spillover (and the corresponding through movement discharge rate). To perform these basic tests, an experimental signalized network was coded in CORSIM, with four PAGE 26 26 approaches. All approaches had one through lane and one exclusive left turn lane, except in the case of the number of lanes test. The length of each approach was specifie d as 3000 ft., traffic arrivals were specified to be Erlang distributed wit h a parameter value of 1 (i.e., negative exponential headways). Simulations were run for one, 3600 s (1 h) time period with sixty 60 s time intervals. The signal phasing for the left turns at the intersection were specified as lagging for the westbound an d eastbound approaches and leading for the northbound and southbound approaches (but this was altered in the left turn phasing sequence test) No right turns were included in the approach flow rates. Signal timings were determined based on the proportions of through and left turn traffic volumes. The traffic stream was composed of only passenger cars for all the variables investigated except in the case of the heavy vehicle composition test. Table 3 1 gives the various parameters and settings of the signal ized intersection that was coded for the experimental network V ehicle length of 25 ft was specified in all tests with the exception of the h eavy v ehicle percentage experiment. The performance measure of interest was the through vehicle discharge rate. The output processor was specified to extract this performance measure for the north bound and south bound approaches. Each of the individual numerical results represents an average of 50 replications The individual tests and results are now described. Left T urn S torage L ength In this test, a left turn percentage of 1 5 % of a total approaching vehicular flow rate of 1600 veh/h was specified in CORSIM and kept constant during the simulation process. A cycle length of 120 s with through green time of 80 s and le ft turn green time of 10 s was specified. The length of the left turn bay was varied, at 50 ft increments with a minimum of 0 ft and a maximum PAGE 27 27 of 1000 ft. The storage lengths were plotted against the t hr ough vehicle discharge rate s extracted from the simul ation results (Figure 3 1 ) A s the storage length of the left turn lane increases, the through movement discharge rate increases sharply until a bay length of about 200 ft (Figure 3 1) with longer storage lengths resulting in modest increases in the disch arge flow rate, until this rate equals the unimpeded capacity of the through lane (1200 veh/h/ln). L eft T urn P hasing Sequence The effect of left turn phasing sequence ( leading versus lagging ) on through vehicle discharge was investigated. In this test, fo ur different combinations of left turn green time, through green time, cycle length, and approach flow rate were run. E ach of the four different variable combinations was run with leading left turn phasing and then lagging left turn phasing Left turn bay lengths were specified as 125 ft while left turn percentage was specified as 15% for all scenarios tested Signal settings and approach flow rates specified are summarized in Table 3 2. The results of the experiment are also shown in T able 3 2 Although t he difference is generally small, lagging left turn phasing generally resulted in slightly lower through vehicle discharge rates than leading left turn phasing. Initially, it was hypothesized that the left turn phasing sequence might be a significant facto r to through movement discharge rate, but this was mostly from the perspective of tre ating each cycle independently. When considering a series of cycles, as would happen over an extended analysis period, cycles are not independent and an oscillating condit ion between spillove r and spillback tends to occur. Thus, the issue of whether the left turn movement goes before or after the adjacent through movement essentially becomes irrelevant. The small difference in the results (Table 3 2) from this test appear t o be largely influenced by the first cycle during the simulation, where the left turn spillover prevents discharge of the through vehicles since the through PAGE 28 28 movement phase occ urs before the left turn phase. After the first cycle, it is expected that the di fference in through movement discharge rate between leading and lagging left tu rn phasing would be negligible. Thus, this variable was dropped from further consideration in this study. Left T urn P ercentage This test was performed t o investigate t he relatio nship between the percentage of left turn volume and the through vehicle disc harge rate when left turn spill over happens. A total approaching flow rate of 800 veh/h was specified. S ignal settings were determined based on the volume split between left turns and t hr ough vehicles. L eft turn storage l ength s w ere varied in relation to the percentage of left turns. L eft turn percentage was then varied at increments of 5% with a minimum value of 5 % and a maximum value of 20 % Signal timing s and the length of the l eft turn bay were updated for each in c rement of left turn percentage. Through vehicle discharge rate was plotted against the left turn composition at each increment and is shown in Figure 3 2 It was hypothesized, that an increase in the left turn percenta ge with all being equal would increase the probability of spillover and hence reduce the through movement discharge rate. For this experiment however, other variables; left turn bay length, through green time left turn green time, and cycle length were va ried for each increment in left turn percentage to capture variance Left turn percentage ha d interactions with these variables used in the experiment leading to the resulting relationship (Figure 3 2). Heavy V ehicle Percentage This test was performed by c oding the isolated signalized intersection with a total approach ing flow rate of 1600 veh/h a left turn percentage of 15% and a left turn bay length of 250 ft The heavy vehicle percentage of the traffic stream was varied by 5% increments with a minimum v alue of 0 % and a maximum value of 20 % The type of heavy vehicle was specified to PAGE 29 29 be a medium truck; 35 ft in length. The relationship between t hr ough movement discharge rate and the heavy vehicle percentage is shown in F igure 3 3 As the composition of he avy vehicles in the traffic stream increases, the through vehicle discharge rate decreases ( Figure 3 3) Heavy vehicles are longer than passenger cars and fill up the left turn bay faster and thereby increase the likelihood of left turn queues spilling ove r to the adjacent through lane, thereby causing a reduction in through vehicle discharge. Number of Through L anes To perform the test of the effect of the number of through lanes on left turn spillover and hence through lane discharge rate a n average app roach flow rate of 1600 veh/h was specified ,with a left turn percentage of 1 5 % of the average approaching flow rate Left turn storage length was specified to be 250 f t .Signal settings were specified to be 10 s left turn green time and 80 s through green time with a cycle length of 120 s The number of through lanes was varied at increments of 1 with a minimum value of 1 and a maximum value of 3. Through vehicle discharge rates were extracted from the output processor Results of this test showing the rel ationship between the number of through lane at the approach of the intersection and through vehicle discharge rate are shown in Figure 3 4. The through vehicle discharge rate increases with increasing number of approaching through lanes (Figure 3 4) This is consistent with expectations that, through vehicles will avoid queues from left turn spillover by weaving around them if there are multiple through lanes, and hence reduce the impact of left turn spillover to through movement discharge rates. Identifi cation of Significant Factors A number of variables were considered for their potential impact on the probability of left turn bay spillover. T hr ough a combination of simulation testing and theoretical relationships, the PAGE 30 30 following variables were identified as having a significant effect on left turn spillover. The general relationship of these variables to the probability of spillover is also described : Left turn storage length: The length of the left turn bay determines its storage capacity. As the length of the left turn bay increases, the more left turning vehicles the bay can hold; thus, reducing the probability of spillover. As the length of the left turn bay approaches the maximum number of queued left turn vehicles expected during any one cycle, the maximum possible t hr ough movement discharge rate approaches that of the unimpeded capacity of the t hr ough movement. Percentage of left turns : All else being equal, the higher the proportion of left turning vehicles in the volume approaching the intersecti on, the higher the likelihood of spillover. Number of approaching t hr ough lanes : A s the number of through lanes increases, the less impact spillover conditions will have on through movement discharge rate due to the ability of through vehicles to move over into lanes further to the right or weave around the spillover condition Left turn green time : For a given cycle length, more left turn green time translates to less red time for the movement and thus less time for left turn vehicles to queue reducing the probability of spillover. T hr ough green time : For a given cycle length, more through green time results in more red time (assuming the cross street times are fixed) for the left turn phase, which results in longer left turn queues and an increased probabi lity of spillover. Cycle length : Assuming the phase split percentages are constant, a longer cycle length will increase the probability of spillover due to longer red times and consequently longer left turn queue lengths per cycle. Approach demand : For an y given left turn percentage (greater than zero), a larger approach demand flow rate will translate to a larger number of left turns; thus increasing the number of left turn queued vehicles and the probability of spillover, as else being equal. Arrival typ e : Arrival type represents the progression quality. Good progression (i.e., a higher percentage of vehicles arriving on green) generally leads to a reduced impact from spillover on through movement discharge. However, there are several complications that must be considered with this variable. For one, favorable progression is generally designed for only the through movement, and as such, the left turn movement often suffers from poor progression. Thus, the probability of spillover can actually increase wh en the progression of the through movement is favorable. On the other hand, having a higher percentage of through vehicles arrive during the green provides more opportunities for vehicles to discharge the intersection that are not blocked by left turn veh icles ( even more so for multiple through lane intersection approaches). PAGE 31 31 Heavy Vehicle Percentage : Heavy vehicles generally have longer lengths than passenger cars and hence fill up the left turn bay storage more quickly. The greater the proportion of heavy vehicle s in the left turning traffic volume, the higher the probability of spillover. Experimental Design An experimental design was developed for the purpose of generating a comprehensive data set to use for model development. The first step in the expe rimental design development was to s elect the independent variables, the second step was to select the number of levels to run each variable at and then the values for those levels, and then the last step was to determine the appropriate number of replicat ions to run for each variable combination. Selection of Variables The following variables were included in the experimental design for this study. Left Turn Bay Length Left Turn Percentage Through Green Time Left Turn Green Time Cycle Length Approach Dema nd Number of Through Lanes Arrival type was not included in this study to prevent the experimental design from becoming too large and complex. The arrival type variable is quite complicated (as previously explained) and should really be incorporated into a second experimental design, rather than complicating this experimental design that has relatively straight forward relationships. Rather than incorporating h eavy vehicles directly into this experimental design (and subsequently the models) and making the required number of runs very large, heavy vehicles can be accommodated by applying the HCM passenger car equivalent (PCE) value and using the heavy vehicle factor to modify the approach demand flow rate It should be noted, however, that PAGE 32 32 with this simpl ification, different heavy vehicle percentages for left turns and through movements cannot be applied. Variable L evels Since each of the variable relationships with through discharge rate was linear (or approximately linear) throughout most of the range of discharge rate, just two levels were chosen for each variable. The variable levels were chosen such that a wide range of conditions would be tested; however, the majority of the scenarios had large demand to capacity ratios for the left turn movement suc h that many of the cases would experience some level of left turn bay spillover The selected values for the two levels for each variable are shown in Table 3 3 A comprehensive list of the combinations of factor levels for the experimental design is given in appendix A. Number of Replications The necessary number of replications to run for each of the experimental design scenarios was estimated with Equation 3 1. [3 1] Where Z /2 = user specified probability level s = standard devi ation of sample = user specified allowable error For the various simulation test scenarios that were run and from the variances obtained from the scenario runs, it was found that 10 replications was sufficient based on a 5% allowable error and a 95% prob ability level. Each replication of each scenario used a different random number seed. The total number of runs require d is calculated according to Equation 3 2. [3 2] Where PAGE 33 33 TR = total number of runs K = number of factors NR = number of replications Two experiments were developed and executed: single through lane and multiple through lanes. This was done because the operation at a single through lane approach is somewhat unique and different from that with multiple through lanes. At s ignalized intersections with a single through lane, vehicles do not have the option of weaving around queues to avoid left turn spillover conditions. Thus, the impact of left turn spillover on through movement discharge is typically greater for intersectio ns with single through lane approaches than for those with multiple through lanes approaches. The single t hr ough lane experiment had six factors, each investigated at two levels, and with 10 replications for each variable combination. Therefore, the number of required runs is 640 (2 6 10). Similarly, the multiple through lanes experiment had seven factors each investigated at two levels and with 10 replications resulting in 1280 (2 7 10) required runs. Network Configuration for Experimental Design The netw ork was coded as an isolated intersection with four approaches For the single through lane experiment, each approach had one through lane and one left turn lane, while the multiple through lane s experiment had either two or four through lanes and one left turn lane. Data was however extracted for only the north bound approach Saturation headways of 2 s (saturation flow rate of 1800 veh/hg/ln), were specified on each approach of the isolated intersection. Free flow speeds were specified as 40 mi/h on each approach. Random arrivals by specifying Erlang distribution with a parameter of 1(negative exponential headways).The signal settings for the experimental design are given in Table 3 4 PAGE 34 34 Only leading left turns were considered in this study because they comp rise the very large majority of left turn phasing in the field. A screen capture of the CORSIM output processor is shown in Figure 3 5 The output processor enables the user to select performance measures to be extracted at the end of simulation and from w hich lanes. The performance measure extracted in this study was the through vehicle discharge rate (through vehicles discharge per hour). It also gives the user the flexibility to select the frequency at which output processing should be done by specifying which interval to extract performance measure. The multi run tab when clicked, allows the user to select the number of runs to be done for each simulation. Finally, the format and options tab allows the selection of the format (Microsoft excel, Comma Sepa rated value) in which output processor reports the results of simulation and which statistical measures to be extracted for the performance measure specified. PAGE 35 35 Figure 3 1 Relationship between left turn storage and through vehicle discharge rate 200 400 600 800 1000 1200 0 100 200 300 400 500 600 700 800 900 1000 Left Turn Storage (ft) Through Vehicle Discharge Rate (veh/h) North Bound Through Movt. South Bound Through Movt. PAGE 36 36 Figure 3 2 Relationship between left turn percent and through vehicle discharge rate 570 580 590 600 610 620 630 640 650 5 10 15 20 Left Turn Percentage (%) Through Vehicle Discharge Rate (veh/h) North Bound Through Movt. South Bound Through Movt. PAGE 37 37 Figure 3 3 Relationship between heavy vehicle percent and through discharge rate 0 200 400 600 800 1000 1200 0 5 10 15 20 Heavy Vehicle Percentage (%) Through Vehicle Discharge Rate (veh/h) North Bound Through Lane South Bound Through Lane PAGE 38 38 Figure 3 4 Relationship of through discharge rate to number of approaching through lanes 500 1000 1500 2000 2500 3000 3500 4000 1 2 3 Number of Through Lanes Through Vehicle Discharge Rate (veh/h) North Bound Through Movt. South Bound T hrough Movt. PAGE 39 39 Figure 3 5 Screen shot of CORSIM output processor settings Table 3 1 Settings coded into e xperimental network Parameters Value Saturation flow rate (veh/hg/ln) 1800 Free flow speed (mi/h) 40 Amber time (s) 3 All r ed period (s) 1 Vehicle lengths (ft) 25 1 1 22 ft vehicle length plus 3 ft intervehicle spacing PAGE 40 40 Table 3 2. Summary of inputs and results for left turn phasing sequence experiment Left Turn Phasing Left Turn Green Time (s) Through Green Time (s) Cycle Length (s) Approach Flow Rate (veh/h) North Bound Through Discharge Rate (veh/h) South Bound Through Discharge Rate (veh/h) Leading 10 54 180 800 519 526 Lagging 10 54 180 800 489 485 Leading 10 54 180 1200 516 516 Lagging 10 54 180 1200 499 50 0 Leading 10 60 120 1000 782 785 Lagging 10 60 120 1000 765 763 Leading 10 60 120 1400 793 794 Lagging 10 60 120 1400 772 773 Table 3 3 Factor levels for e xperimental d esign Levels Factor Low High Left Turn Percentage (%) 15 30 Left Turn Bay Len gth (veh) 5 10 Left Turn Green Time (s) 10 20 Through Green Time (s) 54 81 Cycle Length (s) 120 180 Average Approach Demand Per Lane (veh/h/ln) 800 1200 Number of Lanes 2 2 4 2 This variable is only used in the multiple through lane experiment. Ta ble 3 4 Signal settings used specified in simulation tool for experimental design NB SB Left Through Left Through Phase Sequence Leading left turn phase Leading left turn phase Phase 1 6 5 2 All Red Interval (s) 1 1 1 1 Yellow Interval (s) 3 3 3 3 Cycle Length(s) Low 120 120 High 180 180 Green Times(s) Low 10 54 10 54 High 20 81 20 81 PAGE 41 41 CHAPTER FOUR MODEL DEVELOPMENT AN D ANALYSIS Introduction This chapter describes the develop ed models for estimating through vehicle discharge rate as a functi on of left turn lane spillover This includes a summary of model coefficient values, t statistics, and goodness of fit results. Finally, sample applications of the models are presented, along with guidelines for the application of the models Model Devel opment A full factorial regression analysis was run on the data set obtained from the simulation runs to facilitate the consideration of variable interac tions in the model development. Only two way interactions between variables were included in the regre ssion model, as it was found that the improvement in model predictive accuracy was negligible with the consideration of higher level interactions and model complexity would be significantly increased. Two different models were developed to predict the t hr o ugh movement discharge rate, which are described in the following sections. Single Thr ough Lane Model This model predicts the through movement discharge rate from the t hr ough lane at an isolated signalized intersection with only one t hr ough lane. It captu res the impact of left turn percentage, left turn bay length, left turn green time, t hr ough green time, cycle length and average per lane approach demand The general specification of the single through lane model is shown in Equation 4 1 the model has a good fit (Figure 4 1) with an adjusted R 2 value of 0.9380. A summary of coefficients and t statistics of variables in the model are shown in Table 4 1. All variables included in the model were statistically significant at the 95% or greater confidence lev el. PAGE 42 42 [4 1] Where T hr uput = through lane vehicle discharge rate (veh/h) %LT = percent of the approach demand turning left L = left turn storage length (veh ) 3 G LT = green time for left turn movement (s) G TH = green time for through movement (s) C = cycle length (s) D = approach demand (veh/h/ln) The contribution of each variable to the through movement discharge rate was logical based on an interpretation of variable signs. Note that the effect of variable interactions must be consi dered in addition to the main effects when making this assessment. Multiple Through Lane Model This model captures the impact of left turn percentage, left turn bay length, left turn green time, through green time, cycle length, average per lane approach d emand, and the number of through lanes on the through movement discharge rate. All variables included in the model were statistically significant at the 95% or greater confidence level The model has a good fit (Figure 4 2) with an adjusted R 2 value of 0.9 606 The general form of the model is shown in Equation 4 2 and Table 4 2 summarizes the co efficients and t statistics of the multiple through lane model. 3 This includes vehicle length plus spacing between vehicles. Twenty five feet per vehicle was used in this study. PAGE 43 43 [4 2] Where: T hr uput = through lanes vehicle discharge rate (veh/h) %LT= pe rcent of the average per lane approach demand turning left L = left turn storage length (veh) G LT = green time for left turn movement (s) G TH = green time for through movement (s) C = cycle length(s) D = average approach demand (veh/h/ln) NumLanes =number of through lanes Model Application and Comparisons with Simulation Results This section gives sample applications of the single through lane and multiple through lane models. These applications involve sample calculations using the general model specifica tions; E quations 4 1 and 4 2. Three sample calculations are given for each model one that results in a relatively low estimated through movement discharge rate, one that results in a medium discharge rate, and one that results in a relatively high discharg e rate. The variable values chosen for the three scenarios were values that were also used in the simulation runs so the model estimation results could be compared directly with the simulation results (the average v alue for the 10 replications). Sample C alculation s for the Single Through Lane Model A summary of inputs used in the sample calculations for this model are gi ven in Table 4 3. Comparison of the single through lane model sample calculation results with simulation results obtained for the same se t of inputs is shown in Table 4 4. PAGE 44 44 Sample Calculation 1 Thruput = 192 veh/h Sample Calculation 2 Thruput = 607 veh/h Sample Calculation 3 Thruput = 1015 veh/h Sample Calculation for the Multiple Through Lanes Model Similarly, sample calculations were performed with the genera l specification of the multiple through lanes model using inputs from T able 4 5. A comparison of the multiple through lanes model sample calculation results with simulation results obtained for the same set of inputs is shown in Table 4 6. PAGE 45 45 Sample Calculation 4 Thruput = 1007 veh/h S ample Calculation 5 Thruput = 1454 veh/h Sample Calculation 6 Thruput = 3195 veh/h Comparison of Reductions in Through Vehicle Discharge as Predicted By Single T hrough L ane and Multiple T h rough Lane Model s To verify whether having separate models for a single through lane and multiple through lanes was warrante d, the reduction of through vehicle discharge rates was compared (on a per lane basis), using the same input values. The input values are given in Table 4 7. Three calculations were performed for each model, as follows. PAGE 46 46 Sample Calculations for Single T hr ough L ane Model Reduction Calculation 1 Thruput per lane = = 890 veh/h/l n Thruput Reduction (% ) = Calculation 2 Thruput per lane = = 607 veh/h/ln Thruput Reduction (%) = Calculation 3 Thruput per lane = = 673 veh/h/ln Thruput Reduction (%) = PAGE 47 47 Sample Calculations for Multiple Through Lane Model R eduction Calculation 1 Thruput per lane = =1001veh/h/ln Thruput Reduction (%) = Calculation 2 Thruput per lane = = 627 veh/h/ln Thruput R eduction (%) = Calculation 3 Thruput per lane = = 774 veh/h/ln PAGE 48 48 Thruput Reduction (%) = The results are also summarized in Table 4 8. T he percentage reduction in through vehicle discharge, on a per lane basis, is greater for the single through lane case than for the multiple through lane case (Table 4 8). Again, this was expected since through vehicles do not have the opportunity to weave around a left turn spillov er condition in the case of a single through lane. Many other input conditions were also tested beyond those shown here, and the results from these additional tests were consistent with those shown here. Thus, having separate models for the single throug h lane and multiple through lane cases is justified. Guidelines for Application of Model For nearly all situations where reasonable variable values are used, and over a very wide range of input values, the models can be expec ted to give reasonable results. Certainly, for situations where unreasonable input values are used (e.g., a negative cycle length or green time), unreasonable m odel results will be obtained. Furthermore, for unreasonable combinations of input values (e.g., a green time greater than the cycle length), unreasonable model results can be expected. In the very infrequent case where reasonable input values are used, yet the model predicted value is still unreasonable, use the following guidelines to adjust the model value: If the model predict s a through movement discharge rate greater than the approaching through demand flow rate, use the approaching through demand rate as the limiting value. If the model predicts a through movement discharge rate greater than the capacity of the through movem ent ( as unaffected by left turn spillover), use the through movement capacity as the limiting value PAGE 49 49 Figure 4 1. Comparison of simulation and model estimation results for single through lane model PAGE 50 50 Figure 4 2. Comparison of simulation and model estimation results for multiple through lanes model PAGE 51 51 Table 4 1 Summary of Single through lane model parameters Variable Co efficient t stat Constant 799.0094 7.5912 %LT 6.8054 2.8165 L 4 3.8500 7.0606 G LT 30.9825 9.9774 G TH 1.3245 1.3141 C 0.9251 2.5098 D 0.4918 5.9585 %LT L 0.6805 6.8263 %LT G LT 0.9152 18.3606 %LT G TH 0.2896 15.6873 %LT C 0.0388 4.6763 % LT D 0.0161 12.9053 L G LT 0.6493 4.3419 L G TH 0.1148 2. 0731 L D 0.0241 6.4535 G LT G TH 0.0571 2.0614 G LT D 0.0109 5.8533 G TH D 0.0056 8.0351 C D 0.0045 14.5521 PAGE 52 52 Table 4 2. Summary of Multiple through l ane m odel parameters Variable Co efficient t stat Constant 932.6415 2.8136 %LT 21.6749 3.18 20 L 41.9322 3.5200 G LT 100.4621 12.0127 G TH 39.4056 11.9657 C 8.8626 5.9804 D 0.5795 2.6070 NumLanes 731.7854 14.9939 %LT L 0.9569 3.5644 %LT G LT 1.5033 11.1991 %LT G TH 0.5604 11.2717 %LT C 0.0732 3.2737 %LT D 0.0314 9.3505 %LT NumLanes 5.0604 7.5394 L C 0.2749 4.0962 G LT G TH 0.5900 7.9119 G LT D 0.0281 5.5744 G LT NumLanes 5.5910 5.5534 G TH C 0.0586 4.7109 G TH D 0.0293 15.6866 G TH NumLanes 6.8871 18.4700 C D 0.0151 18.0165 C NumLanes 3.9624 23.6 142 D NumLanes 932.6415 6.6395 Table 4 3. Values of parameters used in sample calculations for single through lane approach model Sample Calculations %LT L (veh) G LT (s) G TH (s) C (s) D (veh/h/ln) 1 30 5 10 54 180 1200 2 15 5 10 81 180 800 3 15 10 20 81 120 1200 Table 4 4 Comparison of sample single through lane model predictions with simulation results Sample Model Calculation Results (veh/h) Simulation Results (veh/h) 192 199 607 608 1015 1025 PAGE 53 53 Table 4 5. Values of parameters used in sample calculations for multiple through lanes model Sample Calculations %LT L (veh) G LT (s) G TH (s) C (s) D (veh/h/ln) NumLanes 4 30 10 10 81 180 1200 2 5 15 10 10 54 120 800 2 6 30 5 10 81 120 1200 4 Table 4 6 Comparison of sample mu ltiple th rough lanes model predictions with simulation results Sample Model Calculation Results (veh/h) Simulation Results (veh/h) 1007 1005 1454 1474 3195 3198 Table 4 7 Summary of i nputs used in s ample c alculations for through discharge reduction model comp arisons Calculation %LT L (veh) G LT (s) G TH (s) C (s) D (veh/h/ln) Num L anes Through Flow Rate (veh/h/ln) 1 15 5 10 81 120 1200 2 1020 2 15 5 10 81 180 800 2 680 3 30 10 20 54 120 120 4 840 Table 4 8. Comparison of reduction in through discharge rat es for both models Calculation Single Through Lane Model Reduction (%) Multiple Through Lane Model Reduction (%) 1 12.74 1.86 2 10.70 7.79 3 19.80 7.86 PAGE 54 54 CHAPTER 5 CONCLUSIONS AND RECO MMENDATIONS Summary The HCM signalized intersection analysis method ology does not explicitly account for the impact to through movement flow rate due to left turn spillover. This study developed two models to estimate the through movement flow rate as impacted by left turn spillover, as a function of traffic, roadway, and control factors for the left turn and through movements. The models were developed from regression analysis and used simulation data as a surrogate for field data. One model is specific to intersections with only a single through lane on the approach whi le the other is specific to intersections with multiple through lanes on the approach. Conclusions The two developed models replicate the simulation results quite reasonably, as indicated by the goodness of fit measures. The relationship between the vario us model variables and their effect on through movement discharge rate are also reasonable and consistent with theoretical expectations. For intersections where left turn spillover is a consistent problem, the models developed in this study can be applied to give a more accurate estimate of the expected through movement flow rate than an analysis that ignores the left turn spillover condition. Recommendations for Further Research Although the results of this study present a significant improvement over the current condition; that is, a signalized intersection analysis methodology that ignores the effect of left turn spillover on through movement discharge rates ( i.e., the HCM), there are still areas that can be improved upon. Ideally, field data should be c ollected from a number of signalized intersections that experience left turn spillover to use for calibrating and/or validating the regression models developed in this study. PAGE 55 55 Further experiments should be conducted to investigate the effect of progression quality on left turn spillover and through movement discharge rate. Once this relationship is established, this variable can be incorporated into the two models developed in this study to further improve its predictive capabilities over a wider range of t raffic and control conditions. PAGE 56 56 APPENDIX A EXPERIMENTAL DESIGN COMBINATIONS Table A 1 Experimental d esign c ombinations for s ingle through lane e xperiment SCENARIO % LT L (veh) G LT (s) G TH (s) C (s) D (veh/h) 1 15 5 10 54 120 800 2 15 5 10 54 120 1200 3 15 5 10 54 180 800 4 15 5 10 54 180 1200 5 15 5 10 81 120 800 6 15 5 10 81 120 1200 7 15 5 10 81 180 800 8 15 5 10 81 180 1200 9 15 5 20 54 120 800 10 15 5 20 54 120 1200 11 15 5 20 54 180 800 12 15 5 20 54 180 1200 13 15 5 20 81 120 800 14 15 5 20 81 120 1200 15 15 5 20 81 180 800 16 15 5 20 81 180 1200 17 15 10 10 54 120 800 18 15 10 10 54 120 1200 19 15 10 10 54 180 800 20 15 10 10 54 180 1200 21 15 10 10 81 120 800 22 15 10 10 81 120 1200 23 15 10 10 81 180 800 24 15 10 10 81 180 12 00 25 15 10 20 54 120 800 26 15 10 20 54 120 1200 27 15 10 20 54 180 800 28 15 10 20 54 180 1200 29 15 10 20 81 120 800 30 15 10 20 81 120 1200 31 15 10 20 81 180 800 32 15 10 20 81 180 1200 33 30 5 10 54 120 800 34 30 5 10 54 120 1200 35 30 5 1 0 54 180 800 36 30 5 10 54 180 1200 PAGE 57 57 Table A 1 Continued. SCENARIO % LT L (veh) G LT (s) G TH (s) C (s) D (veh/h) 37 30 5 10 81 120 800 38 30 5 10 81 120 1200 39 30 5 10 81 180 800 40 30 5 10 81 180 1200 41 30 5 20 54 120 800 42 30 5 20 54 120 1200 4 3 30 5 20 54 180 800 44 30 5 20 54 180 1200 45 30 5 20 81 120 800 46 30 5 20 81 120 1200 47 30 5 20 81 180 800 48 30 5 20 81 180 1200 49 30 10 10 54 120 800 50 30 10 10 54 120 1200 51 30 10 10 54 180 800 52 30 10 10 54 180 1200 53 30 10 10 81 120 800 54 30 10 10 81 120 1200 55 30 10 10 81 180 1200 56 30 10 10 81 180 800 57 30 10 20 54 120 800 58 30 10 20 54 120 1200 59 30 10 20 54 180 800 60 30 10 20 54 180 1200 61 30 10 20 81 120 800 62 30 10 20 81 120 1200 63 30 10 20 81 180 800 64 30 10 20 81 180 1200 PAGE 58 58 Table A 2 Experimental d esign c ombinations for m ultiple through lanes experiment SCENARIO %LT L (veh) G LT (s) G TH (s) C (s) D (veh/h) TOT DEMAND (veh/h) NumLanes 1 15 5 10 54 120 800 1600 2 2 15 5 10 54 120 1200 2400 2 3 15 5 10 54 180 800 1600 2 4 15 5 10 54 180 1200 2400 2 5 15 5 10 81 120 800 1600 2 6 15 5 10 81 120 1200 2400 2 7 15 5 10 81 180 800 1600 2 8 15 5 10 81 180 1200 2400 2 9 15 5 20 54 120 800 1600 2 10 15 5 20 54 120 1200 2400 2 11 15 5 20 54 180 800 1600 2 12 15 5 20 54 180 1200 2400 2 13 15 5 20 81 120 800 1600 2 14 15 5 20 81 120 1200 2400 2 15 15 5 20 81 180 800 1600 2 16 15 5 20 81 180 1200 2400 2 17 15 10 10 54 120 800 1600 2 18 15 10 10 54 120 1200 2400 2 19 15 10 10 54 180 800 1600 2 20 15 10 10 54 180 1200 2400 2 21 15 10 10 81 120 800 1600 2 22 15 10 10 81 120 1200 2400 2 23 15 10 10 81 180 800 1600 2 24 15 10 10 81 180 1200 2400 2 25 15 10 20 54 120 800 1600 2 26 15 10 20 54 120 1200 2400 2 27 15 10 20 54 180 800 1600 2 28 1 5 10 20 54 180 1200 2400 2 29 15 10 20 81 120 800 1600 2 30 15 10 20 81 120 1200 2400 2 31 15 10 20 81 180 800 1600 2 32 15 10 20 81 180 1200 2400 2 33 30 5 10 54 120 800 1600 2 34 30 5 10 54 120 1200 2400 2 35 30 5 10 54 180 800 1600 2 36 30 5 10 54 180 1200 2400 2 37 30 5 10 81 120 800 1600 2 38 30 5 10 81 120 1200 2400 2 PAGE 59 59 Table A 2 Continued SCENARIO %LT (s) L (veh) G LT (s) G TH (s) C (s) D (veh/h) TOT DEMAND (veh/h) NumLanes 39 30 5 10 81 180 800 1600 2 40 30 5 10 81 180 1200 2400 2 41 30 5 20 54 120 800 1600 2 42 30 5 20 54 120 1200 2400 2 43 30 5 20 54 180 800 1600 2 44 30 5 20 54 180 1200 2400 2 45 30 5 20 81 120 800 1600 2 46 30 5 20 81 120 1200 2400 2 47 30 5 20 81 180 800 1600 2 48 30 5 20 81 180 1200 2400 2 49 30 10 10 54 120 800 1600 2 50 30 10 10 54 120 1200 2400 2 51 30 10 10 54 180 800 1600 2 52 30 10 10 54 180 1200 2400 2 53 30 10 10 81 120 800 1600 2 54 30 10 10 81 120 1200 2400 2 55 30 10 10 81 180 1200 2400 2 56 30 10 10 81 180 800 1600 2 57 30 10 20 54 120 800 1600 2 58 30 10 20 54 120 1200 2400 2 59 30 10 20 54 180 800 1600 2 60 30 10 20 54 180 1200 2400 2 61 30 10 20 81 120 800 1600 2 62 30 10 20 81 120 1200 2400 2 63 30 10 20 81 180 800 1600 2 64 30 10 20 81 180 1200 2400 2 65 15 5 10 54 120 800 3200 4 66 15 5 10 54 120 1200 4800 4 67 15 5 10 54 180 800 3200 4 68 15 5 10 54 180 1200 4800 4 69 15 5 10 81 120 800 3200 4 70 15 5 10 81 120 1200 4800 4 71 15 5 10 81 180 800 3200 4 72 15 5 10 81 180 1200 4800 4 73 15 5 20 54 120 800 3200 4 74 1 5 5 20 54 120 1200 4800 4 75 15 5 20 54 180 800 3200 4 76 15 5 20 54 180 1200 4800 4 PAGE 60 60 Table A 2 Continued SCENARIO %LT (s) L (veh) G LT (s) G TH (s) C (s) D (veh/h) TOT DEMAND (veh/h) NumLanes 77 15 5 20 81 120 800 3200 4 78 15 5 20 81 120 1200 4800 4 79 15 5 20 81 180 800 3200 4 80 15 5 20 81 180 1200 4800 4 81 15 10 10 54 120 800 3200 4 82 15 10 10 54 120 1200 4800 4 83 15 10 10 54 180 800 3200 4 84 15 10 10 54 180 1200 4800 4 85 15 10 10 81 120 800 3200 4 86 15 10 10 81 120 1200 4800 4 87 15 10 10 81 180 800 3200 4 88 15 10 10 81 180 1200 4800 4 89 15 10 20 54 120 800 3200 4 90 15 10 20 54 120 1200 4800 4 91 15 10 20 54 180 800 3200 4 92 15 10 20 54 180 1200 4800 4 93 15 10 20 81 120 800 3200 4 94 15 10 20 81 120 120 0 4800 4 95 15 10 20 81 180 800 3200 4 96 15 10 20 81 180 1200 4800 4 97 30 5 10 54 120 800 3200 4 98 30 5 10 54 120 1200 4800 4 99 30 5 10 54 180 800 3200 4 100 30 5 10 54 180 1200 4800 4 101 30 5 10 81 120 800 3200 4 102 30 5 10 81 120 1200 4800 4 103 30 5 10 81 180 800 3200 4 104 30 5 10 81 180 1200 4800 4 105 30 5 20 54 120 800 3200 4 106 30 5 20 54 120 1200 4800 4 107 30 5 20 54 180 800 3200 4 108 30 5 20 54 180 1200 4800 4 109 30 5 20 81 120 800 3200 4 110 30 5 20 81 120 1200 4800 4 1 11 30 5 20 81 180 800 3200 4 112 30 5 20 81 180 1200 4800 4 113 30 10 10 54 120 800 3200 4 114 30 10 10 54 120 1200 4800 4 PAGE 61 61 Table A 2 Continued SCENARIO %LT L (veh) G LT (s) G TH (s) C (s) D (veh/h) TOT DEMAND (veh/h) NumLanes 115 30 10 10 54 180 80 0 3200 4 116 30 10 10 54 180 1200 4800 4 117 30 10 10 81 120 800 3200 4 118 30 10 10 81 120 1200 4800 4 119 30 10 10 81 180 1200 4800 4 120 30 10 10 81 180 800 3200 4 121 30 10 20 54 120 800 3200 4 122 30 10 20 54 120 1200 4800 4 123 30 10 20 54 18 0 800 3200 4 124 30 10 20 54 180 1200 4800 4 125 30 10 20 81 120 800 3200 4 126 30 10 20 81 120 1200 4800 4 127 30 10 20 81 180 800 3200 4 128 30 10 20 81 180 1200 4800 4 PAGE 62 62 REFERENCES Foil, L and A., Qureshi. 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National Research Council, Washington D.C., 2000, pp. 222 230. Zhang, Y. and J.Tong. Modeling Left Turn Blockage and Capacity at Sig nalized Intersections with Short Left Turn Bay. Annual Compendium of Papers, 87th Annual Meeting Transportation Research Board, Washington D.C., 2007. PAGE 63 63 BIOGRAPHICAL SKETCH Abigail Osei Asamoah was born and raised in Kumasi, Ghana. She received her Bachelor of Science degree in c ivil e ngineering at the Kwame Nkrumah University of Science and Technology, Ghana. Upon receiving her undergraduate degree, Abigail worked for a year as a civil engineer at the Department of Urban Roads, Mi nistry of Transportation, G hana after which she proceeded to the University of Florida to pursue a Master of Science degree in civil engineering (emphasis in transportation engineering ). After receiving her M Abigail intends to work in the t ransportation industry as a traffic engineering consultant. 