Citation |

- Permanent Link:
- http://ufdc.ufl.edu/UFE0044933/00001
## Material Information- Title:
- Route Choice Modeling Using GPS Data
- Creator:
- Dhakar, Nagendra S.
- Place of Publication:
- [Gainesville, Fla.]
- Publisher:
- University of Florida
- Publication Date:
- 2012
- Language:
- english
- Physical Description:
- 1 online resource (161 p.)
## Thesis/Dissertation Information- Degree:
- Doctorate ( Ph.D.)
- Degree Grantor:
- University of Florida
- Degree Disciplines:
- Civil Engineering
Civil and Coastal Engineering - Committee Chair:
- Srinivasan, Sivaramakrishnan
- Committee Members:
- Yin, Yafeng
Elefteriadou, Ageliki L Washburn, Scott S Bejleri, Ilir - Graduation Date:
- 12/15/2012
## Subjects- Subjects / Keywords:
- Genetic mapping ( jstor )
Global positioning systems ( jstor ) Modeling ( jstor ) Observed choices ( jstor ) Roads ( jstor ) Route choice ( jstor ) Transportation ( jstor ) Travel ( jstor ) Travel time ( jstor ) Travelers ( jstor ) Civil and Coastal Engineering -- Dissertations, Academic -- UF bfs-le -- choice -- forecasting -- gis -- gps -- map-matching -- modeling -- psl -- route - Genre:
- Electronic Thesis or Dissertation
bibliography ( marcgt ) theses ( marcgt ) government publication (state, provincial, terriorial, dependent) ( marcgt ) Civil Engineering thesis, Ph.D.
## Notes- Abstract:
- The advent of GPS-based travel surveys offers an opportunity to develop empirically-rich route-choice models. However, the GPS traces must first be mapped to the roadway network, map-matching, to identify the network-links actually traversed. In the study, two enhanced map-matching algorithms are implemented and compared for their operational performance using data from a large-scale GPS survey. Once the traversed path is determined, the next step is to determine the other options (routes), choice set generation, that were available to the traveler for making the trip. For this, the enhanced version of the Breadth First Search Link Elimination (BFS-LE) algorithm is implemented. The data assembled from the two steps, map-matching and choice set generation, are then used for developing route choice. The original Path Size Logit (PSL) model is used for developing models for route choice. The PSL models are estimated for three different choice set sizes (15 alternatives, 10 alternatives, and 5 alternatives). The utility functions are expressed in terms of route attributes (time, longest leg time, distance, number of intersections,left turns, right turns, time by facility type, and circuity), trip characteristics (home-based/ non-home-based, weekday/weekend, and peak/off-peak) and travelerâ€™s demographics (gender, age, employment, and household income). The estimation results indicate expected effects. Specifically, free-flow travel time, left turns, right turns, intersections, and circuity are found negatively associated with the attractiveness of a route. Also, the travel time on local roads was found to be a positive factor in choosing a route. A positive sign on the path size attribute indicates that the route with less similarity with the alternatives is more likely to be chosen. Further, travelers indicated less sensitivity to the travel time during peak period, thus suggesting a congestion effect. Trips going to home were the least sensitive to the travel time and right turns than the other trips. While determining a route, males cared less about the intersections, proportion of time on local roads and circuity than females. Further, sensitivity to intersections in a route decreased with age.Compared to home-based trips, non-home-based trips were less sensitive to intersections and time on local roads. Across different choice set sizes, the effects were more or less similar except that some effects became insignificant. In terms of the predictive quality, when the shortest time path was very close to the chosen route, the probabilistic methods produced routes with lower overlaps. However,the overlaps were still reasonably high. For the other cases, the probabilistic methods predicted better overlaps than the deterministic method. Further, on average, there was a probability of 50% that the predicted route will outperform the shortest time path. We envision this study as an important contribution towards the development of empirically rich route choice models. With increasing numbers of GPS surveys and benefits of using high-resolution roadway network, the availability of computationally efficient automatic procedures to generate the chosen routes and alternatives is critical. Further, the examination of route choice behavior in terms of travelersâ€™ demographics provides more insight into the route choice decisions. ( en )
- General Note:
- In the series University of Florida Digital Collections.
- General Note:
- Includes vita.
- Bibliography:
- Includes bibliographical references.
- Source of Description:
- Description based on online resource; title from PDF title page.
- Source of Description:
- This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
- Thesis:
- Thesis (Ph.D.)--University of Florida, 2012.
- Local:
- Adviser: Srinivasan, Sivaramakrishnan.
- Statement of Responsibility:
- by Nagendra S Dhakar.
## Record Information- Source Institution:
- UFRGP
- Rights Management:
- Copyright Dhakar, Nagendra S.. Permission granted to the University of Florida to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder.
- Resource Identifier:
- 870531742 ( OCLC )
- Classification:
- LD1780 2012 ( lcc )
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PAGE 1 1 ROUTE CHOICE MODELING USING GPS DATA By NAGENDRA S DHAKAR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012 PAGE 2 2 2012 Nagendra S Dhakar PAGE 3 3 To my parents PAGE 4 4 ACKNOWLEDGMENTS No research endeavor is ever carried out in solitude. I owe my gratitude to all those people who in one way or another contributed towards this dissertation. First and foremost, I would like to thank my advisor Dr. Sivaramakrishnan Srinivasan for his valuable support, guidance and encouragement, throughout the course of my Ph.D. study. He has been an incredible source of inspiration and one simply could not wish for a better advisor. I would also like to thank my committee members Drs. Yafeng Yin, Scott Washburn, Lily Elefteriadou, and Ilir Bejleri for their valuable comments, feedback and suggestions from various perspectives, throughout the resea rch. On a personal note, I want to thank my parents and family members for their love and support at each and every stage of my life. They have been very understanding and patient in all these years. I would also like to thank all my friends and fellow stu dents at the Transportation Research Center for making my stay, a memorable one. PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 9 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 INTRODUCTI ON ................................ ................................ ................................ .... 12 1.1 Background ................................ ................................ ................................ ... 12 1.2 Structure of the Dissertation ................................ ................................ .......... 15 2 LITERATURE REVIEW ................................ ................................ .......................... 16 2.1 Map Matching ................................ ................................ ................................ 16 2.1.1 Overview ................................ ................................ ............................. 16 2.1.2 On line Methods ................................ ................................ .................. 20 2.1.3 Off line Methods ................................ ................................ .................. 21 2.1.4 Summary ................................ ................................ ............................. 26 2.2 Choice Set Generation ................................ ................................ .................. 27 2.2.1 Overview ................................ ................................ ............................. 27 2.2.2 Methods ................................ ................................ .............................. 28 2.2.3 Comparative Assessment ................................ ................................ ... 36 2.2.4 Summary ................................ ................................ ............................. 41 2.3 Route Choice Models ................................ ................................ .................... 41 2.3.1 Overview ................................ ................................ ............................. 41 2.3.2 Models ................................ ................................ ................................ 42 2.3.3 Empirical Studies: Methods ................................ ................................ 48 2.3.4 Empirical Studies: Explanatory Variables ................................ ............ 53 2.3.5 Summary ................................ ................................ ............................. 54 3 MAP MATCHING ALGORITHMS ................................ ................................ ........... 56 3.1 The GPS Weighted Shortest Path (GWSP) Algorithm ................................ .. 57 3.2 The Multi Path (MP) Algorithm ................................ ................................ ...... 59 3.3 Summary ................................ ................................ ................................ ....... 65 4 EXPLORATORY ANALYSIS OF CHOSEN ROUTES ................................ ............ 66 4.1 Validation ................................ ................................ ................................ ...... 66 4.2 Applicatio n to a Large Scale GPS based Travel Survey ............................... 74 PAGE 6 6 4.2.1 Data ................................ ................................ ................................ .... 74 4.2.2 Aggregate Comparisons ................................ ................................ ..... 78 4.2.3 Measures of Similarity of Pairs of Routes ................................ ........... 79 4.2.4 Extent of Similarity of the Routes Generated by the Two MM Algorithms ................................ ................................ .......................... 81 4.2.5 Comparing the C hosen R outes A gainst the Shortest D istance R outes ................................ ................................ ................................ 83 4.2.6 Comparing the C hosen R outes A gainst the Shortest T ime R outes .... 86 4.2.7 Simultaneously C omparing the C hosen R outes A gainst the SD and ST R outes ................................ ................................ .......................... 90 4.3 Summary ................................ ................................ ................................ ....... 92 5 DATA ASSEMBLY FOR MODEL ESTIMATIONS ................................ .................. 94 5.1 Trip And Traveler Characteristics ................................ ............................... 94 5.1.1 Trip Characteristics ................................ ................................ ............. 95 5. 1.2 Traveler Characteristics ................................ ................................ ...... 97 5.2 Determination And Characterization Of Alternate Routes ............................. 98 5.2.1 Breadth First Search Link Elimination (BFS LE) ................................ 99 5.2.2 Route Attributes ................................ ................................ ................ 106 5.3 Summary ................................ ................................ ................................ ..... 112 6 ROUTE CHOICE MODELS ................................ ................................ .................. 114 6.1 Path Size Logit (PSL) Model ................................ ................................ ....... 114 6.2 Estimation Results ................................ ................................ ...................... 116 6.3 Predictive Assessment ................................ ................................ ................ 123 6.3.1 Comparison of Predicted Overlaps ................................ ................... 125 6.3.2 Outperforming the Shortest Path ................................ ...................... 128 6.4 Summary ................................ ................................ ................................ ..... 131 7 SUMMARY AND CONCLUSIONS ................................ ................................ ........ 133 7.1 Map Matching ................................ ................................ .............................. 133 7.2 Choice Set Generation ................................ ................................ ................ 135 7.3 Route Choice Modeling ................................ ................................ ............... 135 7.4 Future Work ................................ ................................ ................................ 137 APPENDIX A DEMONSTRATION OF MAP MATCHING ALGORITHMS ................................ ... 140 LIST OF REFERENCES ................................ ................................ ............................. 154 BIOGRAPH ICAL SKETCH ................................ ................................ .......................... 161 PAGE 7 7 LIST OF TABLES Table page 2 1 Map matching related empirical studies ................................ ............................. 18 2 2 Choice set generation related empirical studies ................................ ................. 29 2 3 Route choice modeling related empirical studies ................................ ................ 49 4 1 Validation of the map matching algorithms ................................ ......................... 68 4 2 Troublesome trips for the GWSP method ................................ ........................... 70 4 3 Aggregate s tatistics o f r outes from the f our m ethods ................................ ......... 79 4 4 Overlapping index (OI) for routes from MP and GWSP methods ....................... 83 4 5 CR of the chosen routes and the SD routes ................................ ....................... 85 4 6 DDI of the chosen routes with the SD routes ................................ ...................... 86 4 7 CR for the chosen routes and the ST routes ................................ ...................... 89 4 8 TDI of the chosen routes with the ST routes ................................ ....................... 90 5 1 Trip characteristics ................................ ................................ ............................. 95 5 2 Land Use d escriptives at the non home ends ................................ .................... 96 5 3 ................................ ...................... 98 5 4 Choice set size ................................ ................................ ................................ 104 5 5 Comparison of link counts in the first shortest time routes ............................... 104 5 6 Route attributes ................................ ................................ ................................ 106 5 7 Descriptive of route attributes ................................ ................................ ........... 109 6 1 Estimation data descriptive ................................ ................................ ............... 117 6 2 Base model estimations ................................ ................................ ................... 118 6 3 Full model estimations ................................ ................................ ...................... 120 6 4 Overlaps statistic (full sample) ................................ ................................ .......... 125 6 5 Cumulative share of expected overlaps (full sample) ................................ ....... 126 PAGE 8 8 6 6 Overlaps statistic (30% observations) ................................ .............................. 126 6 7 Cumulative overlap with the chosen route (30% observations) ........................ 127 6 8 Overlaps statistic (70% observations) ................................ .............................. 127 6 9 Cumulative overlap with the chosen route (70 % observations) ........................ 128 6 10 Statistic of the outperforming probabilities (full sample) ................................ ... 129 6 11 Cumulative share of the outperforming probabilities (full sample) .................... 129 6 12 Statistic of the outperforming probabilities (30% observations) ........................ 130 6 13 Cumulat ive share of the outperforming probabilities (30% observations) ......... 130 6 14 Statistic of the outperforming probabilities (70% observations) ........................ 131 6 15 Cumulative share of the outperforming probabilities (70% observations) ......... 131 PAGE 9 9 LIST OF FIGURES Figure page 4 1 Missing links in the network example 1 (a) GPS tracks, and (b) MP route ...... 71 4 2 Missing links in the network example 2 ................................ ........................... 72 4 3 A round trip (a) GPS tracks, (b) GWSP algorithm, and (c) MP algorithm ........... 73 4 4 In vehicle GeoLogger (s ource: GeoStats) ................................ .......................... 75 4 5 Time of day frequency distribution ................................ ................................ ...... 77 4 6 Trip length frequency distribution ................................ ................................ ........ 78 4 7 Comparison of routes from the two map matching algorithms ........................... 82 4 8 Commonly ratio (CR) of routes from the MM and SD methods .......................... 84 4 9 Comparison of routes from SD and ST methods ................................ ................ 87 4 10 Commonly ratio (CR) of routes from the MM and ST methods ........................... 88 4 11 Comparison for trip length in time of day ................................ ............................ 9 1 5 1 Basic BFS LE tree ................................ ................................ ............................ 100 5 2 Fr equency distribution of choice set size ................................ .......................... 103 5 3 Link count comparison ................................ ................................ ...................... 105 5 4 Frequency distribution of overlap with the chosen routes ................................ 111 6 1 Example of calculating PS attribute ................................ ................................ .. 115 PAGE 10 10 Abstract of Dis sertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ROUTE CHOICE MODELING USING GPS DATA By Nagendra S Dhakar December 2012 Chair: Sivaramakrishnan Srinivasan Major: Civil Engineering The advent of GPS based travel surveys offers an opportunity to develop empirically rich route choice models. However, the GPS traces must first be mapped to the roadway network map matching, to identify the network links actually traversed. I n the study, t wo en hanced map matching algorithms are implemented and compared for their operational performance using data from a large scale GPS survey. Once the traversed path is determined, the next s tep is to determine the other options (routes), choice set generation, that were available to the traveler for making the trip. For this, the enhanced version of the Breath First Search Link Elimination ( BFS LE ) algorithm is implemented The data assembled from the two steps map matching and choice set generation, are then used for developing route choice. T he original Path Size Logit (PSL) model is used for developing models for route choice T he PSL models are developed for three different choice set sizes (15 alternatives, 10 alternatives, and 5 alternatives). The utility functions are expressed in terms of route attributes, trip cha racteristics and traveler characteristics. The estimation results indicate intuitive effects. Specifically, free flow travel time, left turns, right turns, intersections, and circuity we re found negatively associated with the attractiveness of a PAGE 11 11 route. A positive sign on the path size attribute indicates that the route with less similarity with the alternatives is more likely to be chosen. Trips going to home a re the least sensitive to the travel time and right turns than the other trips. Compared to home based trips, non home based trips a re less sensitive to intersections and time on local roads. O n average, the expected overlap s (probabilistic routes) with the chosen route a re similar to the deterministic overlap s (shortest time path) Also, there i s a probability of about 50% that the predicted route will outperform the shortest time path. We envision this study a s an important contribution towards the development of empirically rich route choice models. With increasing numbers of GPS surveys and benefits of using high resolution roadway network, the availability of computationally efficient automatic procedures to generate the chosen routes and alternatives is critical. provides more insight into the route choice decisions. PAGE 12 12 CHAPTER 1 INTRODUCTION 1.1 Background of traffic (level of congestion) on the different links of the roadway network. One of the important impediments to studying route choice behavior is that the data on actua l routes chosen are never collected in conventional household travel surveys. Arguably, the primary reason for the lack of such data is that routes cannot be easily reported in the Computer Assisted Telephone Interview (CATI) methods used for data collecti on. As a consequence of this lack of data, route choices are predicted assuming that travelers choose the shortest travel time paths for their trips. While travel time is a very important factor that determines the choice of route, i t i s reasonable to expe ct that it is not the only factor considered by travelers in their route choice decisions (see for example, Li et al., 2006 and Papinski and Scott, 2011 a ) The advent of Geographic Position Systems (GPS) based travel surveys now provides an approach to tra ce vehicle movements and, hence, collect data on the actual routes chosen for various trips. To date, the efforts on the empirical modeling of route choices using GPS traces are still limited (see for instance, Schussler, 20 09 and Hood et al., 2010 ). This is probably because the number of GPS based travel surveys has increased quite substantially only in the last decade (consequently some of the past route choice description of r outes). Further, several of the methodological developments relevant to modeling route choices from GPS based travel surveys are relatively recent. PAGE 13 13 In this context, the broad focus of this research is to combine data from GPS based travel surveys and Geogr aphic Information Systems (GIS) based roadway network databases to d evelop models for route choice. There are three main components to the overall approach: (1) Map Matching, (2) Choice Set Generation, and (3) Route Choice Models Map matching is the proce ss of identifying the specific links of the roadway traversed by a vehicle by mapping the points from its GPS trace to an underlying GIS based roadway network database. This step is critical as it identifies the fundamental terest. In this study, two map matching algorithms from the literature are enhanced, implemented, compared, and validated. Both these algorithms include systematic treatment for missing GPS points along the routes; employ efficient techniques to address co mputational time; and are almost entirely automated. options (routes) that were available to the traveler for making the same trip. This process is called choice set genera tion. Since the surveys do not directly query the respondents on alternate options available to them, the choice set is generally constructed by considering the network topology and the trip end locations. In this study, and enhanced version of the link el imination approach to generating the choice set is used. The procedure is shown to generate heterogeneous alternatives which are also generally inclusive of a significant proportion of the chosen route. After assembling the data of the chosen routes and corresponding choice sets, route choice models are developed to examine the route choice behavior. In this study, the path size logit approach is used. The explanatory factors include route attributes PAGE 14 14 (such as travel times, numbers of turns, and number of intersections), trip attributes (time of the day, day of the week, home based versus non home based), and traveler attributes (gender, length of stay at current residence, etc). The models are applied on a validation sample and the predicted routes are com pared to those obtained from predictions using travel time as the only criteria. The primary source of data for this study is the GPS component (in vehicle GPS data only) of the Chicago Regional Household Travel Inventory (CRHTI). In this survey, a GPS data logging device (GeoLogger) was used to record the date, time, latitude, longitude, speed, heading, altitude, number of satellites, and horizontal dilution of precision (HDOP) at 1 second intervals. Original data comprises of GPS streams for 9941 auto trips made by 408 household vehicles. After eliminating trips shorter than 5 minutes in duration and 2 miles in distance, the sample consists of 5294 auto trips. However, the trips with unique OD pairs were retained for the final sample. The two map matching algorithms generated routes for 3885 t rips. After mapping the person demographics and trip characteristics, the sample comprised of 2850 trips. However, with available computational resources and time, choice sets were generated for 2143 trips. Further, 1 913 trips which had at least 15 alternatives in the choice set were included for the model estimations. Additionally, GPS data were also collected by the resea rchers (also using the GeoLogger) in Orlando, FL. A vehicle with a GPS device mounted was driven on different routes to include most of the complex scenarios such as dense urban areas, parallel streets, junctions, and ramps. The collected GPS data comprise s of about 33 trips (37214 GPS points). As vehicle was driven on known routes, results from the map PAGE 15 15 matching process can be verified manually and algorithm efficiency can be evaluated in terms of percentage of correctly identified links. Apart from GPS tr acks of vehicle trips, a high resolution ( presence of local roads and more attributes ) GIS compatible roadway network for the study area was obtained from ArcGIS Data and Maps from ESRI. This GIS layer has information on speed, functional classification, and distance of most links in the roadway (including local streets). Additionally, GIS compatible sub zone and land use layers for the area were also obtained from the Chicago Department of Transportation (DOT). 1.2 Structure of the Dissertation The rest of th is document is organized as follows. Chapter 2 presents a review of the studies related to map matching, choice set generation, route choice models. Chapter 3 describes the map matching algorithms used for generating observed routes. Both conceptual and im plementation details are presented in the chapter. Chapter 4 presents a validation of the map matching algorithm, and subsequently, the results of the application on a large dataset are discussed. Chapter 5 provides the assembly process of the estimation d ataset. The conceptual framework of the choice set generation algorithm is also presented in the chapter. At the end, data descriptive are presented. Chapter 6 presents the route choice models developed in the study and discusses the estimation results. In the end, Chapter 7 presents the summary and conclusions of the study. PAGE 16 16 CHAPTER 2 LITERATURE REVIEW While GPS based travel surveys collect data on vehicle trajectories, these data have to be processed substantially to be transformed into a format that can be used for model estimations. There are two major steps in this processing: Map Matching and Choice Set Generation. Map matching matches a stream of GPS points to a roadway network database to identify the traversed links in the chosen route. Once the c hosen route is determined, choice set generation methods are used to determine possible alternatives that could have been considered by the decision maker. The data on the chosen route and the choice alternatives are then merged with other available inform ation such as trip and traveler characteristics for model estimations. The next t hree sections provide an in depth review of the existing studies i n the areas of map matching, choice set generation and route choice modeling Each section ends with a short discussion of the contribution of this study. 2.1 Map Matching 2.1.1 Overview The map matching can be used for either online or offline t racking of vehicles. Online map matching aims to locate the current position of the vehicle on the network. Therefore, an essential requirement, of the algorithm is to match every GPS point to the link. Moreover, as vehicle location is tracked in real time, a computationally efficient algorithm is desired. On the other hand, offline map matching is focused on determining a ro ute given a GPS trace. This is the approach required to generate data for route choice modeling. In this case, it is not necessary to match every GPS point to a PAGE 17 17 roadway link and the computations need not be accomplished in real time (Yin and Wolfson, 2004) A summary of the map matching related empirical studies is provided in Table 2 1 This table is intended to serve as a broad overview. The methods and findings from these studies are discussed in detail in the next two sub sections Prior to proceeding with a detailed discussion, i t is also useful to acknowledge that the focus of this study is on the modeling of route choice decision using cross sectional (one day) GPS travel survey data which involve high frequency GPS trac ks. Therefore, understanding the route choice dynamics (both day to day variations and changes in choices en route) using multi day GPS data is beyond the scope of this work (See for example L i et al., 2005). Similarly, map matching of low sampling rate GP S tracks, usually collected through mobile technology (for eg. Eisner et al., 2011; Lou et al., 2009) to a high resolution roadway network is also not explored in detail PAGE 18 18 Table 2 1 Map matching related empirical studies Study Dataset Methodology Chosen r oute On line Methods Velaga et al. (2009) Three pre defined routes: two in urban areas and one in a suburban area Online map matching Weight based topological map matching GPS points to links Used heading, proximity, and two weights for turn restrictions at junctions and link connectivity Two consistency checks For urban areas, 96.8% and 95.3% and for suburban area 96.71% of the total links were correctly identified Quddus et al. (2003) A test vehicle with a GPS receiver was driven on a carefully chosen route in London Online map matching Used network topology, vehicle heading and speed information Matches GPS points to the links An efficient method in particular for conditions such as junctions and intersections Off line Methods Chung and Shalaby (2005) 60 multimode trips including 24 auto trips in Downtown, Toronto Approach by Greenfeld (2002) GPS points to links Used network topology Distance and azimuth between GPS points and network links Visual inspection 78.5% corre ctly for all modes 86% for autos Tsui and Shalaby (2006) Transit system Method by Chung and Shalaby (2005) Additionally, introduced interactive link matching sub system to improve efficiency Du (2005) 674 trips on 18 known routes in Lexington, KY Shortest path satisfying network topology Visual inspection, 95% routes constructed entirely Griffin et al. (2011) In a 70 square mile geographical area surrounding Wichita Falls, Texas 200 routes Used driving directions (DD) services from web service provides to get the initial route by providing way points, shortest path Set of rules to remove troublesome points Manual inspection required to identify troublesome routes Visual inspection confirmed a 100% accuracy Significant amount of time is spent to identify problematic routes. Spissu et al. (2011) 697 trips A geometric map matching in ArcGIS Manual intervention is required Matched only 58% of the trips (393 routes) Reasons: missing GPS points, missing links in the network etc. PAGE 19 19 Table 2 1 Continued Study Dataset Methodology Chosen r oute Song et al. (2010) 12 trips in Osaka city, Japan A pipeline approach Data filtering to obtain high quality trajectories Two curve to curve based map matching algorithms based on Hausdroff distance and Frechet distance Frechet distance performs better but with high run time Marchal et al. (2005) 84 paths collected in the Zurich area Multiple hypothesis technique GPS points to link Used network topology Multiple paths are stored and the best path with a lowest score is chosen In most of the cases, no continuous routes because of irregular GPS streams Schssler and Axhausen (2009) 3932 car stages with 2.4 million GPS points High resolution swiss network with 408,636 nodes and 882,120 links In all, 250 OD pairs Multiple Hypothesis Technique Follow the sequence of GPS points Matches GPS points to the links Several route candidates are kept in memory Maximum saved paths between 20 and 40 Very low matched routes Main reasons: Missing links in the network, Off network travel, U turns No validation Menghini et al. (2010) 3387 bike stages and 2498 unique OD pairs Algorithm by Schssler and Axhausen (2009) Zhou and Golledge (2006) A test run with a single GPS trace Multiple hypothesis technique with rank aggregation Matches GPS points to the links Combination of Accumulated 2 norm distance and rotational variation metric to decide the ranking of the candidate paths Performance is comparable for small candidate size and large network PAGE 20 20 2.1.2 On line Methods The reader is referred to Quddus et al (2007) for an in depth review of the existing online map matching algorithms. In this study, the algorithms are c lassified as generic map matching (point to point, point to curve, curve to curve, and road reduction filter (RRF)), topological map matching, probabilistic map matching, and advanced map matching. The constraints and limitations were identified in terms o f initial map matching process, problems at Y junctions, consideration of road design parameters, height data, spatial road network data quality, and validation. Zhou and Golledge (2006) empirically examined algorithms from both categories, online and of fline: weight based map matching by Yin and Wolfson (2004), fuzzy logic based map matching by Syed and Canon (2004) and General map matching by Quddus et al (2003). The examination of the online map matching algorithms indicated that such algorithms, occa sionally, incorrectly select cross streets and also, a fast moving vehicle could cause ignoring a short link. A recent study by Velaga et al (2009) focused on improving the performance of on line map matching algorithms at junctions and intersections. A s imple and efficient weight based topological map matching algorithm is proposed, which, in addition to heading and proximity, uses two new weights for link connectivity and turn restrictions at junctions. An optimization process was introduced to calculat e the relative importance of the weights. The algorithm minimizes the mismatches by using two consistency checks. The algorithm was validated against three routes in different areas (dense urban and suburban) and in all, identified 95% 97% of the links PAGE 21 21 2.1.3 Off line Methods The on line methods could be potentially applied in the case of off line algorithms as well It is useful to note that off line algorithms have benefitted from the literature on on line algorithms in terms of improved computational times and efficiency. For instance, Chung and Shalaby (2005) modified the online map matching algorithm by Greenfeld (2002) to create an offline map matching tool using the ArcGIS platform. Additionally, the algorithm minimized matching errors with the help of topological information of the roadway map and distance and azimuth between GPS points and road links. The tool was evaluated for 60 multi mode trips and was able to identify 78.5% (for all modes) and 86% (for auto) of the traversed links correctly. Howeve r, the developed tool was unable to find a roadway segment if GPS tracks were missing. Another application (limited to transit trips) of the algorithm by Chung and Shalaby (2005) was demonstrated by Tsui and Shalaby (2006). They integrated GPS and GIS to d evelop an automatic process, which processes GPS based personal travel survey data. Additionally, an interactive link matching subsystem was introduced to further improve results of the previous link identifications. In the context of route choice modeling broadly two types of off line map matching methods are examined empirically: shortest path based, and multiple hypothesis technique based. The respective empirical studies are discussed in the next two sub sections. Shortest path Zhou and Golledge (2006) suggested that offline algorithms use optimization techniques such as the shortest path to generate a topologically correct route and to exploit roadway attributes, such as speed limits, one way streets for better accuracy. PAGE 22 22 These s uggestions are also in line with the work undertaken by Du (2005) who proposed a method that predicts the chosen route by determining the shortest path satisfying network topology such as link location, connectivity, one ways, and allowable u turns. The me thod was implemented in ArcGIS and examined against 674 trips collected on 18 known routes of Lexington, KY. For a known OD pair, approximately 95% of the routes were constructed entirely. However, high computational times and manual interventions are also characteristic features of this study. In a recent study, Griffin et al (2011) demonstrated another way to use shortest path for path creation. First, an initial route was obtained by inputting selected GPS points to a driving directions (DD) service, of fered by web service providers such as MapQuest, Yahoo, and Google. The DD service calculates the shortest cost path for the input GPS points. After obtaining the initial route, problematic waypoints were identified using a set of rules that includes point distance, bearing, path ratio, and duplicate points. The revised set of waypoints was then resubmitted to DD services and a correct map matched route was obtained. Algorithm was tested against a real world GPS data for 200 routes and a visual inspection o f the routes confirmed an accuracy of 100%. However, the method involved spending a large amount of time in identifying problematic routes manually. Similar drawbacks (manual methods for correcting for map matching errors) were observed in the method used by Spissu et al (2011). First, a spatial join was used to match the GPS points to the corresponding routes, and afterwards a manual inspection corrected the matching errors. The method was run for 697 trips and it found routes only PAGE 23 23 for 58% of the trips. U nmatched trips were due to missing GPS points, inconsistent activity data and missing links in the roadway network. The map matching methods based on shortest path show limitations related to the involvement of a manual step. To eliminate manual interventi ons from the map matching process Song et al (2010), proposed a pipeline approach, which matches vehicle trajectories to the network by processing several sequential stages. The data filtering and the map matching stages we re chained in a pipeline mode t o get the traversed links The data filleting stage involved two levels of filters: primary and advanced. In the primary filter measures such as horizontal dilution precision (HDOP), fix type, and n umber of satellites we re used to filter out the erroneous GPS points. The advanced filter utilized the information of velocity, angular velocity and heading changes to further detect incorrect GPS points that may ha d not bee n filtered in the primary filter. To match the GPS points to the roads in the network, two curve to curve distance measurement algorithms are used: Hausdroff distance and Frechet distance. The two distance measurements are applied to estimate the similarity between the trip trajectory and the roads in the network. The Hausdroff distance takes the intersecting angle, and the parallel and perpendicular displacements between two segments into consideration. The Frechet distance takes the location and ordering of the points into consideration. Afterwards, the link s with minimal distances are included in the route. The two approaches were tested for 12 trips, collected in the urban areas of Osaka city, Japan. Results indicated better link identification accuracy for Frechet distance but with high er run time. Hausdroff distance was faster but showed a tendency of selecting wrong links. PAGE 24 24 Multi path To improve the efficiency of a map matching process Marchal et al (2005) proposed an algorithm that uses a multiple hypothesis technique (MHT), which was first introduced by Pyo et al (2001) for the application of on line map matching. The MHT stores multiple paths during the process and in the end selects a path with the best score. Marchal et al ance of the link to the GPS point. The algorithm starts with finding a set of links that are closest to the first GPS point. For each link, a new path is created and links are inserted with their scores assigned to the respective paths. GPS points are proc essed in order (time sequence) and a path score is updated by adding the score of the last added link to its previous score. When the end of a link is reached, a copy of the path is created for each outgoing link and then the path is removed from the set o f paths. In the end, the path ( in the set of paths ) with the lowest score is selected as the traversed path. Algorithm limits correctly identified links; instead focus was given to the operational performance using a real world data of 84 paths collected in the Zurich area. The authors argued that the accuracy and the running time are dependent on the maximum number of candidate links/ paths stored in the set. However, the routes in most cases, which the authors reasoned are because of irregular GPS streams caused by tunnels, tree canopies, poor signal, and so forth. As a result, a sequence of paths was generated instead of a continuous route. The authors also added that algorithm is sensitive to outliers in GPS data. PAGE 25 25 Schssler and Axhausen (2009) modified the original algorithm by Marchal et al (2005) to overcome their limitation of not producing a continuous route. Additionally, a mod ified method was used to calculate a score. First, they subdivided each trip into continuous segments depending on the gaps in GPS streams. Afterwards, they created the trip segments by using the algorithm by Marchal et al (2005). Then, a complete trip wa s obtained by connecting trip segments through a shortest path search with a treatment for low quality map matching results. During the study, 3932 car trips encompassing 2.4 million GPS tracks were matched to a high resolution Swiss NAVTEQ roadway network The results showed a smaller number of matched routes in comparison to the total routes. Further investigation of the results showed three main reasons for such low numbers of matched routes: missing links in the roadway network, off network travel, and u turns. Menghini et al (2010) applied the algorithm, developed by Schssler and Axhausen (2009), to match 320, 576 GPS points of 3387 bike trips, also extracted from the same data source. However, they encountered errors for cases of missing good point f low and a dense scatter of points. Zhu and Golledge (2006) used the MHT with rank aggregation and proposed a three step map matching algorithm. Prior to the map matching, GPS data was processed for cluster reduction and density leverage. After map matchin g results, a Dempster belief test was used to detect the noise and off road travel. A combination of accumulated 2 norm distance and rotational variation metric was used to decide the rankings of the candidate paths. The author did not apply the algorithm to real world data. PAGE 26 26 2.1.4 Summary Based on a review of the literature, there are two broad classes of algorithms for map matching (off line map matching of high frequency GPS streams): The GPS weighted shortest path algorithm (GWSP) and the multi path algorithm (MP). The GWSP algorithm directly uses the concept of shortest path in determining the route. However, the links that are not close to observed GPS points are provided higher impedances (making them less likely to be included in the shortest path) than t he links that are near observed GPS points (these links have the true travel times/costs as impedances). The MP algorithm does not use the concept of shortest paths; rather, it traces though the stream of GPS points identifying all the possible routes to r each the destination from the origin. The GWSP algorithm is more straightforward and computationally less demanding (especially if a tool for calculating shortest paths is available) whereas the MP algorithm is more elaborate and demanding (the need to sto re multiple paths can get cumbersome with dense networks). However, the latter algorithm is also free from assumptions such as preference for shortest paths and generally uses the observed data to determine the route. A comparative analysis of these approa ches would therefore be of interest and this study contributes towards that end. Enhanced versions of both GWSP and MP algorithms are implemented and compared. The enhancements are aimed at achieving complete automation and better operational performance. Both algorithms are implemented in ArcObject within ArcGIS framework, using Python and Visual Basic Application (VBA ). PAGE 27 27 2.2 Choice Set Generation 2.2.1 Overview Once the chosen route has been determined, the next step is to determine the set of alternate paths availa ble for the same trip. The universal choice set contains all possible paths between an OD pair. However, it is impossible for a traveler to be aware of all the paths in the universal choice set. Further, this universal choice set would contain high number of unattractive and unrealistic routes that a traveler would never consider during the decision making. The inclusion of these unrealistic routes in a choice set would put an extra burden on computation time and also affect the model estimations. Therefore universal choice set and contains only feasible and attractive paths. Bovy (2009) defined this choice set as the collection of travel options perceived as available by individual travelers in sat isfying their travel demand. Since the surveys do not directly ask the respondents to provide information on the options available/considered, the choice sets have to be determined using the roadway network characteristics and reasonable behavioral rules. Various restrictions are applied to ensure that the number of options in the choice set is reasonable and the options themselves are somewhat different from each other. A summary of studies related to choice set ge neration is provided in Table 2 2 in reve rse chorological order. This table is intended to serve as a broad overview. The methods and findings from these studies are discussed in detail in subsequent sections. PAGE 28 28 2.2.2 Methods In general, the choice set generation approaches can be classified into three c ategories: (1) shortest path based methods, (2) constrained enumeration methods, and (3) probabilistic methods. PAGE 29 29 Table 2 2 Choice set generation related empirical studies Study Dataset Methodology Choice s et Schussler et al., 2012 On person GPS data 36,000 car trips by 2,434 persons Breadth first search link elimination Compared with stochastic Choice set size: 20 100 routes Spissu et al., 2011 GPS data from smart phones All purpose 393 observed routes Two leg survey of 1 week each Min cost algorithm through existing Cagliari model with cost function of time and distance Observed route and last 10 min cost paths from the simulation Quattrone and Vieteatta, 2011 Road side survey (280 chosen routes) of trucks compared with on board GPS (52 routes) trips k shortest path Combination of 5 criteria 30 routes Overlap of 75% chosen routes Papinski and Scott, 2011b GPS data Home based Work Trips In all 237 trips Shortest path using Potential path area (PPA) concept k shortest pat h algorithm k shortest path generates only 52 out of 237 chosen routes Pillat et al., 2011 GPS sensor smart phones Home to work Analysis 300 participants total 18,300 trips with 61 trips per person Personal interview for known routes by clicking link by link on a digital map Path enumeration Parameters were estimated by using known routes from the questionnaire Replicates 60% of the actual chosen routes Maximum allowed commonly factor of 0.90 Menghini et al., 2010 GPS data 3387 bike stages Breadth first search algorithm Frejinger et al., 2009 Synthetic Data A network with 38 nodes and 64 links Probabilistic Method with Random Walk Algorithm Bekhor and Prato, 2009 From two previous studies, Ramming 2002 and Prato 2005 228 observations in Turin, Italy dataset and 181 observations in Boston dataset Labeling, Link elimination, Link penalty, Simulation, and Branch and bound Prato and Bekhor, 2006 Prato and Bekhor, 2007 No GPS data Home to Work Analysis Web based survey of faculty and staff members Chosen routes and possible alternatives 236 routes, 339 possible alternatives and 182 different ODs Branch and Bound Compared with other three: Labeling (4 labels) Link Elimination (10 iterations) Link Penalty (15 penalties) Simulation (25 and 35 draws) For BB, median size 17 and maximum of 44 routes Merged choice set with median size of 32 and maximum 55 routes PAGE 30 30 Table 2 2 Continued Study Dataset Methodology Choice s et Bierlaire and Frejinger, 2005 GPS data Road network with 3077 nodes and 3843 links 1282 observed routes with 927 OD pairs Simulation method Truncated normal distribution with 20 draws Mean and variance based on the observations The observed route is inserted to the choice set Average of 9.3 routes Maximum 22 and min 2 Ramming, 2002 No GPS data Home to Work Analysis Questionnaire survey 188 observations Labeling (16 labels) Link Elimination (2 49 unique paths) Link Penalty (3% for origins that are close to MIT, 5% for most distant ones and 4% for remaining) Simulation (4 8 draws Gaussian distribution with mean and standard deviation from the model of travel time perception) Median of 30 routes Maximum up to 51 routes 160 routes met 80% overlap criteria Ben Akiva, 1984 Labeling method 10 labels Time, distance, scenic, signals, capacity, hierarchical travel pattern, quality of pavement, commercial dev., highway, congestion Time and distance reproduce 70% of the chosen routes All labels together reproduce 90% In the end, 6 labels Time and distance are most effective Signa ls fails to be a significant factor Factors other than time and distance plays effective role PAGE 31 31 Shortest path based methods Shortest path based approaches are the most popular and commonly used methods in the literature. For a given generalized cost, this method repeatedly searches for the alternate shortest cost path in the network. The search for the shortest path can be approached in two ways: deterministic and stochastic. Deterministic shortest path based methods : T he popular algorithms in t he deterministic shortest path based methods in clude k shortest path, labeling, link elimination, and link penalty K shortest path algorithms extend the idea of calculating a single shortest path (e.g. Dijkstra, 1959) to determine k shortest paths for a generalized link cost function. Recently, Papinski and Scott (2011 b ) generated the choice sets by calculating 9 shortest time paths for a GPS dataset of 237 home based work trips collected for auto drivers in Halifax, Nova Scotia, Canada. Spissu et al. (20 11) calculated 10 minimum cost paths with cost function provided by the existing Cagliari model. Over the years, researchers have introduced several variations to the basic approach of finding k shortest paths while maintaining the same computational effic iency. Kuby et al. (1997) construct the choice sets by, iteratively, selecting routes from a subset of k shortest paths that satisfy a similarity measure, whereas Van d er Zijpp and Fieorenzo Catalano ( 2005 ) find feasible paths satisfying some behavioral co nstraints. Instead of calculating multiple shortest paths for one cost, labeling approach finds one optimal path for several costs or attributes or labels. The n umber of paths in a choice set is equal to the number of labels considered. Ben Akiva et al. (1984) proposed the approach and generated routes for 10 labels that include time, distance, PAGE 32 32 scenic, signals, capacity, hierarchical travel pattern, quality of pav ement, commercial development, highway distance, and congestion. Routes with only two labels, time and distance, replicated 70% of the chosen routes and routes with all labels together replicated 90% of the chosen routes. The s tudy found signals not being a significant factor and concluded that factors other than time and distance do play a significant role in route choice. Ramming (2002) used more attributes (e.g. time in secure neighborhood, tolls, left turns, free flow time), total 16 labels, to generate paths for 188 observations (91 OD pairs) collected through a web based survey of faculty and staff of Massachusetts Institute of Technology ( MIT ) Boston. For 236 trips (182 OD pairs) from another web based survey conducted in Turin, Italy Prato and Bekh or (2006) (also Prato and Bekhor 2007) determined paths by using 4 labels distance, free flow time, travel time, and delay. Bekhor and Prato (2009) compared the two datasets, Boston and Turin, by using labeling approach with 5 labels: distance, free flo w time, delay, traffic lights, and traffic lights. Quattrone and Vieteatta, 2011 examined data from a road side survey of truck drivers and generated 30 routes for each of the 5 costs: minimum travel time, minimum monetary cost, maximum motorway route, min imum bridges and viaducts, minimum routes with high levels of accidents. The generated routes overlap 75% of the observed routes. Link elimination a pproaches, presented by Azevedo et al. (1993), iteratively search for the next best path by removing one or more links from the shortest cost path. Bekhor at el. (2006), Prato and Bekhor (2006), Frejinger and Bierlaire (2007) calculated multiple alternate paths by using 50, 10 and 15 iterations respectively. Using this approach, Ramming (2002) obtained up to 49 unique routes. Schussler e t al. (2012) proposed a PAGE 33 33 variation to the approach, called as breadth first search link elimination (BFS LE). It starts with calculating a shortest cost path between origin and destination and searches for the next shortest path by removing links. The resulting shortest paths are set as the starting points, nodes, for next iteration, depth, of link elimination. All nodes at a depth are processed before moving to the next depth. They also proposed two performance optimization methods : a randomization of links at a depth and a roadway topology simplification. More details of the method are provided in the methodology section. Menghini et al. (2010) implemented the BFS LE approach for route choice of cyclists in Zurich, Switzerland. Lin k penalty approaches, introduced by De la Barra et al. (1993), also iteratively determines multiple shortest paths. However, instead of removing links a penalty is imposed on impedances of the links in the current shortest path. Studies have used several m ethods of determining link penalties. Park and Rilett (1997) increased penalties only to the links that are outside a certain distance from the origin and destination of a trip. The variation resulted in less similar and more relevant routes. Scott et al (1997) incorporated an optimization program to determining the penalty factor. Bekhor et al. (2006) defined penalty as the function of distance between origin and destination, therefore, introducing higher penalty for longer routes. Prato and Bekhor (2007) used a fixed penalty factor and iterated the process 15 times. Stochastic shortest path based : These approaches assume that the path costs simulation approach the error is represented by drawing generalized cost functions from probability distributions. Ramming (2002) analyzed home to work commute and PAGE 34 34 extracted 48 draws from a Gaussian distribution with mean and standard deviations to equal to link travel times. Beirlair e and Frejinger (2005) extracted 20 draws from a truncated normal distribution with mean and variance equal to link travel times from the observed data. Average choice set size was 9.3 with maximum and minimum 22 and 2 routes respectively. Prato and Bekhor (2006), Prato and Bekhor (2007), and Bekhor and Prato (2009) implemented two simulation approaches exploiting the same procedure to draw impedances. Twenty five and 35 draws were extracted from a truncated normal distribution with mean equal to travel tim e and variance equal to a percentage of the mean, 20% and 100% respectively. Left truncation limit was set equal to the free flow time and right truncation limit was equal to the travel time calculated for a minimum speed assumed equal to 10 km/hr. Schussl er et al. (2012) draw impedances from a truncated normal distribution with mean equal to travel time and standard deviations equal to different multiples of travel time. The Doubly stochastic method, proposed by Bovy and Fiorenzo Catalano (2007), is an ext ension to the simulation approach where generalized cost functions are in the form of utilities with both the parameters and the attributes are stochastic. Clearly, the use of stochastic shortest path methods requires information on the (perceived and real ) variability of travel times on the roadway network, which may not always be readily available. Constrained enumeration methods Constrained enumeration methods construct choice sets using a set of constraints that reflect cognitive, perceptual, behavioral assumptions. Pillat et al. (2011) proposed a method with path enumeration and branch cutting criteria. The method included a commonly factor criteria within the generation process to keep the choice set size PAGE 35 35 computable and to avoid routes with higher deto ur factors. The commonly factor (CF) calculates the overlap between two routes in terms of distance and is calculated as Where is the common distance of route and route ; is the distance of route and is the distance of route For the route tree, origin is the source of tree and branches are the routes in the network. Branch cutting criteria are used to control detour factors in the route and checked for every new node added as a branch element to the route tree. Parameters of the allowed impedance functions, used to apply detour factors, were estimated using the information on known alternative routes collected during the survey. The final choice set produced reasonable routes and replicated 60% of the observed routes which au thors considered promising given the uniqueness of the trip observations. Prato and Bekhor (2006) introduced Branch and Bound algorithm that enumerates paths by constructing a tree connecting origin and destination of a trip. A set of constraints, such as directional, temporal, loop, similarity, and left turn are satisfied while processing sequence of links to generate the tree. Friedrich et al. (2001) and Hoogendoorn Lanser (2005) applied the branch and bound method for transit network and multimodal netwo rk context respectively. Bekhor and Prato (2009) also used the approach for his comparative study of two datasets: MIT, Boston and Turin, Italy. Probabilistic methods In contrast to the deterministic methods, where an alternative either belongs to a choice set or not, probabilistic methods, fi rst proposed by Manski (1977), also represent intermediate availabilities by assigning perceived probabilities to routes. This set of PAGE 36 36 approaches relies on the assumption that all routes connecting origin and destinatio n belong to the choice set to some degree. Cascetta and Papola (2001) construct fuzzy choice sets with the proposed Implicit in terms of continuous values ranging f rom 0 to 1. Ramming (2002) applied IAP logit with variables related to network knowledge but obtained results we re not satisfactory. Frenjinger ( 2007 ) and Frejinger et al. ( 2009 ) extract a subset of paths with importance sampling approach, which selects at tractive alternatives with higher probability. For an OD pair, the probability of each link in the network is calculated based on its deviation from the actual shortest path. Therefore, links on the actual shortest path have a link probability of 1 and oth er links between 0 and 1. Next, a repeated random walk method, starting at the origin, selects and adds links from node to node until destination is reached. The link selection process at a node is determined by the associated next is approach was applied to a synthetic network with 38 nodes and 64 links and positive results were obtained confirming the superiority of models with sampling corrections than others with no correction 2.2.3 Comparative Assessment Measures for choice set compo sition The discussion thus far focused on methods to generate alternate paths. Next we focus on metrics used to assess the quality of the generate choice sets. Different guidelines are used to assess the structure and quality of the generated choice set or the effectiveness of an algorithm. Typically choice set size (Richardson, 1982; Prato and Bekhor, 2006) and coverage of the observed routes are used to evaluate the choice set composition. Bekhor et al. ( 2006 ) define coverage as the share of observations for PAGE 37 37 which an algorithm produced a route that meets a particular threshold of overlap. Where, the overlap is usually the percentage of the observed route distance. In addition to coverage, Prato and Bekhor (2007) and Prato and Bekhor (2007) calculated a co nsistency index that compares a choice set generation method with the ideal algorithm that would reproduce all the observed routes. Schussler et al. (2012) used four measures to assess the structure of the choice set: choice set size, reproduction of the o bserved route (coverage), route diversity, and hierarchical sequence. The route diversity determines how different the routes are in the choice set. Two indicators are used for the measure: overlap among the routes and d istribution of the route distances. The hierarchical sequence focuses on the shares and sequences of the road types. Comparison of Methods A number of studies have compared choice set generation methods in terms of computational performance and efficiency. Papinski and Scott (2011 b ) compared two choice set generation algorithms using a sample of 237 home based work trips. The first algorithm is a constrained enumeration method. A potential path area (PPA) was defined for an OD pair. Nine links were randomly selected as the midpoints for each alternate route within the PPA. For each midpoint link, a shortest path based on time is found through from the origin (home) to midpoint link to destination (work). The second algorithm (k shortest path) calculates nine shortest time paths for a n OD pair. Constrained enumeration method performed better than the k shortest path, thus emphasizing choice do not depend only on the travel time. PAGE 38 38 Ramming (2002) (also, Bekhor et al., 2006) examined four choice set generatio n algorithms: labeling, link elimination, link penalty, and simulation. Computational time for link penalty approach was high considering the small number of routes generated in the choice set (also, see Prato and Bekhor, 2007). The high computation time w as a result of rewriting the changes the link impedances back to the network. However, as Prato (2009) stated, in link penalty approaches, the value of penalty factor plays a crucial part. While low penalty may result in very similar routes, high penalty m ay produce undesirable routes. For link elimination, Ramming (2002) was not convinced that agreed with it, and pointed out that the major shortcoming of the link eliminati on is the network disconnection, as removing centroid connectors and major crossing does not promise a new route between origin and destination. Also, removing a link, generally, introduces only a short deviation from the previous route and the generated r outes are somewhat similar. Ramming (2002) found that labeling approach was the fastest and three labels distance, free flow time, and time provided enough coverage. Simulation approach, 48 draws from a Gaussian distribution, was easy to implement and showed acceptable computational performance. The final choice sets were constructed by merging routes from the labeling (distance, free flow time and time) and simulation approach. The final choice sets consist of maximum 51 routes and a median size of 30 routes. Prato and Bekhor (2006) (also, Bekhor and Prato, 2009, and Prato and Bekhor, 2007) expanded the comparison by Ramming (2002) with an inclusion of branch and bound approach. Among all the algorithms, branch and bound showed higher PAGE 39 39 consistency index (97.1%) and coverage (up to 97%). Therefore, two choice sets were constructed during the study; first, merging routes from different algorithm, and second, routes from branch and bound algorithm. First choice set contained maximum of 55 routes with median size of 32 routes. Second choice set contained maximum of 44 routes with median size of 17 routes. Comparison of two choice sets indicated a better performance and more heterogeneous routes from branch and bound approach. Based on the recommendations of pr evious studies, Schussler et al. ( 2012 ) selected three algorithms that have performed well and promised to produce realistic routes: stochastic, branch and bound (BB), and constrained random walk (CRW). Additionally, they proposed a breadth first search li nk elimination (BFS LE). Before, implementing the BFS LE approach, they compared the computational performances of the four algorithms on a smaller sample of 500 OD pairs, representative of the main sample. BB and CRW demonstrated long computational times even for small alternatives and short paths. Each of the two algorithms was run for 17 days with a any route for 229 OD pairs and for 161 OD pairs it found only one ro ute. However, CRW found at least 5 routes for 466 OD pairs. High computation times and smaller choice set sizes discourage the use of these algorithms for the application of high resolution networks. Similar concerns were raised by Prato (2009), who observ ed that the computational performance of the branch and bound approach highly depends on the depth of the tree and thus, on number of links in the paths. With this, the author anticipated that the application of the algorithm would be limited to small netw orks. The author also suggested that the routes generated with random walks approach may be PAGE 40 40 very circuitous, contain loops and extremely long since they do not reach the destination in a reasonable number of stops, thus not making the method suitable for e stimation and prediction purposes. Duri ng the study by Schussler et al. ( 2012 ) stochastic and BFS LE methods showed considerably better results in terms of computation time and number of alternatives. The two algorithms, stochastic and BFS LE, constructed the choice sets for 500 OD pairs in 12 days and 7.1 days respectively. The authors further compared the computational efficiency of these two methods and found that, on average, computation time for stochastic method was 32 times higher than the BFS LE me thod. As pointed out by Prato (2009), efficiency of stochastic/ simulation approach depends on the selection of probability function and number of draws. The popular distribution includes normal, log normal, gamma etc. Perceived cost being non negative res ults in truncating negative draws in the normal distribution. However, truncation may lead to biases towards certain routes (Nielsen, 2000). Log normal and gamma distributions guarantee non negative draws (Nielsen and Frederiksen, 2006), and thus preferred Higher number of draws results in increasing computation cost considerably, and do not necessarily generate higher unique routes (Ramming, 2002). Prato and Bekhor (2006) experimented with number of draws and variance of the distribution. They found that both low and high variances are not efficient as former results in fewer unique paths and later produces several unrealistic paths. Prato (2009) also highlights the shortcomings of the doubly stochastic method in the calibration of the probability function coefficients and indicated that the use of incorrect values could lead to unrealistic routes. PAGE 41 41 Schussler et al. (2012) observed that the percentage of reproduced chosen routes from BFS LE was higher than the results of the simple link elimination method, p resented in the studies by Ramming (2002) and Prato and Bekhor (2007). The authors argued that for high resolution networks repeated shortest path search algorithms are more feasible and perform the best. The proposed BFS LE method produce d better results than the basic link elimination method and outperforms the stochastic method in terms of computational efficiency. 2.2.4 Summary Based on the discussion so far and the nature of our dataset, we decided to implement an enhanced version of the BFS LE algorithm to generate choice sets for large number of trips in a high resolution network. The enhancements aim to address computational efficiency and the need to generate heterogeneous routes. Specifically, considered for elimination. It is also ensured that any new route generated does not substa ntially overlap with any of the route alternatives already generated. The algorithm is applied to generate route alternatives for over 2000 trips on the dense Chicago roadway network. 2.3 Route Choice Models 2.3.1 Overview The random utility discrete choice models are the most commonly used approach for analyzing route choice decisions. Such models assume that the utility of an alternative consists of two components: deterministic and stochastic. Specifically, the utility of alternative in the choice set per ceived by individual is give by: PAGE 42 42 Where, is the deterministic or observed component, and is the stochastic or unobserved component. For choice modeling, logit based models are most commonly used. Among the family of logit models, the Multinomial Logit Model (MNL) is the simplest one. For the MNL model, the probability of choosing an alternative in choice set is given by: The MNL model is based on the assumption of Irrelevance of Independent Alternatives (IIA), and therefore, does not consider the similarities between alternatives. The similarity of a route with other alternatives may aff ect the utility of choosing the route and is needed to be accounted in the choice models to have a more realistic representation of the travel behavior. Several models have been proposed in the literature to overcome the limitation of the MNL model. The n ext section presents a br ief description of such models ( for further discussions, refer to Prato, 2009). 2.3.2 Models The computational benefits of the simple closed form MNL model structure have encouraged researchers to propose MNL modifications to capture th e similarities among routes. The modifications are either made in the deterministic or the stochastic part of the utility. Methods that modify the deterministic part of the utilities include the C logit, the Path Size Logit (PSL), and the Path Size Correc tion Logit (PSCL) models PAGE 43 43 C logit : C logit model, proposed by Cascetta et al. (1996), was one of the first MNL modifications. The model introduced a term, commonly factor, in the deterministic part of the utility that measures the physical overlap of a rou te with other routes in the choice set. The commonly factor (CF) reduces the utility of a route due to its similarity with other routes. The probability of choosing an alternative in choice set is given by: Several formulations of CF are proposed in the literature (Cascetta et al., 1996, Cascetta et al., 2001): Where, is the length of route i, is the length of route j, is the length of link l, is the common length between route i and route j, is a parameter to be estimated and is the link path incidence dummy, which is equal to 1 if route i uses link l and 0 otherwise. P ath size logit (PSL) : Ben Akiva and Bierlaire ( 1999 ) proposed the PSL model and measured the similarity using a Path Size term in the deterministic component. Th e PAGE 44 4 4 path Akiva and Bierlaire, 1999). Several formulations of the Path Size have be en presented in the literature. Where, is the length of route i, is the length of link l, is a parameter to be estimated and is the link path incidence du mmy, which is equal to 1 if route j uses link l and 0 otherwise. Frejinger et al. (2009) proposed Expanded PS (EPS), which includes an expansion factor to the PS attribute that corrects for the sampling: Where, is the sampling probability of path j, and is the number of alternatives (excluding the chosen route) drawn to form the choice set. P ath size correction logit (PSCL) : Bovy et al. (2008) argued that the PS attribute in the PSL model does not have a theoretical derivation and assumptions are not clearly PAGE 45 45 stated either. In response, they proposed a Path Size Correction Logit (PSCL) model and presented a systematic derivation of the Path Size Correction term. Where, is the length of route i, is the length of link l, and is the link path incidence dummy, which is equal to 1 if route j uses link l and 0 otherwise. Models that account for similarities in the stochastic part of the utility (error correlations) while still maintaining a closed for m formula for probabilities fall in the family of Generalized Extreme Value (GEV) models. Such models include Paired Combinatorial Logit (PCL), Cross Nested Logit (CNL), and Generalized Nested Logit (GNL). Paired combinatorial logit (PCL): The model assume s that choice decisions are made from pair of alternatives in a choice set. Prashker and Bekhor (1998) provided a formulation of PCL model in route choice context: PAGE 46 46 Where, is the conditional probability of selecting route i provided that the pair (i,j) is chosen is the unobserved probability of selecting the pair (i, j), and is the similarity coefficient between i and j. Two different formulations of the similarity coefficients are provided in the literature: by Prashker and Bekhor (1998), and by G liebe et al. (1999). The two formulations are presented below in respective order: Where, is the length of route i, is the length of route j, is the common length of route i and route j and is a parameter to be estimated. Cross nested logit (CNL) : The model assumes that choices are made within nests. In route choice context, the nests correspond to the links in the choice set (Prashker and Bekhor, 1998). Therefore, a route belongs to multiple nests. The choice probability is given by: Where, is the conditional probability of selecting route i in nest k, is the unobserved probability of selecting the nest k is the inclusion coefficient, is the PAGE 47 47 nesting coefficient, is the length of nest k, is the length of route i, and is the link path incidence dummy, which is equal to 1 if route i uses link k and 0 otherwise. Generalized nested logit (GNL): The model is a generalization of CNL model with the same formulation of inclusion coefficient but each nest has a diffe rent nesting coefficient. The formulation of the nesting coefficient is given by: Where, is the inclusion coefficient, is a parameter to be estimated and is the link path incidence dummy, which is eq ual to 1 if route l uses link k and 0 otherwise. Models that account for similarities in the stochastic part of the utility (error correlations without maintaining a closed form formula for probabilities fall in the class of In these models, the error terms is represented with two components. One part accounts for correlation and heteroscedasticity, and the other is i.i.d. extreme value. Such models include mixed logit, and logit kernel with a factor analytic. Mixed logit model : The mo del, also known as logit kernel (LK), assumes random coefficients. The probability of choosing route i by individual n is computed by simulation and is given by: Where, D is the number of draw s, and is d th draw from the distribution of Different coefficient distributions used in the literature include uniform, normal, log normal, and gamma distributions. PAGE 48 48 LK with a factor analytic : instead of assuming random coefficients, these models simply represent the error term with the components that accounts for similarities. Bekhor et al. (2002) provides a model, LK models with a factor analytic, which assumes that the covariance of the path utilities is proportional to the length by which path s overlap. Where, F is the loading matrix, T is a diagonal matrix of covariance parameters, and is a vector of standard normal variables A different approach of using LK model i n route choice context was presented by Frejinger and Bierlaire (2007). They proposed an Error Component model, LK model with a Subnetwork, and captured the correlations among alternatives using a Subnetwork. The Subnetwork captures the similarities among alternatives for unobserved factors even if the alternatives are not spatially overlapped. The probability if calculated by simulation and is given by: Where, is d th draw from the distribution of and D is the number of draws. 2.3.3 Empirical Studies : Methods Table 2 3 presents a summary of the empirical studies that have performed choice modeling in the route choice context. The alternate modeling methods tested by the different studies are identified in the third column. PAGE 49 49 Table 2 3 Route choice m odeling related e mpirical s tudies Study Data Route choice m odel Explanatory v ariables Frejinger et al. (2009) Synthetic dataset Expanded PS Compared with the original PSL model Length, and Number of speed bumps Schussler and Axhausen (2010) GPS data collected in Zurich with an on person GPS logger 1500 observations C logit, and PSL Time of day dependent travel times on each road types (motorway(MW), extra urban main(EUM), urban main(UM), and local road(LR)), trav el time proportions on each road type, and road type specific path sizes. Bekhor et al. (2006) No GPS data Questionnaire survey of faculty and staff at MIT, Boston Home to work 159 observations with choice sets consisting more than 1 routes Four models: MNL, PSL, and CNL (two models) Distance, free flow time, dummy variables for road sections (Mass. Pike, Tobin Bridge, and Sumner Tunnel), time spend on government numbered routes, delays for different income categories, and dummy for least distance and tim e paths Bovy et al. (2008) Two datasets from different regions, Turin (228 observations) and Boston (181 observations) Forecasting probabilities: a simple hypothetical network of a single OD pair with 12 available routes Proposed Path Size Component Logit (PSCL) model. Compared with: MNL, PSL, and PSCL Total length, travel time, % of travel time on major roads, dummy for the path with the maximum average speed, and % delay with respect to the free flow time Prato and Bekhor (2006) No GPS data Web based su rvey in Turin, Italy Home to work 236 chosen routes 339 possible alternatives 182 different ODs Six models: MNL, C logit, PSL, GNL, CNL, and LNL Level of service(distance, free flow time, and travel time), landmark dummy variables (1 or 0), and behavioral variables (habit, spatial ability, and familiarity) Bliemer and Bovy, 2008 Forecasting probabilities: a simple hypothetical network of a single OD pair with 12 available routes MNL, C logit, PSL, PSCL, PCL, and CNL PAGE 50 50 Table 2 3 Continued Study Data Route c hoice m odel Explanatory v ariables Bekhor et al. (2002) No GPS data Questionnaire survey of faculty and staff at MIT, Boston Home to work 159 observations Adaptation of the logit kernel (LK) model to a route choice situation. Compared with: MNL, and PSL Distance, free flow time, dummy variables for road sections (Mass. Pike, Tobin Bridge, and Sumner Tunnel), time spend on government numbered routes, delays for different income categories Prato and Bekhor (2007) No GPS data Web based survey in Turin, Italy Home to work 216 observations with at least 5 alternatives except the chosen route Six models: MNL, C logit, PSL, GNL, CNL, and LK with a factor analytic Level of service(distance, free flow time, and travel time for experience and non experienced d rivers), landmark dummy variables (1 or 0), and behavioral variables (habit, spatial ability, and familiarity) Frejinger and Bierlaire (2007) Borlange GPS data 2978 observations 2244 unique observed routes 2179 OD pairs Proposed an Error Component (EC) model using Subnetwork Compared five different specifications of an EC model with: MNL, and PSL Forecasting Models: 80% of the observations for the estimation, remaining 20% to validation. In all, five datasets Path size, estimated travel time, number of speed bumps, number of left turns, and avg. link length Bierlaire and Frejinger (2008) No real GPS data Reported trip dataset collected in Switzerland 780 observations Two models: PSL, and EC with Subnetwork Free flow travel time for each road types with linear time category specification, proportion of the travel time on each road type (freeway, cantonal/ nations, main, and small roads) Bekhor and Prato (2009) No GPS data Turin and Boston datasets Three models: MNL, PSL, and LK Distance, travel time, % of time on major roads, dummy for the path with max. average speed, and % of delay w.r.t. free flow time PAGE 51 51 Frejinger et al. (2009) compared two formulations of the PS attribute: original PS and expanded PS. The estimations, however using sy nthetic data, showed that the PSL model with expanded PS performs better than the original PSL model. Schussler and Axhausen (2010) compared different specifications of C logit and PSL models for choice sets of different sizes and composition. The estimati on dataset contained 1500 observations collected from an on person GPS survey in Zurich, Switzerland. Estimation results indicated that PSL model with road type specific Path Size attribute provides the best similarity treatment. Bekhor et al. (2006) compa red the PSL model with CNL model using 159 home to work observations collected through a questionnaire survey of faculty and staff at MIT, Boston. The estimations indicated that the CNL model is an improvement over PSL model and a better fit than the MNL m odel. Bovy et al. (2008) estimated PSCL and PSL models for two datasets from different regions, Turin (228 observations) and Boston (181 observations). The estimation results suggested that the proposed PSCL model is a better fit model than the PSL model. For the two models, predicted probabilities were also compared using a simple hypothetical network with 12 routes for a single OD pair. The results once again indicated the superiority of the PSCL model over PSL model. The authors recommended using PSL an d PSCL models when all the relevant routes are present in the choice set. Prato and Bekhor (2006) and Bliemer and Bovy (2008) compared different models from the families of logit and GEV models. Prato and Bekhor (2006) estimated MNL, C logit, PSL, GNL, CNL and LNL models using 236 observations (182 different ODs) of home to work route choice decisions collected through a web based survey in Turin, Italy. Bliemer and Bovy (2008) estimated MNL, C logit, PSL, PSCL, PCL, and CNL for a PAGE 52 52 simple hypothetical netwo rk of a single OD pair with 12 available routes. Both studies indicated that the CNL model captures the similarity better than other models and performed the best. However, Bliemer and Bovy (2008) also examined the impact of different choice set compositio ns and sizes on route choice probabilities, and found that none of the estimated models was robust. The models were found sensitive to the presence of irrelevant routes in the choice sets. Also, the sensitivity was higher if the irrelevant route was more s imilar to the relevant routes in the choice set. Bekhor et al. (2002) estimated LK with a factor analytic structure, MNL and PSL models using a dataset of 159 home to work observations collected through a questionnaire survey of faculty and staff at MIT, B oston. The LK model performed better than the MNL and PSL models. The study by Prato and Bekhor (2007) also adopted LK model with a factor analytic structure for investigating the impact of choice set composition on model estimates. In all, they estimated and compared six route choice models: MNL, C logit, PSL, GNL, and CNL. The study recommended to use MNL modified models for large number of alternatives and nested or LK models for small alternatives in the choice sets. Frejinger and Bierlaire (2007) sho wed an application of the error component model by using GPS data of 2978 observations (2170 OD pairs) collected in Borlange, Sweden and estimated five different specifications of Error Component model. The Subnetwork was constructed with 5 arbitrary chose n roads in the network. The results of the EC models were compared with the MNL and PSL models. Further, prediction performances of the models were also examined by randomly selecting 80% OD pairs for estimations and the rest for predicting choice probabil ities. MNL and PSL models PAGE 53 53 showed similar prediction performance, however, PSL resulted in a better fit for the estimated data. Bierlaire and Frjinger (2008) adopted the Error Component approach to demonstrate route choice modeling with network free data (G PS data, reported trips). They estimated the Error Component model for 780 observations collected via telephonic interviews in Switzerland. The Subnetwork was defined as consisting of all the main freeways in the roadway network of Switzerland. When compar ed with PSL model estimates, the Error Component model was found a better fit model. Another empirical application of the Error Component Model was presented by Bekhor and Prato (2009). They also estimated MNL and PSL models to examine the methodology tran sferability in route choice modeling using two different datasets: Turin, and Boston. They advised to account similarities within the stochastic part of the utility, however, also warned that it would be more computationally expensive. 2.3.4 Empirical Studies: E xplanatory Variables Table 2 3 presents a summary of the empirical studies that have performed choice modeling in the route choice context. The explanatory variables used by the different studies are identified in the fourth column. Distance and travel time (free flow or estimated) are the common explanatory variables used in utility functions. Numerous specifications of the travel time are used by the researchers. Prato and Bekhor (2006) and Prato and Bekhor (2007) specified travel t imes for experienced and inexperienced drivers and found that the experienced drivers are concerned about the travel time more than the in experienced drivers. Schussler and Axhausen (2010) and Bierlaire and Frejinger (2008) used travel times on each road type, defined according to an existing hierarchy of roadway links. Schussler and Axhausen (2010) used the time of day dependent travel times, whereas Bierlaire and PAGE 54 54 Frejinger (2008) created piecewise linear specifications of free flow travel time. The corre sponding proportions of the total travel time were also included in the utility functions. In addition to the free flow travel time, Bekhor et al. (2002) and Bekhor et al. (2006) created a variable for time spent on government numbered routes. Some studies examined the effect of travel time delay on path utilities. For example, Bovy et al. (2008) and Bekhor and Prato (2009) included percent delay with respect to the free flow travel time and Bek h or et al (2002) and Bekhor et al. (2006) included delays for three different income categories in the utility functions. Path utilities are also specified with dummy variables to capture the effect of landmarks (Prato and Bekhor, 2006; Prato and Bekhor, 2007), maximum average speed (Bovy et al 2008; and Bekhor an d Prato, 2009), least distance and least time path (Bekhor et al. 2002; and Bekhor et al. 2006) on choosing a path. Prato and Bekhor (2006) and Prato and Bekhor (2007) believed that the behavioral variables (habit, time saving skills, and navigation abilit ies) are also determinant factors in path utilities. Frejinger and Bierlaire (2007) specified utility functions with some route attributes (effect of number of speed bumps and left turns on uncontrolled signals) as the explanatory variables. 2.3.5 Summary Based on the discussion so far, The PSL, CNL, and EC with Subnetwork models have shown good empirical performances in route choice modeling The CNL and EC models consist of complex probability structures and require high computation time for model estimations (Bovy et al 2008). Moreover, estimations with large number of observations generated from a high resolution network would increase the computation time even more. Prato and Bekhor (2007) suggested using MNL modified models if PAGE 55 55 large number of alternatives is present in the choice set. Among MNL modified models, PSL and PSCL models have produced good estimates. Although, PSL and PSCL models do not differ very much in terms of results (Bovy et al 2008). The only difference between the two models is availab ility of a systematic derivation of PSCL model. To our knowledge, only a few empirical studies have used demographic characteristics as predictor variables ( e.g. household income by Bekhor et al., 2002 and Bekhor et al., 2006) Moreover, the use of a large scale GPS dataset for route choice modeling is also recent and limited ( only Bierlaire and Fr e jinger, 2008, and Schussler and Axhausen, 2010). Except for the study by Bierlaire and Fr e jinger (2008), predictive assessments of the model on non syntheti c data are also limited. In our study, we adopt the PSL model with the original PS formulation proposed by Ben Akiva and Bierlaire (1999). The original PS formulation has shown the best empirical performance (Frejinger and Bierlaire, 2007). The model e stimations are performed for a large GPS dataset containing 1913 observations. In addition to the several route attributes, trip and traveler attributes are also included in the utility functions. The models are estimated using three choice set sizes (5, 10, and 15 alternatives). Predictive assessments are done using a hold out validation sample. PAGE 56 56 CHAPTER 3 MAP MATCHING ALGORIT HMS Based on a review of the literature, there are two broad classes of algorithms for map matching: The GPS weighted shortest path algorithm (GWSP) and the multi path algorithm (MP). The first uses the concept of shortest path in determining the route and is a computationally enhanced version of the approach proposed by Du (2005) The second is new multipath map matching algorithm, w hich uses the concept of multiple paths proposed by Marchal et al. (2005) and also implemented by Schssler and Axhausen (2009). The GWSP algorithm is more straightforward and computationally less demanding (especially if a tool for calculating shortest p aths is available) whereas the MP algorithm is more elaborate and demanding (the need to store multiple paths can get cumbersome with dense networks). However, the latter algorithm is also free from assumptions such as preference for shortest paths and gen erally uses the observed data to determine the route. A comparative analysis of these approaches would therefore be of interest and this study contributes towards that end. Further, we enhance each of the two algorithms computationally and to achieve autom ation to the greatest extent possible. Both algorithms are implemented in ArcObject within ArcGIS framework, using Python and Visual Basic Application (VBA). Prior to the discussion of each of our implementations of the two map matching algorithms, it i s useful to outline a generic procedure employed to treat missing GPS points. Factors such as loss of signal while traveling in dense urban areas (canyon effect) can cause GPS points to be missing over parts of a trip. During the map matching procedure, su ch missing GPS points can lead to incompleteness in the final PAGE 57 57 predicted routes and/or premature termination of the algorithm (for e.g. see Chung and Shalaby, 2005, Spissu et al., 2011, Marchal et al., 2005). In order to overcome such implementation issues, points are artificially added to the GPS traces at times when the true GPS recordings are missing. Given that the recording frequency of the GPS devices is known, the occurrence of missing points can be detected by simply comparing the time stamps of cons ecutive points. Whenever missing data are detected, additional points spaced 75 feet apart are added using a simple extrapolation from the Python. Overall the trip smoothing procedure provides a definitive direction for the algorithm to proceed at locations with missing GPS points thereby reducing the possibility of a breakdown in the algorithm. The algorithms are applied on the processed GP S streams. 3.1 The GPS Weighted Shortest Path (GWSP) Algorithm The algorithm is described in following steps: 1. Network preparation 2. Sub network creation 3. Update link cost 4. Final path creation The steps are described below with each step consisting two description s: conceptual and implementation. During the implementation stage, steps 1 to 3 are completed for all trips, and then step 4 is executed. An illustrative example of the algorithm is provided in Appendix A. Step 1: Network preparation: T he step prepares the network by assigning the links in the network a very high cost. A very high cost of a link discourages the shortest path method to use it in the route. PAGE 58 58 To implement this step, cost of the links in the network are set equal to 5000 times the link travel times. Step 2: Sub network creation: This step involves extracting out a sub network, created around each GPS point and all the links within this area are identified. Th e set of all links within the buffer zones of at least one of the GPS points in the trip comprises the sub network. All subsequent processing is done on this sub network instead of the entire roadway network. The above process was implemented as follows: for every GPS points in the stream, a buffer of 200 meters was created and the links in the roadway network that intersect the resulting buffers were selected. The selected links were then exported to a new shapefile to form the sub network. Step 3: Update link cost: This step identifies the links in the sub network with high size is created around each GPS point and the links that are completely within one or more of th ose buffers are assigned a lesser cost. Only a link with enough GPS points will be covered by the buffers. The step is implemented by, first, constructing a buffer of 75 feet for each GPS point and subsequently, dissolving all the buffers to form a polyg on for a trip. After this, the links in the sub roadway network that falls completely within the buffer polygon are selected and the cost is set equal to the link travel times. Step 4: Final path creation: The step aims to identify the chosen path during the trip. The final chosen path is determined by calculating the shortest cost path between PAGE 59 59 the origin and destination of a trip within the updated sub network. The links with high GPS counts are more likely to have been actually traversed during the trip. The fact that the link costs are lower for such links (see step 3) and much higher for other links (see initialization in step 1), makes the shortest path algorithm more likely to pick a route with links that have more GPS points. To implement this step, a network dataset is created for the updated sub network ; afterwards, the route solver is run to find the shortest path for the OD pair of a trip. The shortest path constitutes the final chosen path. 3.2 The Multi P ath (MP) Algorithm The proposed multipath a lgorithm sequentially iterates th rough the following five steps: 1. Sub network creation 2. 3. 4. Creation of link to nodes and node to links incidence matrices 5. Construc tion of the final chosen route (which in itself is an iterative process) The steps are described below with each step consisting two components: conceptual and implementation. It is important to note that these steps are performed for one trip at a time. Also, during the implementation, all steps are automated, and the algorithm itself is automated for all trips in the dataset. An illustrative example of the algorithm is provided in Appendix A. Step 1: Sub network creation: The first step involves extracti ng out a sub network, created around each GPS point and all the links within this area are indentified. The set of all links within the buffer zones of at least one of t he GPS points in the trip comprises PAGE 60 60 the sub network. All subsequent processing is done on this sub network instead of the entire roadway network. The above process was implemented as follows: for each GPS point in the stream, a buffer of 200 meters was cre ated and the links in the roadway network that intersect the resulting buffers were selected. The selected links were then exported to a new shapefile to form the sub network. (s equential) set of links within the sub network that could have been potentially traversed by the trip. For this purpose, each GPS point is mapped to the nearest roadway link within the sub network. In this process, every link in the sub network could have been mapped to zero, one, or more GPS points. The set of links with at least one GPS point mapped to it constitutes the initial chosen route. The time stamp on the earliest (first) GPS point mapped to each link in the initial chosen route (ICR) is determin ed. The links in the ICR initial chosen links (ICL), are then sorted based on this time stamp so that the sequence of links in the initial chosen route reflects the general temporal trajectory of the trip. The step was implemented by first performing a s patial join between the GPS points and the sub roadway network. The spatial join finds the nearest link to a GPS point and that link is assigned to the GPS point. A summary of links and corresponding GPS counts is exported to a text file and subsequently, joined to the sub network attribute table. Links in the sub network that have at least one GPS count are selected and exported to a shapefile to form the initial chosen route (ICR). The links in the ICR, PAGE 61 61 initial chosen links (ICL), are permanently sorted b ased on the time stamp to follow the same temporal trajectory as the trip. aims to identify the (sequential) set of nodes within the sub network that could have been potentiall y traversed by the trip. The set of nodes at the end of the ICL identified nearest GPS point and its time stamp is extracted. The segment nodes are then sorted by the time stamp so that the sequence of nodes reflects the general temporal trajectory of the trip. The set of end nodes of the links in the sub roadway network, excluding the This step, programmatically, extracts the end nodes of the ICL. These nodes are sub both type of nodes, shared nodes are represented as one. However, the obtained segment nodes do not necessarily follow the temporal trajectory of the trip. Therefore, a spatial join is used between the GPS points and the segment nodes. The spatial join identifies the nearest GPS point to a segment node and assigns its timestamp to the node. Afterwards, this timestamp is used to sort the segment nodes. Step 4: Creation of link to nodes and node to links incidence matrices: The segment node to links matrix has the list of all the links terminating on each segm ent node. Similarly, the local node to links matrix has the list of all the links terminating on each local node. The link to segment nodes matrix has the list of all the nodes from the SN associated with each link. Similarly, the link to local nodes matri x has the list of all PAGE 62 62 the local nodes associated with each link. Note that even though each link has two nodes in general, both nodes need not be either SN or LN. To construct the matrices of node to links, a small buffer (0.00001 meters) is created for a node and the links in the sub roadway network intersecting the buffer were selected and inserted to the matrix. The process is performed twice, once for each node type (segment nodes and local nodes). Similarly, the link to nodes matrices are created by co nstructing a small buffer (0.00001 meters) for a link and selecting the nodes that are within the buffer. Once again, this process too performed twice, once for each node type. In addition to the list of links/ nodes, the matrices contain link/node count c orresponding to each node/link. Step 5: Constructing the final chosen route: The step identifies multiple possible paths between an origin and destination and selects the best one as the final chosen route. The algorithm starts at the first segment node, also the one closest to the origin, and sequentially iterates through all the segment nodes (SN) in the list. Following definitions are key to the conceptual framework of the algorithm: Route: a collection of links Saved routes: a collection of possible ro utes between the origin and destination Dead end: a node is a dead end if there are no connecting links Eligible link: a link is defined as an eligible link if it does not have a dead end Disqualified link: a link is a disqualified link if it is encounter ed at a segment node but not added to a route PAGE 63 63 Right node: a segment node is defined as a right node if it is an end node to a link in one of the saved routes. In a special case, where no right nodes are available, the next segment node (in chronological se quence) automatically qualifies as a right node Wrong node: a segment node is defined as a wrong node if it is an end node of one of the disqualified links At any segment node, first the links originating from the segment node are found using the segment n ode to link matrix. Then, the links are identified in terms of eligible and disqualified links. Now the following process is iterated through the eligible links at the segment node. For an eligible link, a copy of the current route leading up to this node is created and subsequently the eligible link is added to this. The end node of the added link is then obtained from the link to nodes matrices. The end node can either be a segment node or a local node. If a segment node, it is labeled as a right node. Ho wever, if it is a local node, the algorithm processes it similar to a segment node. Specifically, the links at the local node are found by using the local node to links matrix. The links are then identified in terms of eligible and disqualified links. A ne w route is created for each eligible link. The algorithm continues to create more routes until all the new routes at the segment node are met with either a segment node or a dead end. After this, the current route is deleted from the saved routes and the a lgorithm moves to the next segment node in the list of SN. However, the end node of a disqualified link is also found and if a segment node, it is termed as a wrong node. PAGE 64 64 After all segment nodes in the list of SN are processed (note that a segment node is processed only if it is a right node. Wrong segment nodes are skipped), the algorithm provides multiple possible routes for the trip. In the end, a route with the highest GPS count is selected as the final chosen route. The proposed algorithm introduces t wo novel innovations to the field of map matching methods: Use of a Sub network: In general, the entire roadway network is used for all trips irrespective of the spatial location of the trip. A high resolution network even of a small region contains a very large number of links and nodes, and hence, a very large number of alternate paths can be constructed by the multi path algorithm thereby affecting the computational efficiency. Therefore, we propose to construct a sub network for every trip and use that to find the traversed path. The sub roadway network includes only those links in the network that are within the vicinity of the GPS points. The smaller size of the sub roadway network helps producing fewer paths and also prevents stored paths from deviati ng too much away from the traversed path. Iteration over Segment Nodes: The earlier multipath algorithms (e.g. Marchal et al. 2005; Schssler and Axhausen, 2009 ) iterates through every GPS point in a stream (i.e., the possibility of alternate paths are exp lored at every GPS point). A high frequency GPS stream can easily contain thousands of GPS points, thus making the process computationally intensive. The proposed algorithm iterates over segment nodes. Hence, the possibility of alternate paths is explored at only nodes along the roadway links. Such nodes are much fewer compared to the number of GPS points thereby improving computational efficiency. Additionally, classification of segment PAGE 65 65 nodes in terms of right nodes and wrong nodes helps reducing number o f iterations as the algorithm iterates only through the right nodes and skips the wrong nodes. 3.3 Summary It is fairly evident that the MP algorithm is significantly more computationally intensive than the GWSP approach. Two innovations help enhance the opera tional performance. First, the multi paths are constructed over a sub network that comprises of roadway links in the general vicinity of the GPS points. This prevents the needs to store an excessive number of paths and ensures that, at any point in the alg orithm, the 2005; Schssler and Axhausen, 2009) iterate through every GPS point in a stream (i.e., the possibility of alternate paths are explored at every GPS point). A high frequency GPS stream can easily contain thousands of GPS points, thus making the process computationally intensive. The proposed algorithm iterates over segment nodes. Hence, the possibility of alternate paths is explored at only nodes along the roadway links. Such nodes are much fewer compared to the number of GPS points thereby improving computational efficiency. PAGE 66 66 CHAPTER 4 EXPLORATORY ANALYSIS OF CHOSEN ROUTE S The chapter presents the analysis that validates the two (multipath and shortest path based) map matching algorithms presented in the previous chapter. This is accomplished by performing local data collection and comparing the generated routes Subsequent to the small scale validation exercise, the two algorithms were applied to data from a larger scale GPS based travel survey. The relative performances of the two algorithms are compared. Further, the routes determined from each of these algorithms are compared against the shortest distance, and shortest time paths for the same trip end locations 4.1 Validation Prior to a large scale application of the map matching algorithms, it is important to validate these against true routes. Data collected from GPS based travel surveys are (only the GPS traces are passively obtained). Therefore, we performed our own data collection in Orlando, Florida, USA, the Chicago and several other GPS based travel surveys nationwide). The reader is referred to the Chapter on Data for a brief description of the device and the data collection procedure. The GPS data were collected for about 33 trips (37,214 GPS points) with each trip being at least 5 minutes in duration and 2 miles long. As the vehicle was driven on known routes, the routes from the map matching process were first verified manually and al gorithm efficiency was subsequently evaluated in terms of the proportion of the true nodes, distance, and time replicated by the algorithms. PAGE 67 67 For 26 out of the 33 trips, both methods generated routes (In the rest, the shortest path based algorithm did not generate a route these are discussed later). Table 4 1 presents a summary of overlap measures for these trips and for each algorithm. The results indicate that both algorithms are able to replicate the true routes to a very large extent (overall, over 98 % of the distance and time are replicated and over 95% of the nodes are replicated). The freeway only trips (>98% on freeway) are replicated almost 100% by both algorithms. However, for trips with arterials and local streets over 96% of the distance and ti me are replicated. The primary reason for the inaccuracy with the MP algorithm was because of routes containing loops; the algorithm struggles to include a loop in the route. Additionally, the algorithm occasionally selects links that are closer to true li nks because they have higher GPS points. Also, both algorithms find a way if some links are missing in the network, thus selecting other links in the route. PAGE 68 68 Table 4 1 Validation of the map matching algorithms True r oute Overlap from MP ( %) Overlap from GWSP (%) Nodes Distance (Miles) Time (Minutes) Avg. Speed % Distance o n e xpressway % Distance o n a rterial % Distance o n l ocal r oad Nodes Distance Time Nodes Distance Time (a) Freeway Trips 74 29.7 34.38 74.47 100 0 0 100 100 100 100 100 100 40 20.61 22.49 72.72 100 0 0 100 100 100 100 100 100 68 26.21 30.78 69.82 98.51 1.49 0 100 100 100 100 100 100 63 25.60 28.76 75.87 98.24 1.76 0 100 100 100 100 100 100 37 24.63 26.87 78.25 100 0 0 100 100 100 100 100 100 25 18.90 20.62 74.75 100 0 0 100 100 100 100 100 100 60 15.62 17.04 73.84 100 0 0 100 100 100 100 100 100 36 16.27 19.74 73.61 100 0 0 100 100 100 100 100 100 26 13.57 14.8 64.8 100 0 0 100 100 100 100 100 100 121 15.80 17.23 71.05 100 0 0 97.52 98.6 98.6 100 100 100 40 17.18 18.74 68.69 100 0 0 100 100 100 100 100 100 46 20.66 24.02 72.19 100 0 0 100 100 100 100 100 100 48 17.28 18.85 73.18 100 0 0 100 100 100 100 100 100 28 16.47 17.97 72.62 100 0 0 100 100 100 100 100 100 Total 99.58 99.92 99.92 100 100 100 (b) Arterial and Local Streets Trips 77 27 31.46 66.36 91.55 8.19 0.26 100 100 100 100 100 100 104 5.12 6.81 37.06 14.98 78.91 6.11 100 100 100 77.66 79.51 82.98 90 4.4 8.7 25.78 19.75 43.22 37.03 67.78 66.63 57.86 100 100 100 145 9.65 13.69 36.04 70.79 7.25 21.96 96.97 96.58 97.55 100 100 100 80 5.05 9.59 14.12 14.02 15.14 70.84 85.53 95.21 95.38 100 100 100 166 10.48 17.23 32.36 35.22 32.90 31.88 89.16 90.04 89.4 100 100 100 124 7.12 11.22 26.85 29.49 48.98 21.53 97.58 99.26 99.17 100 100 100 76 11.52 15.45 52.42 66.77 32.27 0.96 98.68 99.24 98.3 100 100 100 98 16.65 21.28 55.07 76.22 23.17 0.60 100 100 100 100 100 100 34 17 26.64 67.13 95.64 0.00 4.36 100 100 100 100 100 100 176 26.02 30.91 66.58 89.15 10.84 0.00 92.61 97.3 95.2 100 100 100 78 6.90 9.52 44.26 0 72.46 27.54 89.47 90.13 82.46 89.47 90.13 82.46 Total 92.93 96.86 95.17 97.48 98.82 98.60 PAGE 69 69 As already mentioned, there were 6 cases in which the shortest path did not generate a route (The multi path algorithm generates the routes for all trips). Further, one trip had a significantly different route generated by the shortest path algorithm relative to the true route. A summary of these seven trips is presented in Table 4 2 PAGE 70 70 Table 4 2 Troublesome trips for the GWSP method True r oute Overlap from MP (%) Overlap from GWSP (%) Nodes Distance ( m iles) Time ( m inutes) Avg. s peed (mph) % Distance o n e xpressway % Distance o n a rterial % Distance o n l ocal Roads Nodes Distance Time Nodes Distance Time 55 13.82 15.09 81.2 99.94 0.00 0.06 100 100 100 Stop on the wrong side 99 12.56 18.61 80.4 75.53 21.72 2.75 100 100 100 Missing links in network 256 16.09 22.19 68.9 29.52 63.27 7.21 91.34 95.02 94.43 Missing links in network 157 21.32 24.22 84.1 84.01 13.34 2.64 97.47 99.25 99.11 Missing links in network 60 6.53 9.46 65.3 0.00 73.64 26.36 100 100 100 Missing links in network 52 16.26 19.12 83.8 91.07 8.79 0.14 100 100 100 Missing links in network 53 2.45 4.29 38.8 0.00 0.00 100.00 90.2 93.71 91.36 9.8 6.29 8.64 PAGE 71 71 One of the major reasons for the failure of the GWSP algorithm is the absence of certain links in the roadway. In one of such cases, as shown in Figure 4 1 the GWSP algorithm cannot find a route but the MP algorithm selects off path links to complete a route. This suggests that the MP algorithm is less sensitive than the GWSP algorithm to the errors in the underlying roadway network in terms of generating a complete, feasible route for the trips. To overcome this issue, it would be necessary to pre process the network GIS data and add any missing links. Figure 4 1 Missing links in the network example 1 (a) GPS tracks, and (b) MP route A second example with missing links in the roadway is presented in Figure 4 2 In this case, the GWSP method does find a route; however, this is much farther away from the true route relative to the route determined by the MP method. PAGE 72 72 Figure 4 2 Missing links in the network example 2 A second reason leading to the failure of the GWSP method occurs when trip origin/destination is close to a divided roadway represented by two separate links in the dire opposite link), the algorithm fails. To overcome this issue, the algorithm has to be expanded to ensure that the GPS points are snapped to not just the nearest link but also to the one in which the direction of flow is consistent with the bearing of the GPS points. This extension is currently not accommodated in our algorithm. Finally, it is also interesting to note that the GWSP algorithm for trip 9 is very different from t he true path which is also reasonably well detected by the MP algorithm. The schematic of this trip represented in Figure 4 3 quickly highlights why this is the case. For this trip, the two trip ends are fairly close to each other spatially but the actual PAGE 73 73 not have a GPS point are assigned a very high impedance to prevent the algorithm fr o m choosing these links, it is possible (as in this example) that the total impedance o f the set of links with GPS points is still larger than the large artificial impedance assigned to the link without GPS points. This problem could be potentially overcome d by assigning ever higher impedances to the links without GPS points. The MP algorith m less affected by the relative locations of origin and destination and, hence, correctly finds the links traversed during the trip. Figure 4 3 A round trip (a) GPS tracks, (b) GWSP algorithm, and (c) MP algorithm PAGE 74 74 Overall, th e small scale validation exercise demonstrates the feasibility of the proposed algorithms to generate reasonable routes that are fairly close to the true routes chosen. Issues such as incomplete roadway networks were identified to cause the GWSP algorithm to fail to generate a route in certain cases. It is also useful to note here that this study relies on the algorithms built into ArcGIS for shortest path calculations. Developing customized algorithms that are sensitive to missing links can help (in additi on to the other methods discussed above) address the problem of failure to generate the routes. 4.2 A pplication to a Large Scale GPS based Travel Survey 4.2.1 Data The GPS data comes from the in vehicle GPS survey component of the Chicago Regional Household Travel Inventory (CRHTI). A high resolution, GIS compatible roadway network for the study area was obtained from ArcGIS Data and Maps from ESRI. This GIS layer has information on speed, functional classification, and distance of most links in the roadway (includi ng local streets). Additionally, a GIS compatible sub zone layer for the area was also obtained from the Chicago Department of Transportation (DOT). Chicago Regional Household Travel Inventory (CRHTI) NuStats (2008) is a recently conducted, between January 2007 and February 2008, comprehensive study of the demographics and travel behavior characteristics of a large number of households (10,552 households) in the greater Chicago area. Travel information for either 1 d ay or 2 day of travel by household members was collected in conjunction with the socio demographics of the households and its members. Additionally, the study also had a PAGE 75 75 GPS data collection component, collected in four stages for both in vehicle and on per son, for the trips made by the selected households. In stage 1, in vehicle GPS data was collected for households that travel a lot (travel throughout the region as part of their job or who traveled into Chicago for personal or business reasons at least three times per week). Stage 2 had in vehicle GPS data for households with at least one member making more than 10 trips per day by auto or who traveled more than 75 miles per day as part of their job. In stage 3 in vehicle GPS data was c ollected for heavy travelers for the period of 7 days. In stage 4, wearable GPS data was also collected for the period of 7 days. ( NuStats and GeoStats, 2008 ) For the collection of in vehicle travel data, a simple GPS data logging device GeoLogger Figure 4 4 was used Figure 4 4 In vehicle GeoLogger ( s ource: GeoStats) The GeoLogger recorded date, time, latitude, longitude, speed, heading, altitude, number of satellites, and HDOP for a vehicle at 1 seocnd interval. The Original data PAGE 76 76 comprises of 6089852 GPS points from 9941 trips made by 408 vehicles (259 household s). T he original data comprises of 6,089,852 GPS points from 9941 trips made by 408 vehicles (from 259 households). From these, trips shorter than 5 minutes in duration or 2 miles in distance were removed. The origin and destination of the remaining 5290 trips were mapped to the sub zones and the trips with unique subzones at both ends were identified. The resulting 4406 trips have unique origin destination pair s. The two map matching algorithms were applied to all these 4406 trips. The MP and GWSP methods generated complete routes for 4093 and 3889 trips respectively. It is useful to note that these were generated without any manual interventions such as visual inspections. There were 3886 trips for which both map matching algorithms generated a route. For these cases, the shortest distance (SD) and shortest (free flow) travel time (ST) routes were also generated. After further cleaning to remove outliers and in consistent cases, the final sample consists of 3513 trips each of which has four routes; two from the map matching algorithms (MP and GWSP) and two from normative route choice algorithms (SD and ST). It is useful to recognize that the GPS traces do not ne cessarily start/end at nodes ensure consistency in the start and end locations of all four routes generated for any trip, the origin and destination nodes determined f rom the MP algorithm were used as the terminal nodes in the determination of the other three routes (all of which use the ArcGIS based shortest path methods). PAGE 77 77 For the final sample, b ased on the trip start times (available from the GPS data), six discrete time periods are defined for the time of day: early morning (midnight 6:30 AM), AM peak (6:30 AM 9:00 AM), AM off peak (9:00 AM noon), PM off peak (noon 4:00 PM), PM peak (4:00 PM 6:30 PM), and evening (6:30 PM midnight). The frequency distribu tion of trips for the time of day, Figure 4 5 shows that the travelers preferred PM off peak period, noon 4 pm, for their travel as 30% of the trips, the most, were undertaken during the time period. Also, only 3% of the trips, the least, started in the early morning suggesting this period as the least preferred. Further, the examination of the trip length s Figure 4 6 indicates that the dataset consists of trips with considerable lengths. More than 50% of the trips are longer than 5 miles in length. Figure 4 5 Time of day frequency distribution PAGE 78 78 Figure 4 6 Trip length frequency distribution 4.2.2 Aggregate Comparisons The useable data from Chicago comprise a total of 3513 trips each representing a unique origin destination pair. For each OD pair, four routes are constructed: two chosen routes from the two map matching algorithms (MP and GWSP), a shortest distance (SD) r oute, and a shortest time (free flow) (ST) route. Table 4 3 shows aggregate statistics of the routes produced by the four methods. Both the MP and GWSP algorithms produced similar routes as the summary measures (averages and deviances) for link count, dis tance and time are quite comparable. algorithms) path is higher than median distance of the shortest distance (and shortest time) path between the same sets of origin destination pairs. Similarly, median (free PAGE 79 79 higher than the median (free flow) travel time of the shortest distance (and shortest time) path between the same sets of origin destination pair s. Table 4 2 Aggregate s tatistics o f r outes from the f our m ethods MP GWSP SD ST Links (Count) Mean 112.10 111.02 108.57 110.58 Median 76 76 72 75 Std. Deviation 97.63 96.83 100.55 98.32 Min 8 8 5 5 Max 662 678 711 668 Q1 48 47 44 46 Q3 138 135 133 137 Distance (Miles) Mean 8.27 8.23 7.36 7.76 Median 5.23 5.21 4.72 4.89 Std. Deviation 7.90 7.90 6.81 7.31 Min 2.01 2.01 0.67 0.67 Max 57.12 57.12 46.59 52.72 Q1 3.15 3.12 2.89 3.01 Q3 10.08 10.01 9.14 9.68 Time (Minutes) Mean 14.03 13.86 13.97 12.10 Median 9.64 9.48 9.16 8.28 Std. Deviation 11.64 11.56 12.39 10.02 Min 2.78 2.78 1.60 1.60 Max 80.84 83.30 87.40 64.59 Q1 6.07 5.97 5.72 5.28 Q3 17.68 17.46 17.46 15.28 4.2.3 Measures of Similarity of Pairs of Routes The above analysis presented an overall (aggregate) summary across all the trips in the sample. Next, we examine the extent to which the routes generated between any OD pair are similar. The overlap (i.e., the set of common links) between any pair o f routes is determined in ArcGIS by using the intersect tool. Once the common set of links have been identified, it is possible to calculate the number of common links, the total PAGE 80 80 distance across the common links (overlap distance), and the total (free flow ) travel time across the common links (overlap time). From the three values identified above, four route level measures of similarity can be constructed. These are (1) overlapping index (OI), (2) commonly ratio (CR), (3) distance deviation index (DDI), an d (4) time deviation index (TDI). The overlapping index (OI) is the ratio of number of links common to the two routes to the total number of unique links in both routes (Spissu et al., 2011). An OI value of 0 indicates that the two routes are completely d links) and a value of 1 indicates that both routes overlap perfectly (all links are the same). Commonly ratio (CR) of two routes is calculated as: where is the distance of common links in route and ; is the distance of the route and is the length of the route (Pilat et al., 2011). As in the case of OI, the CR measure also takes values between 0 and 1 with 0 representing no overlap and 1 representing perfect overlap. The previous two metrics can be applied to any pair of routes. The next two metrics, DDI and TDI (Spissu et al., 2011) are used to compare an algorithm generated route to the SD and ST routes respectively. The Distance Deviation Index (DDI) determines the extent to which the chosen route is longer (in distance) than the shortest distance path between the same OD pair and is calculated as: where is the distance of the chosen route and is the distance of the SD route. PAGE 81 81 Similarly, Time Deviation Index (TDI) determines the extent to which the chosen route is longer (in time) than the shortest time path between the same OD pair and is calculated as: where is the time of the chosen route and is the time of the ST r oute. Using the similarity measures as described, the routes are compared in a pair wise manner. First, the routes generated by the two map matching algorithms are compared to determine the extent to which they are similar. Next, the routes from each of th e algorithms are compared to the SD path. Finally, the routes from each of the algorithms are compared to the ST path. 4.2.4 Extent of Similarity of the Routes Generated by the T wo MM Algorithms The routes generated by the two map matching algorithms (MP and GWS P) are compared using the overlap index and commonly ratio measures. The frequency distributions of OI and CR are presented in Figure 4 7 Almost 88% of the routes have a commonly ratio of higher than 0.90 and 70% of the routes have an OI of 0.9 or greater. In fact, 49.44 % of the trips have a perfect overlap (OI = 1 and CR = 1). About 95% of the routes have a CR value of greater than 0.8 and 85% of the routes have an OI value of greater than 0.8. Thus, in most (~ 85%) of cases, both algorithms gener ate routes that overlap significantly (80% or more) in terms of links and distance. Further, the overlaps are greater in terms of distance than in terms of links. This indicates that even if slightly different links are determined by two map matching algor ithms, these are likely to be short distance links. PAGE 82 82 Figure 4 7 Comparison of routes from the two map matching algorithms The routes are further examined by classifying the trips based on the trip length and time of day. First, the trip length is categorized into three groups: short (2 5 miles), medium (5 10 miles), and long (more than 10 miles). The time of day was reclassified into two periods: peak period (AM peak and PM peak) and off peak period (early morning, AM off peak, P M off peak, and evening). After this, six discrete categories are created: peak short trips, peak medium trips, peak long trips, off peak short trips, off peak medium trips, and off peak long trips. From the Table 4 4, t he OI and CR values marginally decre ase with increasing length of the trips (for both peak and off peak trips). This seems reasonable as, for network thereby increasing the probability of generating different paths. However, the median OI and CR values are PAGE 83 83 significantly large even for the longest trips. For trips of any length, there is not an appreciable difference between peak and off peak trips. Table 4 3 Overlapping index (OI) for routes from MP and GWSP meth ods Peak Off p eak Overall Short Medium Long Short Medium Long Sample s ize 499 301 330 1219 623 541 3513 Overlapping Index (OI) Mean 0.93 0.91 0.89 0.92 0.91 0.89 0.91 Median 1.00 0.96 0.93 1.00 0.96 0.93 0.97 Std. Dev 0.14 0.13 0.12 0.14 0.13 0.12 0.13 Min 0.18 0.24 0.36 0.14 0.06 0.32 0.06 Max 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Q1 0.90 0.87 0.85 0.90 0.88 0.85 0.88 Q3 1.00 1.00 0.98 1.00 1.00 0.97 1.00 Commonly Ratio (CR) Mean 0.97 0.96 0.95 0.96 0.96 0.95 0.96 Median 1.00 0.99 0.98 1.00 0.99 0.98 0.99 Std. Dev 0.08 0.08 0.07 0.08 0.08 0.07 0.08 Min 0.26 0.48 0.52 0.34 0.17 0.40 0.17 Max 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Q1 0.97 0.96 0.94 0.96 0.96 0.94 0.96 Q3 1.00 1.00 1.00 1.00 1.00 1.00 1.00 4.2.5 Comparing the C hosen R outes A gainst the Shortest D istance R outes The comparison of the chosen routes against the shortest distance routes was performed using the commonly ratio (CR) and the distance deviation index (DDI). PAGE 84 84 Figure 4 8 Commonly ratio (CR) of routes from the MM and SD methods The Figure 4 8 presents the CR values calculated between the chosen routes and the shortest distance paths. It is evident that the chosen routes are considerably different from the shortest distanc e routes. On an average (median), the CR value is about 0.40 with a significantly large deviation across the trips. Less than 15% of the trips have a CR value of over 0.9 and about 22% of the trips have a value less than 0.1.The trends are quite similar ir respective of the algorithm used to generate the chosen route. This is not surprising given that we have already established that the two map matching algorithms generate fairly similar routes. Commonly ratios of the chosen routes and the SD routes are pr esented in Table 4 5 The CR of the chosen routes decreases sharply with the trip length (0.56 for short, PAGE 85 85 0.4 for medium, and 0.16 for long) for both peak and off peak conditions. This suggests that chosen path is likely to be more different from the SD pa th for longer trips. Table 4 4 CR of the chosen routes and the SD routes Peak Off p eak Overall Short Medium Long Short Medium Long Sample s ize 499 301 330 1219 623 541 3513 CR of MP and SD Routes Mean 0.54 0.43 0.28 0.52 0.44 0.28 0.44 Median 0.56 0.38 0.16 0.53 0.37 0.15 0.39 Std. Dev. 0.34 0.34 0.29 0.34 0.34 0.29 0.34 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Q1 0.23 0.12 0.04 0.19 0.11 0.04 0.11 Q3 0.85 0.75 0.46 0.85 0.75 0.45 0.76 CR of GWSP and SD Routes Mean 0.56 0.45 0.29 0.54 0.45 0.29 0.46 Median 0.58 0.40 0.16 0.55 0.39 0.16 0.41 Std. Dev. 0.35 0.34 0.30 0.35 0.35 0.29 0.35 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Q1 0.23 0.13 0.04 0.20 0.12 0.04 0.12 Q3 0.89 0.76 0.48 0.87 0.78 0.46 0.79 From the Table 4 6 on average, DDI increases with the trip length, indicating that the chosen route is generally longer than the shortest distance route and the disparity is greater for longer trips. On an average (median), a distance along the chosen route for a short dis tance trips is about 4% longer than the shortest distance path for the same route. The corresponding values are 6% and 10% for medium and long distance trips respectively. PAGE 86 86 Table 4 5 DDI of the chosen routes with the SD route s Peak Off p eak Overall Short Medium Long Short Medium Long Sample s ize 499 301 330 1219 623 541 3513 DDI of MP routes with SD Routes Mean 0.11 0.12 0.15 0.12 0.12 0.15 0.13 Median 0.04 0.06 0.10 0.05 0.07 0.11 0.07 Std. Dev. 0.21 0.27 0.18 0.24 0.23 0.13 0.22 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 2.48 3.89 2.21 2.97 3.62 0.82 3.89 Q1 0.01 0.02 0.06 0.01 0.02 0.06 0.02 Q3 0.12 0.15 0.18 0.14 0.16 0.19 0.15 DDI of GWSP routes with SD Routes Mean 0.10 0.12 0.14 0.11 0.11 0.14 0.12 Median 0.04 0.05 0.10 0.04 0.06 0.11 0.06 Std. Dev. 0.21 0.25 0.18 0.23 0.21 0.13 0.21 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 2.48 3.51 2.31 2.97 3.10 0.82 3.51 Q1 0.00 0.01 0.05 0.00 0.02 0.06 0.01 Q3 0.10 0.13 0.18 0.12 0.15 0.19 0.14 Looking at the results for the CR and the DDI measures simultaneously is quite illuminating. It is clear that even though the chosen routes share only about 40% (overall median) of the distance in common with the shortest distance path, the distance along the chosen route is only about 6% (overall median) longer than the distance along the shortest distance path. This is possibly because of the presence of alternate (possibly parallel) links/paths in the network that are very comparable i n terms of distances. 4.2.6 Comparing the C hosen R outes A gainst the Shortest T ime R outes Prior to comparing the chosen routes against the shortest time routes, it is useful to demonstrate that the SD and the ST paths are generally not the same in many cases. A c omparison of the SD and ST routes, Figure 4 9 showed that only about 24% routes depicted OI of 0.9 or higher. Moreover, about 21% routes showed OI of less than 0.1. PAGE 87 87 This confirms that for an OD pair the SD path is not necessarily the ST path. Also, the co mparison of the chosen routes with the SD path, previous section, showed that as the trip length increases, the traveler tends to avoid the SD path. Therefore, to further understand the chosen routes, they are compared against the ST routes. Figure 4 9 Comparison of routes from SD and ST methods The comparison of the chosen routes against the shortest time routes was performed using the commonly ratio (CR) and the time deviation index (TDI). Figure 4 10 and Table 4 7 present the CR values calculated between the chosen routes and the shortest time paths. Similar to the shortest distance routes, the chosen routes are considerably different from the shortest time routes too. On an average (median), the CR value is about 0.55 wit h a significantly large deviation across the trips. PAGE 88 88 Less than 23% of the trips have a CR value of over 0.9 and about 17% of the trips have a value less than 0.1.The trends are quite similar irrespective of the algorithm used to generate the chosen route. The CR of the chosen routes decreases with the trip length (0.58 for short, 0.51 for medium, and 0.42 for long) for both peak and off peak conditions. This suggests that chosen path is likely to be more different from the ST path for longer trips. Figur e 4 10 Commonly ratio (CR) of routes from the MM and ST methods PAGE 89 89 Table 4 6 CR for the chosen routes and the ST routes Peak Off p eak Overall Short Medium Long Short Medium Long Sample s ize 499 301 330 1219 623 541 3513 CR of MP and ST Routes Mean 0.58 0.51 0.42 0.59 0.51 0.45 0.53 Median 0.63 0.51 0.39 0.67 0.49 0.41 0.53 Std. Dev 0.35 0.35 0.33 0.35 0.35 0.32 0.35 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Q1 0.26 0.16 0.10 0.26 0.19 0.14 0.19 Q3 0.93 0.85 0.69 0.93 0.86 0.74 0.88 CR of GWSP and ST Routes Mean 0.60 0.53 0.45 0.61 0.52 0.47 0.55 Median 0.67 0.52 0.42 0.69 0.51 0.44 0.57 Std. Dev. 0.36 0.36 0.34 0.36 0.35 0.34 0.36 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 1.00 1.00 1.00 1.00 1.00 1.00 1.00 Q1 0.28 0.17 0.10 0.28 0.19 0.15 0.20 Q3 0.98 0.88 0.74 0.99 0.88 0.79 0.91 From the Table 4 8 for peak travel, TDI increases with the trip length, suggesting that the more time is spend on the roads compared to the shortest time between the OD pair and disparity is greater for longer trips. Therefore, with more distance travelled during peak peri od, more time is spent in the congestion. However, for the off peak travel less disparity is observed for longer trips. On an average (median), a time along the chosen route for a short distance trips is about 8% longer than the shortest time path for the same OD pair. The corresponding values are 11% and 14% for medium and long distance trips respectively. PAGE 90 90 Table 4 7 TDI of the chosen routes with the ST routes Peak Off p eak Overall Short Medium Long Short Medium Long Sample s ize 499 301 330 1219 623 541 3513 TDI of MP routes with ST Routes Mean 0.18 0.19 0.19 0.18 0.18 0.16 0.18 Median 0.08 0.11 0.14 0.08 0.11 0.12 0.10 Std. Dev. 0.35 0.26 0.22 0.32 0.28 0.15 0.28 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 4.45 2.69 2.36 4.82 3.24 0.86 4.82 Q1 0.01 0.04 0.05 0.01 0.03 0.05 0.03 Q3 0.22 0.26 0.25 0.22 0.23 0.23 0.23 TDI of GWSP routes with ST Routes Mean 0.16 0.17 0.17 0.16 0.16 0.15 0.16 Median 0.06 0.09 0.13 0.07 0.09 0.11 0.09 Std. Dev. 0.35 0.24 0.21 0.31 0.25 0.14 0.27 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 4.45 2.38 2.42 4.82 3.02 0.85 4.82 Q1 0.00 0.01 0.05 0.00 0.02 0.04 0.01 Q3 0.19 0.23 0.23 0.20 0.22 0.20 0.21 Results for the CR and the TDI measures clearly show that even though the chosen routes share only about 53% (overall median) of the time in common with the shortest time path, the time along the chosen route is only about 10% (overall median) longer than the time along the shortest time path. This suggests that the travel is made on links with comparable travel times to the links in the shortest time path. 4.2.7 Simultaneously C omparing the C hosen R outes A gainst the SD and ST R outes Further, to understand whether the traveler followed the SD route more or the ST route, a simultaneous comparison of the chosen routes against the SD and ST routes was conducted. For this, distance overlap, commonly ratio, of the chosen route with the SD route and the ST route were compared Figure 4 11 Specifically, if the CR of the chosen route with the SD route is higher than the CR of the chosen route with the ST route then it can be deduced that the traveler followed the SD route more than the ST PAGE 91 91 route. Similarly, if the CR of the chosen route with the ST route is higher than the CR of the chosen route with the SD route then it can be deduced that the traveler followed the ST route more than the SD route. To avoid the comparison of fairly similar shortest cost routes, the trips with CR of the SD and ST routes higher than 0.9 were n ot considered for the comparison. Also, if the observed route have no overlap with either of the shortest cost routes, it was removed from the analysis. It is important to note that as the observed route from MP and GWSP are mostly similar, the similar re sults were obtained for the either route, therefore results are shown only for one MM method. Figure 4 11 Comparison for trip length in time of day The comparison of the chosen routes with the SD and ST routes for trips length in different time periods is shown in Figure 4 11 The graph clearly sh ows that trips prefer PAGE 92 92 to travel on ST route more than the corresponding SD route. Moreover, as the trip length increases ST route is followed more. However, ST route is travelled less during the peak period indicating that during congestion people prefer t ry to follow the SD path more. 4.3 Summary The algorithms were first validated on locally collected GPS data on known routes. While both algorithms performed well, it is observed that the GWSP was more sensitive to missing links in the network than the MP appr oach. On applying the algorithms to large dataset comprising almost 4000 trips, both algorithms generated complete trips for a vast majority of the cases (again the MP produced mode complete trips than the GWSP). On comparing the 3500 trips for which both algorithms produced results, we find a substantial similarity between the routes generated in terms of both common links and the extent of distance overlap. This holds irrespective of trip distance and time of day of travel. Broadly, this result suggests that the simpler GWSP algorithm might be appropriate to generate chosen routes from GPS traces if a good (complete) roadway network database is available. distance and shortest path routes between the same locations, we find that the extent of overlap between the between these routes generally increases with distance but is generally the same across the peak and off (free flow) time paths more than they follow the shortest distance paths, especially for PAGE 93 93 longer trips. This clearly reflects a preference for using higher speed facilities for longer trips. Ev en though the chosen paths are quite deviant from the shortest paths in terms of the actual links traversed, the overall distance/time along the chosen path is fairly close to the distance/time along the shortest paths. This is possibly because of the pres ence of alternate (possibly parallel) links/paths in the network that are very comparable in terms of distances and times PAGE 94 94 CHAPTER 5 DATA ASSEMBLY FOR MO DEL ESTIMATIONS The chapter describes the procedure to assemble the data for model estimations. Th is process involves two major steps. First, several characteristics of the trip and trip maker are determined for use as explanatory variables in the models. This is discussed in Section 5.1. Next, alternative routes are constructed and characterized for each trip leading to the formation of the choice set for each route. An enhanced version of the BFS LE algorithm proposed by Schussler et al. (2012) is used for choice set generation. This procedure and the various attributes determined for each of the ro utes in the choice set are discussed in Section 5.2. This section also presents a descriptive summary of the analysis sample to be used for building the route choice models. 5.1 Trip And Traveler Characteristics The two map matching algorithms generated observed routes for 3513 routes. Of these trip and traveler characteristics were completely determined for 2850 trips. The loss of samples was mainly because of our inability to determine the trip maker character istics for over 600 trips. The reader will note that the GPS streams do not directly identify the trip maker and, therefore, secondary data had to be used to determine the drivers of the vehicles being tracked by the GPS devices. Section 5.1.1 discusses t he trip characteristics and Section 5.1.2 the characteristics of the trip makers. PAGE 95 95 5.1.1 Trip Characteristics Certain characteristics of a trip such as the total travel duration and the time of day of travel are directly obtained from the GPS streams. One of the major trip attributes that is not obtainable purely from the traces is the trip purpose. The travel survey did include the resident ial location (latitude and longitude) of the respondents. If a trip end fell within a buffer zone of radius 0.5 mile around the home location of the respondent, the trip end was classified as fied as HB trips. Table 5. 1 presents descriptive of the trip characteristics for the sample. 56% of the trips are home based and among them, about 30% originated at home. Further, majority of the trips (61.4%) are performed during weekdays (excluding Frid ay) with about 26% during weekends.32.5% of the trips are made during peak period. Also, trips shorter than 5 miles in length are prominent (48.8%) in the sample. Table 5 1 Trip characteristics Characteristic Share (%) Trip Type From Home 30.4 To Home 25.6 NHB 44.0 Travel Day Weekday (Monday Thursday) 61.4 Friday 12.7 Weekend 26.0 Travel Time Peak 32.5 Off Peak 67.5 Trip Length Short (2 5 miles) 48.8 Medium (5 10 miles) 26.6 Length (>10 miles) 24.6 PAGE 96 96 Next, the land uses at the non home ends of the trips were determined. Using the same 0.5 mile buffer zone around the trip ends, the proportion of the area covered by seven different land uses was determined. Following seven categories of the land use were considered: Residential, C ommercial and Services, Institutional, Industrial, and warehousing, Transportation, Communication, and Utilities, Agricultural land, and Others (Open space, Vacant, and Water). The land use data was obtained from the Chicago Department of Transportation (C DOT). Table 5 2 presents the descriptive of the land use at non home trip ends. A large proportion of the area at trip ends is residential. However, commercial area is in a substantial proportion (about 14%) at no n home based trip ends. Further, other lan d use type such as open space also has a significant (at least 14%) share at all trip ends suggesting that some trips ended/ originated in a large parking lot or at a remote place. Table 5 2 Land Use d escriptive at the non home ends HB Origin HB Dest NHB Origin NHB Dest Count 731 866 1253 1253 Mean SD Mean SD Mean SD Mean SD Residential 59.92 17.72 59.62 18.16 46.91 22.09 47.23 22.91 Commercial 5.90 5.91 6.19 6.28 14.03 13.48 15.46 14.59 Institutional 5.64 5.75 5.63 5.78 7.27 8.15 6.95 7.88 Industrial 2.65 5.02 2.48 4.96 5.73 11.38 5.73 11.02 Transportation 2.53 4.72 2.36 4.19 3.33 5.77 3.54 7.01 Agricultural land 4.40 9.52 5.48 12.07 4.28 11.07 3.74 10.23 Others 18.96 15.34 18.23 14.67 18.45 14.93 17.36 14.44 It is useful to acknowledge that advanced methods are available to determine the trip purpose using GPS streams and GIS based land use layers PAGE 97 97 (for ex. Deng and Ji, 2010). For this study, we chose to simply include the land use as a proxy of trip purpose. 5.1.2 Traveler Characteristics Traveler characteristics include both household attributes (such as composition and income) and person attributes (such as age and gender). The determination of the household attributes of the trip maker was rather straightforward given that there were explicit identifiers in the data linking the GPS traces to specific vehicles, and the vehicles to the households surveyed. The household attributes determined include size, vehicles, licensed drivers, type, home ownership, and income The determination of the person attributes was not as straightforward as there was no explicit identifier linking the GPS traces to a specific person in the household. As a consequence, a primary driver was identified for every household vehicle using th e self reported (CATI) component of the overall travel survey. The primary driver of a vehicle is the household member who used the vehicle the most during the survey day (for the one day CATI survey). To a large extent (over 75%), a unique household membe r was identified as the primary diver for each vehicle. This primary driver was assumed to the trip maker for all include age, gender, ethnicity, and employment/student statu s. Table 5 3 PAGE 98 98 Table 5 3 Household c haracteristics Person c haracteristics Attribute Share (%) Attribute Share (%) Household Size 2.84 (1.29)* Gender Household V ehicles 2.17 (0.97)* Male 46.7 Home Type Female 53.3 1 family detached 81.1 Age (years) 48.08 (18.45)* 1 family attached to other houses 11.8 < 16 5.7 Building with multiple apartments 5.9 16 25 6.1 Refused 1.3 25 35 10.1 Home Ownership 35 45 17.2 Owned 91.0 45 55 27.3 Rented 7.6 >55 33.5 Refused 1.4 Ethnicity Household Income (per year) White 49.9 Less than $20,000 1.2 Black/ African American 3.7 $20,000 $34,999 6.4 Other 1.2 $35,000 $49,999 8.8 Refused 45.1 $50,000 $59,999 4.9 Employment $60,000 to $74,999 8.7 Yes Full Time 52.8 $75,000 to $99,999 27.5 Yes Part Time 18.6 More than $100,000 35.8 Not 23.5 Refused 6.7 Refused 5.1 Time at current home location Student New (<2 years) 9.1 Yes Full Time 7.2 Medium (2 10 years) 44.7 Yes Part Time 3.8 Experienced (> 10 years) 46.2 No 89.0 Note: *presents mean (std. deviation) On average, a household in the sample is consist of about 3 members and owns 2 vehicles. The sample is dominated by the households that live in a 1 family detached home (81.1%) and owns the home (91%). Also, about 72% of the households have annual income of higher than $60k. The sample has a mix of males and females and majority (78%) of the individuals is older than 35 ye ars. Most of the individuals (49.9%) in the sample are of white ethnicity and about 45% refused to reveal their ethnicity. 71.4% of the individuals are employed and only 11% are students. 5.2 Determination And Characterization Of Alternate Routes A major step in the data assembly process is to determine a set of alternate routes for each OD pair (i.e. the choice set) and to characterize the routes in the PAGE 99 99 set using several attributes. The Breadth First Search Link Elimination (BFS LE) procedure to determine the alternate routes is discussed in 5.2.1 and the characterization of the routes is described in Section 5.2.2 5.2.1 Breadth First Search Link Elimination (BFS LE) The fundamental BFS LE algorithm from Schussler et al. (2012) was implemented using Visual Basic App lication (VBA) in ArcGIS including some operational enhancements. The algorithm begins by constructing the shortest cost path considering the full network. Subsequently, a BFS LE tree (i.e. the set of alternate routes for the OD pair) is developed by repea tedly constructing shortest cost paths after removing a link from a previously constructed shortest path. In this study, free flow travel time on links is used as the generalized cost and the built in shortest path calculation tools from ArcGIS are used. PAGE 100 100 Figure 5 1. Basic BFS LE tree First shortest path No shortest path Same path Route 1 Route 2 Route 3 Route 4 Route 5 Route 6 Route 7 Barrier PAGE 101 101 Figure 5 node of the BFS LE tree and comprises a sub roadway network (The root node or the top most node has the full roadway network). All nodes at the same level (or depth) represent sub networks th at were obtained by removing links from the same previously generated shortest path. In the current implementation, the point of the link. All the nodes (sub networks) at the same depth are examined before proceeding to nodes at a lower depth implying a breadth first search. Some iteration may result in no feasible shortest path. Moreover, s imilar paths could be calculated at different nodes. In that case, only the first path is saved into the choice set. The following implementation details are of interest. In a high resolution network, a least cost path between an OD pair can easily contain a large number of nodes and links as even the local streets and the corresponding int ersections are represented. Further, even a continuous roadway segment could be represented by several links of small lengths (in other words not all nodes are intersections) to capture differences in one or more attributes along the roadway. Thus, the num ber of possible links that could be removed is too large making the BFS LE tree quite complex. At the same time, removing links that are simply a part of a contiguous segment would not lead to truly alternate paths thereby affecting the overall computation al efficiency of the algorithm. To address this issue, only links that end on intersections are PAGE 102 102 It is useful to note that Schussler et al. 2012 addressed this issue by adjusting the roadway topology by connected by an intersection into bigger segments. Essentially, this procedure ensures that all the nodes in the corrected network are intersections. However, one could lose the detailed roadway attribute informati on during this process as these get averaged to represent the longer segment. Our approach of eliminating only links ending in intersections addresses the computational issues while still preserving the detailed roadway characteristics. Further links tha t are very close to the origin and/or destination (within 0.15 miles) are also not candidates for elimination as these can quickly lead to sub networks with infeasible paths. This procedure was also adopted by Park and Rilett (1997). Once a link has been eliminated and a sub network has been developed, the algorithm first checks for the uniqueness of the sub network. The reader can see that it is possible to arrive at the same sub network (node) by removing the same set of links but in a different order. E nsuring uniqueness prior to re running the shortest path within the sub network is another approach to reduce processing time. Once a shortest path has been identified within a sub network, its between the newly identified route and all the previously identified routes in the choice set. If this factor i s less than 0.95, the new route is introduced into the PAGE 103 103 choice set as another alternative. If not, the new route is deemed to be very similar to one of the routes already in the choice set and is therefore excluded. Finally, it is also very useful to set termination conditions. The algorithm is set to terminate after generating a minimum set of alternatives for each route (20 in this study). However, sometimes it might take an excessively long time to identify 20 alternatives. To take care of this issue, a maximum run time threshold is also imposed with this time being dependent on the speed of the computer being used. The algorithm was run for 2692 of the 2850 trips (the trips longer than 25 miles were excluded considering run time issues). As shown in F igure 5 2 and Table 5 4, for over 72% of these trips, 14 or more alternative routes were generated within stipulated run times. Less than 15% of the cases had fewer than 10 routes and less than 2% had fewer than 5 routes. Figure 5 2 Frequency distrib ution of choice set size PAGE 104 104 Table 5 4 Choice set size Choice set s ize Count % Share >= 14 1941 72.10 >= 10 2303 85.55 >= 5 2653 98.55 Further, the observations with fewer than 14 alternatives in the choice set were examined for not having enough routes. As the path generation algorithm starts with the true shortest time route and generates more alternatives by removing links from it, the comparison of link counts in these routes may provide an insight into the behavior. The comparison of the link count in the shortest time route is presented in Table 5 5 and Figure 5 3 The comparisons indicate that the average link count in the shortest time route of the observations with fewer than 14 alternatives is significantly higher than the observations w ith at least 14 alternatives. Also, as mentioned before, a route is included in the choice set only if it meets the commonly factor criteria of 0.95. Therefore, with longer trips it is more difficult to keep generating highly diverse routes that meet the s et CF criteria. This is due to the high trip lengths in the denominator of the CF calculation and would, compare to shorter trips, need a larger portion of non overlapped distance to meet the CF criteria of 0.95. Table 5 5 Comparison of link counts in t he first shortest time routes With at least 14 a lternatives Fewer than 14 a lternatives Mean SD Mean SD Link Count 74.87 48.11 147.71 81.54 Distance 5.13 3.52 10.24 5.81 Time 8.83 5.63 15.80 8.19 PAGE 105 105 Figure 5 3 Link count comparison Again, about 72% (1941) of the choice sets have 14 alternatives or higher. With this, we decided to use the choice set size of 15 for model estimations. Therefore, the observations with less than 14 alternatives in the choice set were filtered out. Further 28 observations out of the remaining 1941 observations had the choice set of 14 alternatives and the chosen route was one of them. Again such observations were also eliminated. Finally, the estimation sample (CS15) consists of 1913 observations with eac h having 15 alternatives in the choice set. For the same observations, two more samples with choice set sizes of 10 (CS10) and 15 (CS10) were also constructed. It is important to note that to construct choice sets with size 10, first 10 alternatives genera ted from the path generation algorithm were considered. A similar process was used for constructing the sample with choice set size 5. PAGE 106 106 5.2.2 Route Attributes Several attributes were generated for the chosen route and for each of the alternatives in the choice se t. A summary of these attributes is presented in table 5 6. The procedures employed to generate these attributes are discussed subsequently. Table 5 6 Route attributes Attribute n ame Definition Link Count Number of links in the route TotalDistance (miles) Total length of the route TotalTime (minutes) Total (free flow) time spent in traversing the route IntersectionCount Number of intersections along the route LongestLegDistance (miles) Distance of the longest continuous stretch between two inters ections LongestLegTime (minutes) Travel time of the longest continuous stretch between two intersections LeftTurns Number of left turns made traversing the route (include all left turns and does not distinguish based on the left turn type) RightTurns Number of right turns made traversing the route ExpresswayDistance (miles) Distance of the expressway segments in the route ExpresswayTime (minutes) Travel time on the expressway segments in the route LongestExpresswayDistanceLeg (miles) Distance of the longest continuous expressway segments LongestExpresswayTimeLeg (minutes) Travel time on the longest continuous express segments in the route ArterialDistance (miles) Distance of the arterial segments in the route ArterialTime (minutes) Travel time on the arterial segments in the route LongestArterialDistanceLeg (miles) Distance of the longest continuous arterial road segment in the route LongestArterialTimeLeg (minutes) Travel time on the longest continuous arterial segments in the route LocalRoadDistance (miles) Distance of the local road segments in the route LocalRoadTime (minutes) Travel time on the local road segments in the route LongestLocalRoadDistanceLeg (miles) Distance of the longest continuous local road segments in the rout e LongestLocalRoadTimeLeg (minutes) Travel time on the longest continuous local road segments in the route MaxSpeed (mph) Average speed during the trip MeanSpeed (mph) Maximum speed attained during the trip Circuity Deviation in terms of total length from the straight line distance between the origin and destination PAGE 107 107 A node is considered as an intersection if there is three or more segments meet on that node. Hence, the number of intersections is calculated by determining the number of nodes with thre e or more segments. A leg is defined as the stretch of the route between two intersections. Therefore, the longest leg by distance and time is calculated as the maximum leg distance and leg time respectively for a route. Number of turns in a route are determined by reading the directions output provided by the route solver in ArcGIS. The directions window explicitly specifies the types of turn, if required, along a route. The output also distinguishes the turns in terms of sharp and normal turns. The te xt in the output is read to determine the number of turns. The roads in the network are classified into three categories: freeways, arterials, and local roads. The total distance and time on each road types is calculated and then the corresponding proporti ons are determined. The longest continuous travel (distance and time) made on each road type is also estimated. Two measures of speed are calculated for a route: average speed, and maximum speed. The average speed is calculated by taking the time weighted average of the posted speeds on the segments of a route. Circuity is used as a measure of the route distance deviation from the network free straight line distance between the origin and destination. The straight line distance (SLD) is calculated using t he Haversine formula of calculating distance between two points: PAGE 108 108 Where, lat1 and long1 are the latitude and longitude of a point, and R is the earth radius (3949.99 miles). The circuity is th en calculated by taking the ratio of the route length with the straight line distance. The circuity is always greater than or equal to 1. PAGE 109 109 Table 5 7 Descriptive of route attributes Attributes Chosen r oute Choice set a ltern atives CS15 CS10 CS5 Mean SD Mean SD Mean SD Mean SD Link Count 75.03 47.86 79.75 49.66 79.07 49.59 78.29 49.50 TotalDistance (miles) 5.31 3.69 5.48 3.67 5.44 3.66 5.37 3.63 TotalTime (minutes) 9.75 6.44 9.83 6.16 9.69 6.04 9.52 5.95 Intersection s 16.28 11.21 17.75 11.40 17.60 11.43 17.36 11.36 LongestLegDistance (miles) 1.47 1.77 1.35 1.49 1.35 1.52 1.34 1.50 LongestLegTime (minutes) 2.70 2.83 2.39 2.49 2.37 2.29 2.34 2.25 LeftTurns 1.31 1.21 3.18 1.55 3.04 1.53 2.81 1.51 RightTurns 1.36 1.25 3.23 1.58 3.09 1.56 2.84 1.55 Distance Proportion on Expressway s 0.59 5.82 0.58 5.41 0.62 5.60 0.64 5.71 Time Proportion on Expressway s 0.46 4.74 0.42 4.09 0.46 4.28 0.47 4.37 LongestExpresswayDistanceLeg (miles) 0.08 0.81 0.07 0.69 0.07 0.70 0.07 0.67 LongestExpresswayTimeLeg (minutes) 0.08 0.90 0.07 0.77 0.08 0.78 0.07 0.75 Distance Proportion on Arterial s 33.14 33.52 36.50 31.07 37.01 31.35 38.00 32.09 Time Proportion on Arterials 29.08 31.11 31.15 27.92 31.72 28.30 32.80 29.17 LongestArterialDistanceLeg (miles) 1.75 2.81 1.80 2.59 1.79 2.58 1.85 2.75 LongestArterialTimeLeg (minutes) 2.57 3.99 2.60 3.65 2.58 3.62 2.67 3.86 Distance Proportion on Local Road s 66.27 33.80 62.92 31.28 62.37 31.58 61.37 32.30 Time Proportion on Local Roads 70.46 31.36 68.43 28.12 67.83 28.51 66.74 29.37 LongestLocalRoadDistanceLeg (miles) 1.08 1.94 1.19 1.61 1.16 1.59 1.13 1.59 LongestLocalRoadTimeLeg (minutes) 2.26 3.96 2.51 3.48 2.43 3.29 2.38 3.28 MaxSpeed (mph) 40.09 6.37 41.13 5.87 41.14 5.90 41.11 5.90 MeanSpeed (mph) 34.19 4.98 33.17 4.64 33.32 4.68 33.55 4.76 Circuity 1.39 0.36 1.44 0.34 1.42 0.31 1.40 0.28 PAGE 110 110 Distance and time on expressway is really low compared to arterials or local roads, Table 5 7. As most of the trips (64.6%) are shorter than 10 miles, it is reasonable to expect low expressway usage Among choice sets with different sizes, average distance and average time increase with more alternatives in the choice sets. As the path generation algorithm starts with the true shortest time route, and determines the next shortest time route, next alternative, by eliminating a link in the route, with more alternatives the routes get longer. As expected, the average intersections, left turns and rig ht turns in the chosen route are less than the alternatives in the choice sets. The average mean speed on the chosen routes is higher than the alternatives in the choice sets. Choice set composition is examined in terms of the maximum overlap of alternati ves with the chosen route. The overlaps are calculated using a python script and the results are presented in Figure 5 4 for three datasets For CS15, about 36% of the observations already include the chosen route in the choice set. Moreover, more than 51 % of the observations replicate at least 90% of the chosen route in the choice set. These numbers are lower for sample with lesser alternatives; nevertheless more than 40% of the observations include at least 90% of the observed route. This indicates that the choice sets are composed of reasonable alternatives. PAGE 111 111 Figure 5 4 Frequency distribution of overlap with the chosen routes Further, to assess the heterogeneity of alternatives in the choice sets, the variation of the commonly factor (CF) within a cho ice set is calculated and its distribution over all the observations is examined, Figure 5 5. As expected, the variation in the variation of CF within a choice set grows as the choice set size dec reases. Precisely, CS5 contains more diverse routes (higher CF) in the choice sets than the other two datasets. The inclusion of more alternatives in the choice sets results in lesser variation in CF, thus suggesting the presence of more similar routes in the choice sets. The behavior seems reasonable with the fac t that fewer alternatives are more likely to have higher diversity than high alternatives. In general, all datasets contain routes with varied commonly factor within the choice sets which suggests that the choice set contains dissimilar routes. PAGE 112 112 Figu re 5 5 Frequency distribution To prepare the samples for model estimations, the chosen route is manually added to the choice se t if it is not already present and the extra alternative is eliminated to maintain the choice set size. 5.3 Summary Out of the 3513 observations, for which the map match algorithms generated routes, 2850 observations had trip and traveler characteristics determined. Further, an enhanced version of the Breadth First Search Link Eli mination (BFS LE) was used to generate choice sets for 2692 observations that were shorter than 25 miles. The enhancements to the BFS LE were aimed to generate diverse and yet attractive routes in the choice sets. The generated choice sets were assessed fo r the choice set size, coverage and heterogeneity. Over 72% of the generated choice sets contained 14 PAGE 113 113 alternatives or higher. Also, the alternatives in the choice sets provided reasonable coverage of the chosen routes and were found to be different from ea ch other. PAGE 114 114 CHAPTER 6 ROUTE CHOICE MO D ELS This chapter presents the empirical results of the route choice models estimated using data from Chicago. The first section presents an overview of the modeling methodology. The second section presents the model re sults. The third section discusses the predictive assessments made using the estimated models. The last section presents an overall summary of the chapter. 6.1 Path Size Logit (PSL) Model The path size logit ( PSL ) model is used in the analysis of route choices. As already discussed, this approach provides a closed form structure for choice probability, has been shown to have good empirical performance. This model introduces a similarity term called the Path Size (PS) Factor within the deterministic component of the utility to account for similarities among alternatives in a alternative (Prato, 2009) and is greater than 0 but less than or equal to 1 In the original formulation, path size for route i in choice set C is given by the following (Ben Akiva and Bierlaire,1999): Where, is the set of links in path i is the length of link a in path i, is the length of the path i, is the link path incidence dummy, it is equal to 1 if link a is on path l, and 0 otherwise. If a path is unique, i.e., does not share any link with any of the other alternatives, its PS value is 1. The probability expres sion of choosing a route i from the choice set C is given by: PAGE 115 115 Where, and are deterministic utilities for routes I and j in choice set C, is the parameter for Path Size to be estimated. For demonstratio n, consider a roadway network Figure 6 1, with three alternative paths ( 1: O A D, 2: O A B D, and 3: O D) for an OD pair. Figure 6 1 Example of calculating PS attribute Path 1 and path 2 share the link OA. The PSL model captures t his similarity using the path size attribute. The path size attribute for path 1 is: Similarly, the path size attribute for path 2 is: Path 3 does not share any link with the other paths; therefore the corresponding PS attribute is 1. The path size factor in the path utility, LnPS, is a higher negative number with more path similarity (lower PS). With no similarity, the factor is 0. PAGE 116 116 and model s are estimate d The two models are estimated for three choice set sizes (5, 10, and 15 alternatives). The bas e model includes only the route attributes (such as distance, turns, intersections, and circuity) on in the utility function The trip and person characterist ics are introduced in the full model in addition to the route attributes Note that the alternatives in the choice set are not labeled and therefore the trip and person attributes are introduced into the utility function by interacting them with the rout e attributes. Thus, in the full model, the sensitivity to various route attributes are allowed to vary based on the trip and traveler characteristics. 6.2 Estimation Results The PSL models were estimated using NLOGIT software. As described in Chapter 5, a t otal of 1913 observations are selected to develop route choice models. Table 6 1 presents the descriptive of the observations. Table 6.1 presents the descriptive statistics of the explanatory variables of the observations. On average, the households consi st of 3 members and 2 vehicles. Most of them are single family and owned the house Further, 20.3% households have annual income of less than $60k and 35.7% have annual income of more than $100k. 7.3% households refused to report their annual income. In to tal, 46.5% of the households were at the current home location for a long period (more than 10 years) and about 10% were new to the location. PAGE 117 117 Table 6 1 Estimation data descriptive Note: presents mean (std. dev.) About 60% of the observations are performed by male and on average the age of the individuals lies at the higher end (48.25 years). Specifically, about 60% are older than 45 years in age About 56% are white Americans and 39.6% did not report their ethnicity. Over 72% are workers and about 90% are not students. In terms of trips, 56.5% are home based trips and among them more than 31% originated at home. Most of the trips (62.4%) were performed during weekdays with about 12% on Fridays. Attribute Share (%) Attribute Share (%) Household Characteristics Person Characteristics Household Size 2.84 (1.32)* Gender Household V ehicles 2.18 (0.98)* Male 44.1 Home Type Female 55.9 1 family detached 80.7 Age (years) 48.25 (15.30)* 1 family attached to other houses 11.8 < 16 -Building with multiple apartments 5.8 16 25 9.0 Refused 1.7 25 35 11.6 Home Ownership 35 45 19.8 Owned 89.8 45 55 27.7 Rented 8.4 >55 32.0 Refused 1.9 Ethnicity Household Income(per year) White 55.7 Less than $20,000 1.3 Black/ African American 3.1 $20,000 $34,999 6.7 Other 1.5 $35,000 $49,999 7.6 Refused 39.6 $50,000 $59,999 4.7 Employment $60,000 to $74,999 9.9 Yes Full Time 51.7 $75,000 to $99,999 26.9 Yes Part Time 20.9 More than $100,000 35.7 Not 26.8 Refused 7.3 Refused 0.6 Time at current home location Student New ( < 2 years) 9.7 Yes Full Time 6.2 Medium (2 10 years) 43.8 Yes Part Time 4.0 Experienced ( > 10 years) 46.5 No 89.8 Trip Characteristics Trip Type From Home 31.4 To Home 25.1 NHB 43.5 Travel Day Weekday (Monday Thursday) 62.4 Friday 11.8 Weekend 25.8 Travel Time Peak 31.8 Off Peak 68.2 PAGE 118 118 Out of the 1913 observations, 80% (1530) were selected to estimate PSL models and remaining 20% (383) were set aside for t he validation of the models. Three datasets with the same 1530 observations but different choice set sizes of 15, 10, and 5 discussed first followed by a discussion of The empirical results for the base models (only route attributes are introduced into the utility functions) are presented in Table 6 2. The results are presented for the three choice set sizes (15, 10, and 5 alternatives). The followi ng discussion applies to the estimation results all three models unless stated otherwise explicitly. Table 6 2 Base model estimations Variable CS 15 CS10 CS5 Est. T stat Est T stat Est T stat Time 0.081 2.85 0.046 1.37 0.066 1.64 Shortest time path 0.899 8.68 0.519 4.92 0.060* 0.60 Longest leg time 0.059 2.32 0.051 1.84 0.051 1.60 Left turns per min 8.257 27.77 8.110 25.98 7.626 21.86 Right turns per min 7.791 26.92 7.691 25.25 7.272 20.79 Intersections per min 0.483 6.04 0.484 5.67 0.538 5.65 Proportion of time on Local Roads 0.017 7.33 0.018 7.29 0.021 7.31 Circuity 2.851 11.70 2.528 9.98 1.802 7.19 Ln (Path Size) 0.869 11.84 0.800 8.86 1.192 8.16 Number of Observations 1530 1530 1530 Log likelihood (at convergence) 2000.70 1698.40 1172.42 Log likelihood (equal shares) 4143.32 3522.96 2462.44 R Sqr 1 0.517 0.518 0.524 Adj. R Sqr 2 0.515 0.515 0.520 Note s : indicates that the estimate is insignificant at 95% confidence interval 1. R Sqr = 1 LL(at convergence)/LL(equal share s ) 2. Adj. R Sqr = 1 {LL(at convergence) No. of parameters}/LL(equal share s ) As expected, the free flow travel time was found to be negatively associated with the p robability of choosing a route indicating that travel ers do avoid the routes with high er travel time. However, the effect of travel time became insignificant at 95% PAGE 119 119 confidence interval if the alternatives in the choice sets are reduced to 10. Further, the shortest time path between the origin destination (OD ) pair is also more likely to be chosen by the traveler (after controlling for the effect of travel time in general). The effect was estimated insignificant for the dataset with the least alternatives (CS5). Longest (time units) stretch of roadway without intersections also enhance s the attractiveness of a route. Higher number of left or right turns per minute of travel along a route was found to negatively a ffect the choice of the corresponding route. Similarly, intersections per minute of travel were neg atively associated with the selection of a route. The time spent on local roads was positively associated with the possibility of choosing a route. However, the effect does not seem unreasonable considering that a significant fraction of the trips in the d ataset were of shorter length and did not use the freeway. Further a high resolution network was used in the choice set generation resulting in significant volume of local streets in the choice set. Circuity was found to be a negative factor in choosing a route. Travelers prefer to travel on a route that deviate less from the straight line path between an origin and destination. Finally the positive sign on the path size indicates that if a route is less similar to the alternatives, its chances of getting chosen will be high. This positive effect of the path size variable was also reported in several past stu dies on route choice models (for ex. Prato and Bekhor, 2006; Prato and Bekhor, 2007; Bierlaire, and Frejinger, 2008 ) Overall the base models do indic ate intuitive effects of several route specific attributes on choice of route for any trip. Next the route attributes were interacted with the trip and person characteristics are presented in Table 6 3. Once again the models PAGE 120 120 are estimated for the three choice set sizes. The discussion applies to the estimation results all three models unless stated otherwise explicitly. Table 6 3 Full model estimations Variable CS 15 CS10 CS5 Est. T stat Est. T stat Est. T stat Time 0.102 3.18 0.059 1.58 0.068 1.50 Time Peak 0.104 2.20 0.076 1.49 0.034 0.61 Shortest time path (S T P ) 0.598 3.58 0.316 1.87 0.285 1.64 S T P Experienced 0.367 1.95 0.229 1.21 0.281 1.42 Longest leg time (LLTM) 0.072 2.72 0.059 2.01 0.061 1.84 Left turns per min (LTRN) 8.734 16.84 8.434 15.80 7.784 13.27 LTRN From Home 1.374 1.92 0.623 0.82 0.648 0.78 LTRN To home 2.005 2.79 1.969 2.67 1.574 1.88 LTRN New 2.536 2.64 1.818 1.87 2.522 2.14 LTRN Medium 2.273 2.93 1.957 2.42 1.721 1.95 Right turns per min (RTRN) 10.227 15.12 10.118 14.23 9.930 11.96 RTRN From Home 1.404 2.06 1.352 1.85 1.595 1.91 RTRN To home 1.178 1.63 1.093 1.44 1.563 1.76 RTRN Experienced 2.030 3.08 2.018 2.90 2.167 2.66 Intersections per min (INTR) 1.223 4.50 1.298 4.46 1.217 3.67 INTR Male 0.348 2.28 0.393 2.44 0.491 2.65 INTR Age 0.008 1.70 0.008 1.51 0.005 0.90 INTR Weekend 0.294 1.70 0.253 1.38 0.041 0.18 INTR Non home based 0.262 1.73 0.399 2.50 0.380 2.06 Proportion of time on Local Roads (LRTP) 0.016 3.97 0.017 4.12 0.019 3.96 LRTP Male 0.008 1.80 0.008 1.79 0.008 1.59 LRTP From Home 0.011 2.11 0.014 2.42 0.015 2.36 LRTP To Home 0.010 1.80 0.008 1.34 0.011 1.59 Circuity (CRCT) 6.663 11.79 6.152 10.74 5.384 8.22 CRCT Male 1.940 4.84 2.117 5.17 1.471 3.24 CRCT Experienced 3.310 6.24 2.923 5.56 3.110 5.03 Ln (Path Size) 0.884 11.77 0.822 8.87 1.280 8.47 Number of Observations 1530 1530 1530 Log likelihood (at convergence) 1935.21 1637.41 1126.24 Log likelihood (equal shares) 4143.32 3522.96 2462.44 R Sqr 1 0.532 0.535 0.543 Adj. R Sqr 2 0.526 0.528 0.532 Note s : indicates that the estimate is insignificant at 95% confidence interval 1. R Sqr = 1 LL(at convergence)/LL(equal share) 2. Adj. R Sqr = 1 {LL(at convergence) No. of parameters}/LL(equal share) The travel time was negatively associated with the probability of choosing a route. Further, t ravelers indicated less sensitivity to travel time during peak hours than off peak. The effect is probably capturing the influence of congestion during peak period. As the study uses free flow travel time, congestion on shortest travel time route may PAGE 121 121 have forced travelers to take a route wit h higher free flow travel time. For CS5, this effect was estimated insignific ant at 95% confidence interval. If a route is the shortest time path, a higher preference was given to it than the other alternatives. T he travelers who have been living at the c urrent home location for more than 10 years (experienced travelers) preferred the shortest time path even more than other travelers (people who have lived in their current residence for less than 10 years). With experience, travelers have an enhanced knowl edge of the network, and therefore, they are more likely to be aware of the shortest time paths than the other travelers. Left turns per minute of travel were negatively associated with the probability of choosing a route. Further, home based trips were l ess sensitive to left turns than non home based trips. Among home based trips, travelers going to home showed more tolerance to left turns than travelers departing on a trip from home. For smaller number of alternatives (10 and 5), the effect of left turns on the trips originating at home was insignifi cant at 95% confidence interval The number of years spent at the current home location was also found to be a factor in willingness to go through the left turns during a trip. The experienced travelers were m ore tolerant to the left turns and travelers who were re latively inexperienced (less than 2 years at their current home location ) showed the most sensitivity to left turns. Perhaps, less time at the current home locations reflects in their limited knowledg e of the roadway network and intersection performance of the area. The estimates of the CS10 indicated that the trav elers who were living for 2 to 10 years were the most PAGE 122 122 sensitive to the left turns and the ones who had been living f or longer durations (more than 10 years) were the least sensitive. Number of right turns per min of travel was also estimated as a negative factor in choosing a route. Similar to left turns, the route choice decisions for home based trips were affected less by right turns th an non home based trips. T he travelers were willing to take right turns while leaving from home than when there are going back home. This effect can be explained in conjunction with the effect of left turns on home based trips. As left turns going to a pla ce becomes right turns coming back using the same path, the trace on ward paths when going back home Experienced travelers were relatively less concerned about making right turns during a trip. N umber of intersections per minute of travel on a route reduced the attractiveness of a route. While choosing a route, men were less sensitive to intersections than women. While making a decision for route choice, younger travelers were more concerned about the number of intersections than the older travelers. The effect is expected as young people are generally like to drive on a route with fewer interruptions. For CS 10 and CS 5, the effect was estimated insignificant at 95% confidence interval. Further, tra velers were more willing to go through the intersections on weekends than weekdays possibly reflecting the difference in traffic volumes at intersections across the days of the week. This effect of travel day was insignificant at 95% confidence interval fo r datasets with fewer alternatives (10 and 5) in a choice set. PAGE 123 123 Non home based t rips were less sensitive to intersections than the home based trips. These trips are more likely to be made in less familiar areas (not in the vicinity of home) and, hence, the travelers may not be aware of alternate options. The proportion of the total travel time spent on the local roads was positively associated with the probability of choosing a route. The effect is a result of high proportion of local roads in the datasets. Men showed less preference to a route with high l ocal street time than women. T ime on local roads was given more preference for the home based trips than the non home based trips. A mong home based trips, the trips originating at home chose routes with more time on local road s than the trips that were goi ng to home. Circuity was a negative factor in choosing a route. M ale were less sensitive to circuity than female. Similarly travelers who were li ving at the home location for long er time (more than 10 years) were less sensitive to circuity than other tra velers. Once again, this could be indicating the knowledge of congested routes in the roadway network. The people with more time in the area are more likely to be aware of the congested routes, therefore, choose to take more circuitous route rather than sp ending time in traffic. 6.3 Predictive Assessment To assess the predictive quality, the models (base and full) developed using 15 alternatives (the CS15 models) were applied to the validation sample with 383 observations. The prediction performances of the mod els were compared against the performance of the deterministic method (shortest time path). In each case the extent of the distance overlap of the predicted route with the chosen route was compared. PAGE 124 124 In the case of the deterministic model, there is exactly one predicted route (the shortest time path). Therefore the determination of the overall of the predicted path and the observed path is straightforward. However, the prediction from the path size logit model is in the form of the probability of choosing a route in the choice set. Therefore, we focus on comparing the expected overlap by considering the overlap of each option in the choice set with the chosen route and the probability assigned to each option. T he expected overlap for a trip i is the probability weighted average of the Where, N is the total number of alternatives in the choice set, P j is the probability of choosing route j, and O j is th e physical overlap of route j with the chosen route. If there are more alternatives in the choice set, then it is more likely to have an option that is closer (greater overlap) to the chosen route. At the same time the probability assigned to each option i s reduced (since the probabilities should sum to 1 across the options). If there are fewer options in the choice set used for prediction, the probability assigned to each option is generally higher but the chance of having an option with a greater overlap is lesser. In the context of the above discussion, we examine the predictive performance when the model (estimated using 15 alternatives) is applied to three different choice set sizes (4, 9, and 14 alternatives ). The last alternative in any choice set as sembled for model estimation was the chosen alternative which was added in to the other options generated by the BFS LE algorithm (if the choice set generated did not automatically PAGE 125 125 include the chosen option). Therefore the alternatives used for predictions represent the first 4, 9, and 14 alternatives that would be generated by the BFS LE algorithm. 6.3.1 Comparison of Predicted O verlaps The deterministic overlap was simply calculated as the distance overlap between the shortest time path and the chosen path. Tab le 6 4 shows the statistic of the predicted overlaps. Table 6 4 Overlaps statistic (full sample) Base m odel Full m odel Shortest t ime CS14 CS9 CS4 CS14 CS9 CS4 CS1 Avg 50.46 51.43 52.25 50.56 51.57 52.40 58.48 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 96.54 96.12 97.49 96.53 96.11 97.47 100.00 Std Dev 27.63 28.33 29.36 27.70 28.40 29.42 35.52 On average, the deterministic overlap s were high er than the expected overlaps. However, with fewer alternatives, higher expected overlap s were generated. The lower probabilities. This was also reflected in the maximum overlap for the probabilistic routes as it was always less than 100. To get more insight i nto the results, frequency distributions of the predicted overlaps were performed, shown in Table 6 5 PAGE 126 126 Table 6 5 Cumulative share of expected overlaps (full sample) Base m odel Full m odel Shortest t ime Overlap CS14 CS9 CS4 CS14 CS9 CS4 CS1 10 9.40 10.70 10.97 10.44 10.44 11.49 14.10 20 17.23 17.23 19.06 17.23 17.23 19.06 21.15 30 27.68 28.20 27.68 27.94 27.94 27.68 28.46 40 38.90 38.38 37.60 38.38 38.38 37.86 34.99 50 48.30 45.69 46.74 45.69 45.69 46.74 42.56 60 58.22 55.09 55.35 55.09 55.09 55.09 47.78 70 68.41 66.32 64.23 66.58 66.58 63.45 53.52 80 80.94 79.37 76.76 78.85 78.85 76.24 61.88 90 93.21 93.73 89.56 93.73 93.73 89.56 70.50 100 100.00 100.00 100.00 100.00 100.00 100.00 100.00 About 30% of the deterministic paths were very close (greater than 90% overlap) to the chosen routes. Moreover, about 71% of those were the chosen routes. This may have influenced the average overlaps for the deterministic paths. Therefore, the validation sample was segregated into two samples. Fi rst sample consisted of the 30% observations for which the deterministic path was very close to the chosen route. The remaining 70% observations formed the second sample. For the first sample, the statistic and frequency distributions of the path overlaps were calculated and are presented in Table 6 6 and Table 6 7 respectively Table 6 6 Overlaps statistic (30% observations) Base m odel Full m odel Shortest t ime CS14 CS9 CS4 CS14 CS9 CS4 CS1 Avg 79.14 81.79 82.68 79.29 81.99 82.94 98.70 Min 15.81 20.22 41.33 16.55 21.29 43.22 90.49 Max 96.54 96.13 97.49 96.54 96.12 97.48 100 Std Dev 13.80 11.24 12.08 13.87 11.20 11.96 2.58 PAGE 127 127 Table 6 7 Cumulative overlap with the chosen route (30% observations) Base m odel Full m odel Shortest t ime Overlap CS14 CS9 CS4 CS14 CS9 CS4 CS1 < 10 0.00 0.00 0.00 0.00 0.00 0.00 0.00 20 0.88 0.00 0.00 0.88 0.00 0.00 0.00 30 0.88 0.88 0.00 0.88 0.88 0.00 0.00 40 0.88 0.88 0.00 0.88 0.88 0.00 0.00 50 3.54 0.88 1.77 3.54 0.88 1.77 0.00 60 11.50 3.54 5.31 11.50 3.54 5.31 0.00 70 19.47 14.16 15.04 19.47 15.04 14.16 0.00 80 39.82 33.63 33.63 37.17 32.74 32.74 0.00 90 76.99 78.76 66.37 76.11 78.76 66.37 0.00 100 100.00 100.00 100.00 100.00 100.00 100.00 100.00 For the observations where the shortest time path was chosen to make the trip, probabilistic methods predicted routes with at least 50% overlap with the chosen route. Moreover, for about 80% observations the predicted routes were with an overlap of equal o r higher than 70%. This suggests that although probabilistic methods predicted lower overlaps than the deterministic method, the attenuation was low as overlaps were at the higher end. Further, the statistic and the frequency distributions of the path ove rlaps for the seco nd sample are shown in Table 6 8 and Table 6 9 Table 6 8 Overlaps statistic (70% observations) Base m odel Full m odel Shortest t ime CS14 CS9 CS4 CS14 CS9 CS4 CS1 Avg 38.46 38.74 39.52 38.54 38.84 39.62 41.66 Min 0.00 0.00 0.00 0.00 0.00 0.00 0.00 Max 83.17 84.56 90.77 83.16 84.52 90.54 89.72 Std Dev 22.70 23.21 24.75 22.77 23.29 24.78 28.74 PAGE 128 128 Table 6 9 Cumulative overlap with the chosen route (70% observations) Base m odel Full m odel Shortest t ime Overlap CS14 CS9 CS4 CS14 CS9 CS4 CS1 10 13.33 15.19 15.56 13.70 14.81 16.30 20.00 20 24.07 24.44 27.04 24.07 24.44 27.04 30.00 30 38.89 39.63 39.26 39.63 39.26 39.26 40.37 40 54.81 54.07 53.33 55.19 54.07 53.70 49.63 50 67.04 64.44 65.56 66.67 64.44 65.56 60.37 60 77.78 76.67 76.30 77.78 76.67 75.93 67.78 70 88.89 88.15 84.81 89.26 88.15 84.07 75.93 80 98.15 98.52 94.81 98.15 98.15 94.44 87.78 90 100.00 100.00 99.26 100.00 100.00 99.26 100.00 100 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Compared to the deterministic overlaps, the frequency of the probabilistic overlaps was lower at the lower end (less 30% overlap) and was higher at the upper end. With this, it can be deduced that the probabilistic methods produce routes closer to the chosen routes than t he deterministic method. 6.3.2 Outperforming the S hortest P ath To examin e the extent to which the probabilistic path outperforms the shortest time path, the probability of a path with an equal or better overlap than the shortest path is calculated. Therefore, t h e probability of outperform ing is calculated as following: Where, P j is the predicted probability of route j, and is the overlap performance index, which is equal to 1 if overlap between route j and the chosen route is equal to or greater than the overlap between the shortest time path and the chosen route, and 0 otherwise. PAGE 129 129 Table 6 1 0 shows the statistic of the probabilities of outperforming the shortest time path. Table 6 1 0 Statistic of the outperforming probabilities (full sample) Base m odel Full m odel CS14 CS9 CS4 CS14 CS9 CS4 Avg 0.370 0.407 0.499 0.372 0.410 0.504 Min 0.025 0.042 0.093 0.021 0.034 0.076 Max 1.000 1.000 1.000 1.000 1.000 1.000 Std Dev 0.349 0.357 0.336 0.348 0.356 0.333 On average, there is a probability of 50% (CS4) that the predicted path will have an overlap of equal to or better than the shortest time path. The frequency distributions of the outperforming probabilities are presented in Table 6 1 1 Table 6 1 1 Cumulative share of the outperforming probabilities (full sample) Base m odel Full m odel Probability CS14 CS9 CS4 CS14 CS9 CS4 0.1 35.77 37.34 0.26 35.25 35.51 0.52 0.2 48.30 48.04 26.37 47.52 46.74 19.58 0.3 55.09 53.52 47.26 55.09 53.52 47.26 0.4 61.88 57.70 48.83 61.36 57.70 48.04 0.5 69.19 63.19 61.10 69.19 62.92 60.31 0.6 72.85 69.45 63.71 72.58 69.45 63.71 0.7 75.46 73.89 65.80 75.20 73.89 65.80 0.8 80.68 77.02 74.67 80.42 77.02 74.67 0.9 85.12 83.03 75.98 85.12 82.51 75.98 1 100.00 100.00 100.00 100.00 100.00 100.00 For over 30% of the observations, there was at least 50% probability of outperforming the shortest path. The probability of outperforming increased with the reduction in the choice set size, as for 4 alternatives about 40% observations showed a p robability of 50% or higher. PAGE 130 130 For the observations for which the shortest path was very close (over 90% overlap) to the chosen route the average probability of o utperforming the shortest path wa s very low, Table 6 1 2 S imilar results were indicated in the frequency distribution (Table 6 1 3 ) of the outpe rforming probabilities, as most of the observations showed the probability of less than 30%. Table 6 1 2 Statistic of the outperforming probabilities (30% observations) Base m odel Full m odel CS14 CS9 CS4 CS14 CS9 CS4 Avg 0.055 0.086 0.204 0.058 0.090 0.211 Min 0.025 0.042 0.093 0.021 0.034 0.076 Max 0.135 0.223 0.515 0.140 0.223 0.511 Std Dev 0.022 0.031 0.071 0.022 0.031 0.071 Table 6 1 3 Cumulative share of the outperforming probabilities (30% observations) Base m odel Full m odel Probability CS14 CS9 CS4 CS14 CS9 CS4 0.1 92.04 92.04 0.88 92.04 87.61 1.77 0.2 100.00 98.23 59.29 100.00 97.35 44.25 0.3 100.00 100.00 94.69 100.00 100.00 94.69 0.4 100.00 100.00 94.69 100.00 100.00 94.69 0.5 100.00 100.00 99.12 100.00 100.00 99.12 0.6 100.00 100.00 100.00 100.00 100.00 100.00 0.7 100.00 100.00 100.00 100.00 100.00 100.00 0.8 100.00 100.00 100.00 100.00 100.00 100.00 0.9 100.00 100.00 100.00 100.00 100.00 100.00 1 100.00 100.00 100.00 100.00 100.00 100.00 For the remaining sample (70% observations) on average (Table 6 1 4 ) the probability of outperforming was higher than 50%. Moreover for about 65% observations, the chances of predicting a path with equal or better overlap than the shortest path was more than 50% (Table 6 15) PAGE 131 131 Table 6 1 4 Statistic of the outperforming probabilities (70% observations) Base m odel Full m odel CS14 CS9 CS4 CS14 CS9 CS4 Avg 0.501 0.542 0.623 0.503 0.544 0.626 Min 0.044 0.068 0.135 0.040 0.066 0.123 Max 1.000 1.000 1.000 1.000 1.000 1.000 Std Dev 0.337 0.346 0.326 0.336 0.344 0.323 Table 6 1 5 Cumulative share of the outperforming probabilities ( 7 0% observations) Base m odel Full m odel Probability CS14 CS9 CS4 CS14 CS9 CS4 0.1 12.22 14.44 0.00 11.48 13.70 0.00 0.2 26.67 27.04 12.59 25.56 25.56 9.26 0.3 36.30 34.07 27.41 36.30 34.07 27.41 0.4 45.93 40.00 29.63 45.19 40.00 28.52 0.5 56.30 47.78 45.19 56.30 47.41 44.07 0.6 61.48 56.67 48.52 61.11 56.67 48.52 0.7 65.19 62.96 51.48 64.81 62.96 51.48 0.8 72.59 67.41 64.07 72.22 67.41 64.07 0.9 78.89 75.93 65.93 78.89 75.19 65.93 1 100.00 100.00 100.00 100.00 100.00 100.00 6.4 Summary The original PSL model was used to develop route choice models for three different choice sets sizes (CS15, CS10, and CS5). In addition to the trip and route characteri stics. In general expected effected were indicated by the estimation results. Specifically, free flow travel time, left turns, right turns, intersections, and circuity are found negatively associated with the attractiveness of a route. If a route is the shortest time path, it was more attractive to the traveler. Also, if a route is very different from the other alternatives it is more likely to be chosen. Additionally travelers indicated less sensitivity to the travel time during peak period, thus suggesting a congestion effect. Trips going to home were the least sensitive to the travel time and right turns than the PAGE 132 132 other trips. While determining a route, male s cared less about the intersections, proportion of time on local roads and ci rcuity than female s The s ensitivity to the number of intersections in a route decreased with age. Compared to home based trips, non home based trips were less sensitive to intersections and time on local roads. T he effects were more or less similar a cross different choice set sizes, except that some effects became insignificant. In terms of the predictive quality, when the shortest time path was very close to the chosen route, the probabilistic methods produced routes with lower overlaps. However, the over laps were still reasonably high. For the other cases, the probabilistic methods predicted better overlaps than the deterministic method. O n average, there was a probability of 50% that the predicted route will outperform the shortest time path. PAGE 133 133 CHAPTER 7 SUMMARY AND CONCLUSI ON S The study combines data from GPS based travel surveys and Geographic Information Systems (GIS) based roadway network databases to develop models for route choice. The GPS data comes from the Chicago Regional Household Travel Invento ry (CRHTI) and a high resolution roadway network was obtained from ArcGIS Data and Maps. Three modules are performed during the study: map matching, choice set generation, and route choice modeling. The summary of the three modules is presented below, foll owed by some insight on extending the research. 7.1 Map Matching The GPS traces must first be mapped to the roadway network to identify the chosen route in terms of the network link actually traversed. Two broad classes of map matching methods are available. The GPS weighted shortest path (GWSP) is a simpler choice. The Multi Path (MP) algorithm is free from such assumptions, but is considerably elaborate in terms of methodolog y. This study contributes to the map matching literature by presenting enhanced implementations of both classes of algorithms and comparing their operational performance using data from a large scale GPS survey. The implementation enhancements were aimed to achieve full automation of the method (no need for manual interventions such as visual inspections) and to improve computational performance. The methods were implemented in ArcGIS using VBA with ArcObjects. The algorithms were first validated on locall y collected GPS data on known routes. While both algorithms performed well, it is observed that the GWSP was more sensitive PAGE 134 134 to missing links in the network than the MP approach. On applying the algorithms to large dataset comprising almost 4000 trips, both algorithms generated complete trips for a vast majority of the cases (again the MP produced mode complete trips than the GWSP). On comparing the 3513 trips for which both algorithms produced results, we find a substantial similarity between the routes ge nerated in terms of both common links and the extent of distance overlap. This holds irrespective of trip distance and time of day of travel. Broadly, this result suggests that the simpler GWSP algorithm might be appropriate to generate chosen routes from GPS traces if a good (complete) roadway network database is available. distance and shortest path routes between the same locations, we find that the extent of overlap between the between these routes generally increases with distance but is generally the same across the peak and off (free flow) time path s more than they follow the shortest distance paths, especially for longer trips. This clearly reflects a preference for using higher speed facilities for longer trips. Even though the chosen paths are quite deviant from the shortest paths in terms of the actual links traversed, the overall distance/time along the chosen path is fairly close to the distance/time along the shortest paths. This is possibly because of the presence of alternate (possibly parallel) links/paths in the network that are very compa rable in terms of distances and times. PAGE 135 135 7.2 Choice Set Generation Once the chosen route has been determined, the next step is to determine the set of alternate paths available for the same trip. The shortest path based path generation algorithms are recommended for generating alternatives in a high resolution roadway network. The Breadth First Search Link Elimination (BFS LE) method has shown to contribution to the choice set gene ration literature includes the enhanced implementation of the BFS LE algorithm. The enhancements were aimed to generate diverse and yet attractive routes in the choice sets. The method was implemented in ArcGIS using VBA with ArcObjects. Out of the 3513 tr ips with observed routes, 2850 trips that had person information available were selected for generating choice sets. However, with the available resources and time, the choice sets were generated for 2692 trips. For over 72% of the observations, 14 or more alternative routes are generated within stipulated run times and among them over 51% of the observations replicated at least 90% of the chosen route in the choice set. With this, 1913 observations that have at least 14 alternatives are selected for model estimations and three estimation datasets with different choice set sizes (15, 10, and 5) were constructed. The chosen route is manually added to the choice set if not already present. 7.3 Route Choice Modeling The Path Size Logit (PSL) model with original Pa th Size formulation was adopted to develop route choice models for each of the datasets. The study contributes to the route choice modeling literature empirically by expressing the utility functions in terms of route attributes (time, longest leg time, dis tance, number of intersections, left turns, right PAGE 136 136 turns, time by facility type, and circuity), trip characteristics (home based/ non home based, weekday/weekend, and peak/off age, employment, and household income) The models were estimated using NLOGIT software. The estimation results indicated expected effects. Specifically, free flow travel time, left turns, right turns, intersections, and circuity were found negatively associated with the attractiveness of a ro ute. Travelers indicated a preference to the route with higher proportion of the travel time on local streets. The effect can be attributed to the large share of local roads in the dataset. The effect of the path size attribute was consistent with the othe r studies in the literature. Specifically, travelers were more inclined to choose a route that was less similar to the other alternatives in the choice set. Further, a congestion effect was observed during the peak period as travelers chose to travel on a route with higher free flow travel time. Sensitivity to the travel time was estimated the least for the trips going back to home. The result indicated that the travelers are more concerned about the travel time when they travel to a place other than home. Men showed a higher tolerance to the number of intersections and the circuity of the route than women. Additionally, compare to women, they indicated a lower preference to the routes with higher travel time proportions on local roads. Sensitivity to numbe preference to the routes with fewer intersections than the older travelers. Furthermore, the intersections were less of a negative factor in choosing routes for home based trips PAGE 137 137 than non home based trips. Home based trips also assigned lesser importance to routes with higher travel time on local streets than the non home based trips. Across different choice set sizes, the effects were more or less similar except that some effects became insignificant in estimations with fewer alternatives. In terms of the predictive quality, when the shortest time path was very close to the chosen route, the probabilistic methods produced routes with lower overlaps. However, the overlaps were stil l reasonably high. For the other cases, the probabilistic methods predicted better overlaps than the deterministic method. Further, on average, there was a probability of 50% that the predicted route will outperform the shortest time path. We envision this study as an important contribution towards the development of empirically rich route choice models. With increasing numbers of GPS surveys and benefits of using high resolution roadway network, the availability of speedy automatic procedures to generate t he chosen routes and alternatives is critical. Further, the insight into the route choice decisions. 7.4 Future Work Loss of observations and efficiency during the map match ing process was primarily due to the roadway network dis connectivity. Presence of new roads or mis representation of the older roads could result in missing links in the roadway network. The missing links that were traveled during a trip could result in a n immature breakdown of the map matching algorithm or the algorithm would be forced to select alternative links that were not traveled. Therefore, an increase in the accuracy of the GIS based roadway network data will contribute towards further increasing the accuracy and operational performance of map matching algorithms. Nevertheless, ArcGIS offers a PAGE 138 138 tool to improve the network connectivity. The tool identifies if there is a disconnection between two nodes and subsequently, inserts a new link connecting t he nodes. Yet, the tool cannot identify all the missing links as it may classify some nodes as dead ends and may not consider them as disconnections. In the roadway network used in the study, the two directions of a road are represented as a single link. That is the network does not distinguish between the directionalities of a two way road. Some other roadway network providers such as NAVTEQ provide dual center line representation in the roadway network. With dual center line, the direction (heading) of the GPS points can be used to match them to the l ink with correct directionality, thus minimizing the map matching errors. Therefore, the use of a more detailed roadway network can contribute towards further increasing the accuracy of map matching algorith ms. The primary focus of the present GPS data collection efforts is on obtaining vehicle locations at a pre defined interval during a trip. A very little efforts are directed tion etc. Due to lack of these information, the researchers are forced to invent/ adopt time consuming methods to derive the information. Therefore, availability of trip information nd contribute towards developing empirically rich models for route choice. Due to unavailability of dynamic travel times, the study used free flow travel times to characterize the chosen routes and generate alternatives in a choice set. However, the estima tion results showed the effects of congestion in choosing a route. For example, perhaps the higher congested travel times on the shorter routes forced PAGE 139 139 travelers to choose higher free flow travel time routes during peak periods. So, the use of congested tra vel times can help in capturing such effects precisely. Due to time constraints, the PSL model, which has a logit structure, was used for developing route choice models. However, literature suggests that some more complex models such as CNL (GEV structure) and Error Component (non GEV structure) have shown good performances too. However, a little empirical application is presented using these models. Therefore, it would be interesting to estimate CNL or error component models and compare the results with th e PSL estimates. PAGE 140 140 APPENDIX A DEMONSTRATION OF MAP MATCHING ALGORIT HMS The GPS Weighted Shortest Path Step 1: Network preparation C ost of the links in the network are set equal to 5000 times the link travel times. Step 2 : Sub network creation First, the GPS stream is overlaid on the roadway network Figure A 1 (a) GPS stream with the roadway network (b) A closer look of the GPS stream (b) (a) PAGE 141 141 Next, a buffer zone is constructed for the GPS points by creating a buffer of 200 meters around each GPS point. Figure A 2 Buffer zone PAGE 142 142 Lastly, the links in the roadway network that intersect the buffers are selected and exported to a new shapefile to form the sub roadway network. Figure A 3 (a) Sub network with the original roadway network (b) Sub network (a) (b) PAGE 143 143 Step 3: Update link cost F irst, a buffer of 75 feet for each GPS point is constructed. Subsequently, all the buffers are dissolved to form a polygon for a trip. Figure A 4 Buffer plo lygon After this, the links in the sub roadway network that falls completely within the buffer polygon are selected and the cost is set equal to the link travel times. PAGE 144 144 A closer look of the selected links reveals that in addition to the travelled links, there are several cross street links present. Therefore, more processing is required to obtain the final chosen route. Figure A 5 (a) Links within the buffer polygon (b) A closer look at the selected links (a) (b) PAGE 145 145 Step 4: Final path creation F irst, a network dataset is created for the updated sub network and afterwards, the route solver is run to find the shortest path for the OD pair of a trip. The shortest path constitutes the final chosen path. Figure A 6 Final chosen route Final chosen route PAGE 146 146 The Multi Path Algorithm Step 1: Creation of the sub network: Same as the GWSP algorithm Step 2 : Initial chosen r oute First, a spatial join between the GPS points and the sub roadway network is performed t o find the nearest link to a GPS point. Links in the sub roadway network that have at least one GPS counts are then selected exported to a new shapefile to form the initial chosen route. The links in the ICR, initial chosen links (ICL), are permanently sor ted based on the time stamp to follow the same temporal trajectory as the trip. Figure A 7 Initial chosen route with the sub network PAGE 147 147 A closer look of the ICR shows that it includes several cross streets that were not travelled during the trip and also the path may not be continuous Figure A 8 (a) Initial chosen route (b) A closer look of the links in the ICR ( a ) (b) PAGE 148 1 48 S tep 3 : Creation of End nodes of ICL are extracted and the Similar ly, the nodes of the links in the sub roadway network, excluding ICL, are extracted and are Figure A 9 Segment nodes and local nodes T he obt ained segment nodes do not necessarily follow the temporal trajectory of the trip. Therefore, a spatial join is used between the GPS points and the segment PAGE 149 149 nodes. The spatial join identifies the nearest GPS point to a segment node and assigns its timestamp to the node. Afterwards, this timestamp is used to sort the segment nodes. Step 4 : Creation of link to nodes and node to links incidence matrices To construct the matrices of node to links, a small buffer (0.00001 meters) is created for a node and the links in the sub roadway network intersecting the buffer were selected and inserted to the matrix. The process is performed twice, once for each node type (segment nodes and local nodes). Similarly, the link to nodes matrices are created by constructing a small buffer (0.00001 meters) for a link and selecting the nodes that are within the buffer. Once again, this process too performed twice, once for each node type. In addition to the list of links/ nodes, the matrices contain link/node count corresponding to each node/link. Figure A 1 0 (a) Small buffers for segment nodes and local nodes (b) Small buffers for segments S egment node Local node ( a ) ( b ) PAGE 150 150 Step 5 : Construct the chosen route The algorithm starts at the first segment node, also the one closest to the origin, and sequentially iterates through all the segment nodes (SN) in the list At the first segment node, first the links originating from the segment node are found using the segment node to link matrix. As there is only link at the segment node, the algorithm creates one new path and the link is added to it. The end node of the added link is then obtained from the link to nodes matrices. As t he end node is a segment node, it is labeled as a right node. Figure A 1 1 (a) First segment node, (b) Eligible link, and (c) A new route Possible link at the segment node First segment node First link in the route Right segment node Eligible link ( a ) ( b ) ( c ) PAGE 151 151 The algorithm moves to the next segment node, and checks if it is a right node. After confirming this, the links originating from the segment node are found. Among the obtained links, one is the previous link which was added to a path. Therefore, it is exc luded from the considered links. The remaining links are then examined for their eligibility by looking at the next forward link at a link. One link has a dead end ( no forward link) therefore; it is termed as the disqualified link. The end segment node of the disqualified link is labeled as a wrong node. The other link is termed as an eligible link and a new route is created and the link is added to it Additionally the end segment node of the added link is labeled as a right node. After this, the current route is deleted from the saved routes Figure A 1 2 (a) Next segment node (b) A new route The algorithm continues to add links to the saved route until multiple eligible links are encountered at a segment node. When multiple eligible links are available, a new route is created for each eligibl e link and in addition the link, the links in the path until Next segment node Previous link Eligible link Disqualified link Second link in the route Right node Wrong node ( a ) ( b ) PAGE 152 152 the segment node is added to each new route. After this, the current route is deleted from the saved routes When a local node is the end node of an eligible link, the algorithm iterates through the encountered local nodes the same way as the segment nodes The algorithm continues to create more routes until all the new routes at the segment node or local node are met with either a segment node or a dead end. 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Golledge. A Three Step General Map Matching Method In The GIS Environment: Travel/T ransportation Study P erspective. International Journal of Geographical Information System Vol. 8(3), 2006, pp. 243 260. PAGE 161 161 BIOGRAPHICAL SKETCH Nagendra S Dhakar was born in India in 198 3 He studied civil engineering at Indian Institute of Technology (IIT) Bombay India 200 5. H e joined the University of Florida, Gainesville for the Ph.D. program in transportation engineering in f all 2007 During his Ph.D. study at the Transportation Research Center in University of Florida, Nagendra S Dhakar was a research assistant under t he supervision of Dr. Sivaramakrishnan Srinivasan and worked on various research projects. Nagendra S Dhakar has co authored four papers in transportation journals and conference proceedings and made presentations at various conferences. His primary research interes ts include transportation planning travel demand modeling, spatial analysis, GIS application in transportation, and intelligent transportation system He received his Doctor of Philosophy degree in Decem ber 201 2 |