Simple analytical models for estimating the queue lengths from probe vehicles at traffic signals

Transportation Research Part B: Methodological

Volumn 55, Issue , 2013, Pages 59-74

  Comert, Gurcan ^a  

^a BENEDICT COLLEGE   (United States)

Author keywords

Moment generating function; Probability distribution; Probe vehicles; Queue; Traffic signal

Indexed keywords

ANALYTICAL MODELS; COMPUTER AIDED SOFTWARE ENGINEERING; ESTIMATION; INTELLIGENT SYSTEMS; PROBABILITY DISTRIBUTIONS; PROBES; QUEUEING THEORY; SIGNAL RECEIVERS; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; VEHICLES;

ANALYTICAL ESTIMATIONS; APPROXIMATION MODEL; CLOSED-FORM EXPRESSION; INTELLIGENT TRANSPORTATION SYSTEMS; MICROSCOPIC SIMULATION; MOMENT GENERATING FUNCTION; PROBE VEHICLES; QUEUE;

TRAFFIC SIGNALS;

COMPUTER SIMULATION; ERROR ANALYSIS; ESTIMATION METHOD; INTELLIGENT TRANSPORTATION SYSTEM; NUMERICAL MODEL; PROBABILITY; PROBE; STOCHASTICITY;

EID: 84879173314     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2013.05.001     Document Type: Article

References (74)

1. Abate J., Whitt W. Numerical inversion of probability generating functions. Operations Research Letters 1992, 12(4):245-251.
2. Adams W.F. Road traffic considered as a random series. Institution of Civil Engineers Journal 1936, 4(1):121-130.
3. Akçelik R. Time-dependent Expressions for Delay, Stop Rate and Queue Length at Traffic Signals 1980, Australian Road Research Board Melbourne, Australia.
4. Bowei X., Michailidis G., Nair V.N. Estimating network loss rates using active tomography. Journal of the American Statistical Association 2006, 101(476):1430-1448.
5. Boyce D.E., Hicks J., Sen A. In-vehicle navigation requirements for monitoring link travel times in a dynamic route guidance system. Operations Review 1991, 8(1):17-24.
6. Buckley, D., 1962. Road traffic headway distributions. In: Australian Road Research Board (ARRB) Conference, 1st, vol. 1, Canberra.
7. Calabrese F., Colonna M., Lovisolo P., Parata D., Ratti C. Real-time urban monitoring using cell phones: a case study in Rome. IEEE Transactions on Intelligent Transportation Systems 2011, 12(1):141-151.
8. Cantieni G., Ni Q., Barakat C., Turletti T. Performance analysis under finite load and improvements for multirate 802.11. Computer Communications 2005, 28(10):1095-1109.
9. Cetin M., List G.F., Zhou Y. Factors affecting the minimum number of probes required for reliable travel time estimation. Transportation Research Record 2005, 1917:37-44.
10. Chen M., Chien S.I.J. Determining the number of probe vehicles for freeway travel time prediction by microscopic simulation. Transportation Research Record 2000, 1719:61-68.
11. Cheu R.L., Xie C., Lee D. Probe vehicle population and sample size for arterial speed prediction. Computer-Aided Civil and Infrastructure Engineering 2002, 17(1):53-60.
12. Coifman B., Kim S. Speed estimation and length based vehicle classification from freeway single-loop detectors. Transportation Research Part C 2009, 17(4):349-364.
13. Comert G. Effect of stop line detection in queue length estimation at traffic signals from probe vehicles data. European Journal of Operational Research 2013, 226(1):67-76.
14. Comert G., Cetin M. Queue length prediction from probe vehicle location and the impacts of sample size. European Journal of Operational Research 2009, 197(1):196-202.
15. Comert G., Cetin M. Analytical evaluation of the error in queue length estimation at traffic signals from probe vehicle data. IEEE Transactions on Intelligent Transportation Systems 2011, 12(2):563-573.
16. Comert, G., Cetin, M., Nichols, E., 2009. Incorporating queue length measurements into actuated signal control: Evaluation of efficiency benefits at an intersection. In: TRB 88th Annual Meeting Compendium of Papers DVD, vol. 1, Washington, DC.
17. Dailey D.J. A statistical algorithm for estimating speed from single loop volume and occupancy measurements. Transportation Research Part B 1999, 33(5):313-322.
18. Darroch J.N. On the traffic-light queue. The Annals of Mathematical Statistics 1964, 35(1):380-388.
19. Dion F., Oh J.-S., Robinson R. Virtual testbed for assessing probe vehicle data in intellidrive systems. IEEE Transactions on Intelligent Transportation Systems 2011, 12(3):635-644.
20. Du J., Barth M.J. Next-generation automated vehicle location systems: positioning at the lane level. IEEE Transactions on Intelligent Transportation Systems 2008, 9(1):48-57.
21. Duffield N.G. Network tomography of binary network performance characteristics. IEEE Transactions on Information Theory 2006, 52(12):5373-5388.
22. Fekpe E., Windholz T., Beard K., Novak K. Quality and accuracy of positional data in transportation (NCHRP Report 506). 2003. Transportation Research Board 2006, 20:25-26.
23. Ferman M.A., Blumenfeld D.E., Dai X. An analytical evaluation of a real-time traffic information system using probe vehicles. Journal of Intelligent Transportation Systems 2005, 9(1):23-24.
24. Fu L., Hellinga B. Delay variability at signalized intersections. Transportation Research Record 2000, 1710:215-221.
25. Garetto M., Chiasserini C.-F. Performance analysis of 802.11 wlans under sporadic traffic. NETWORKING 2005. Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; Mobile and Wireless Communications Systems 2005, 1343-1347. Springer.
26. Gartner N.H., Pooran F.J., Andrews C.M. Optimized policies for adaptive control systems: implementation and field testing. Transportation Research Record 2002, 1811:148-156.
27. Haight F.A. Overflow at a traffic flow. Biometrika 1959, 46(3-4):420-424.
28. Hao P., Sun Z. Real time queue length estimation for signalized intersections using travel times from mobile sensors. Transportation Research Part C 2011, 19(6):1133-1156.
29. Heidemann D. Queue length and delay distributions at signalized intersections. Transportation Research Part B 1994, 28(5):624-635.
30. Hellinga B., Fu L. Assessing expected accuracy of probe vehicle travel time reports. Journal of Transportation Engineering 1999, 125(6):524-530.
31. Hellinga B.R. Improving freeway speed estimates from single-loop detectors. Journal of Transportation Engineering 2002, 128(1):58-67.
32. Hellinga B.R., Fu L. Reducing bias in probe-based arterial link travel time estimates. Transportation Research Part C 2002, 10(4):257-273.
33. Herrera J., Work D., Herring R., Ban X., Jacobson Q., Bayen A. Evaluation of traffic data obtained via gps-enabled mobile phones: the mobile century field experiment. Transportation Research Part C 2010, 18(4):568-583.
34. Hofleitner A., Herring R., Bayen A. Arterial travel time forecast with streaming data: a hybrid approach of flow modeling and machine learning. Transportation Research Part B 2012, 46(9):1097-1122.
35. Jenelius E., Koutsopoulos H.N. Travel time estimation for urban road networks using low frequency probe vehicle data. Transportation Research Part B 2013, 53:64-81.
36. Kang, Y.S., 2000. Delay, Stop and Queue Estimation for Uniform and Random Traffic Arrivals at Fixed-time Signalized Intersections. Ph.D. Thesis, Virginia Polytechnic Institute and State University, Blacksburg, Virginia.
37. Kianfar J., Edara P. Optimizing freeway traffic sensor locations by clustering global-positioning-system-derived speed patterns. IEEE Transactions on Intelligent Transportation Systems 2010, 11(2):738-747.
38. Kwella B., Lehmann H. Floating car data analysis of urban road networks. Lecture Notes in Computer Science 2000, 1798:357-367.
39. Li B. On the recursive estimation of vehicular speed using data from a single inductance loop detector: a Bayesian approach. Transportation Research Part B 2009, 43(4):391-402.
40. Li B. Bayesian inference for vehicle speed and vehicle length using dual-loop detector data. Transportation Research Part B 2010, 44(1):108-119.
41. Li, S., Zhu, K., van Gelder, B., Nagle, J., Tuttle, C., 2002. Improving Efficiency of INDOT Traffic Data Collection Using GPS Devices. Tech. Rep. FHWA/IN/JTRP-2002/19.
42. Lin I., Rong H., Kornhauser A.L. Estimating nationwide link speed distribution using probe position data. Journal of Intelligent Transportation Systems 2008, 12(1):29-37.
43. Liu H., Ma W. A virtual vehicle probe model for time-dependent travel time estimation on signalized arterials. Transportation Research Part C 2009, 17(1):11-26.
44. McNeil D.R. A solution to the fixed cycle traffic light problem for compound poisson arrivals. Journal of Applied Probability 1968, 5(3):624-635.
45. Medhi J. Stochastic Models in Queuing Theory 1991, Academic Press Inc. Harcourt Brace Jovanovich Publishers.
46. Miller A. Settings for fixed-cycle traffic signals. Operations Research Quarterly 1963, 14:373-386.
47. Mirchandani P.B., Zou N. Queuing models for analysis of traffic adaptive signal control. IEEE Transactions on Intelligent Transportation Systems 2007, 8(1):50-59.
48. Mung K.S.G., Poon A.C.K., Lam W.H.K. Distributions of queue lengths at fixed time traffic signals. Transportation Research Part B 1996, 30(6):421-439.
49. Newell G.F. Approximation methods for queues with application to the fixed-cycle traffic light. SIAM Review 1965, 7(2):223-240.
50. Newell, G.F., 1982. Applications of Queueing Theory, second ed.
51. Ohno K. Computational algorithm for a fixed cycle traffic signal and new approximate expressions for average delay. Transportation Science 1978, 12(1):29-47.
52. Olszewski P. Modeling of queue probability distribution at traffic signals. Transportation and Traffic Theory 1990, Elsevier, Amsterdam. M. Koshi (Ed.).
53. Ou Q., Bertini R.L., van Lint J., Hoogendoorn S. A theoretical framework for traffic speed estimation by fusing low-resolution probe vehicle data. IEEE Transactions on Intelligent Transportation Systems 2011, 12(3):747-756.
54. Papoulis A. Probability, Random Variables, and Stochastic Processes 1984, McGraw-Hill. second ed.
55. Paxson V., Floyd S. Wide area traffic: the failure of poisson modeling. IEEE/ACM Transactions on Networking 1995, 3(3):226-244.
56. Qing O., Bertini L.R., Lint J.W.C.V., Hoogendoorn S.P. A theoretical framework for traffic speed estimation by fusing low-resolution probe vehicle data. IEEE Transactions on Intelligent Transportation Systems 2011, 12(3):747-756.
57. Quiroga C.A., Bullock D. Travel time studies with global positioning and geographic information systems: an integrated methodology. Transportation Research Part C 1998, 6(1):101-127.
58. Ramezani M., Geroliminis N. On the estimation of arterial route travel time distribution with markov chains. Transportation Research Part B 2012, 46(10):1576-1590.
59. Rouphail, N., Tarko, A., Li, J., 2001. Traffic flows at signalized intersections. In: Traffic Flow Theory Monograph.
60. Sohn K., Hwang K. Space-based passing time estimation on a freeway using cell phones as traffic probes. IEEE Transactions on Intelligent Transportation Systems 2008, 9(3):559-568.
61. Srinivasan K.K., Jovanis P.P. Determination of number of probe vehicles required for reliable travel time measurement in urban network. Transportation Research Record 1996, 1537:5-22.
62. Tarko A., Rouphail N. Distribution-free model for estimating random queues in signalized networks. Transportation Research Record 1994, 1457:192-197.
63. Tong D., Merry C.J., Coifman B. New perspectives on the use of gps and gis to support a highway performance study. Transactions in GIS 2009, 13(1):69-85.
64. Turner, S., Holdener, D., 1995. Probe vehicle sample sizes for real-time information: the Houston experience. In: Proceedings of the Vehicle Navigation and Information Systems Conference, Seattle, WA.
65. Van Den Broek M., Van Leeuwaarden J., Adan I., Boxma O. Bounds and approximations for the fixed-cycle traffic-light queue. Transportation Science 2006, 40(4):484-496.
66. Van Leeuwaarden J. Delay analysis for the fixed-cycle traffic-light queue. Transportation Science 2006, 40(2):189-199.
67. Viti, F., 2006. The Dynamics and the Uncertainty of Delays at Signals. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands.
68. Viti F., Van Zuylen H. Modeling queues at signalized intersections. Transportation Research Record 2004, 1883:68-77.
69. Viti F., Van Zuylen H. Probabilistic models for queues at fixed control signals. Transportation Research Part B 2010, 44(1):120-135.
70. Webster, F.V., 1958. Traffic Signal Settings. Road Research Technical Paper No. 39. Road Research Laboratory.
71. Weisstein E.W. CRC Concise Encyclopedia of Mathematics 2003, CRC Press, pp. 1135-1138. second ed.
72. Williams T., Alves P., Lachapelle G., Basnayake C. Evaluation of gps-based methods of relative positioning for automotive safety applications. Transportation Research Part C 2012, 23:98-108.
73. Zheng, F., 2011. Modeling Urban Travel Times. Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands.
74. Zheng, F., Van Zuylen, H., 2012. Urban link travel time estimation based on sparse probe vehicle data. Transportation Research Part C, in press. doi:10.1016/j.trc.2012.04.007.