M / G / c / c state dependent travel time models and properties

Physica A: Statistical Mechanics and its Applications

Volumn 395, Issue , 2014, Pages 560-579

  Smith, J Macgregor ^a   Cruz, F R B ^b  

^a University of Massachusetts   (United States)

^b FEDERAL UNIVERSITY OF MINAS GERAIS   (Brazil)

Author keywords

Approximations; State dependent queue; Transportation; Travel time

Indexed keywords

QUEUEING THEORY; TRAFFIC CONTROL; TRANSPORTATION;

APPROXIMATIONS; STATE-DEPENDENT QUEUES; TRADITIONAL APPROACHES; TRAFFIC FLOW MODELING; TRAFFIC FLOW THEORY; TRANSPORTATION NETWORK; TRAVEL TIME FUNCTIONS; TRAVEL TIME MODEL;

TRAVEL TIME;

EID: 84889888729     PISSN: 03784371     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physa.2013.10.048     Document Type: Article

References (55)

1. B.S. Kerner The Physics of Traffic 2004 Springer Berlin
2. J. Hausner, W. Walker, and A.J. Swersey An Analysis of the Deployment of Fire-Fighting Resources in Yonkers, New York, Tech. Rep., Report Number R-1566/2-HUD/CY 1974 RAND Corporation Santa Monica, CA URL http://www.rand.org/ pubs/reports/R1566z2
3. Insurance Services Office, Response Time Considerations, 2011, URL http://www.isomitigation.com.
4. L.S. Buriol, M.J. Hirsch, P.M. Pardalos, T. Querido, M.G.C. Resende, and M. Ritt A biased random-key genetic algorithm for road congestion minimization Optimization Letters 4 4 2010 619 633
5. Y. Sheffi Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods 1985 Prentice-Hall Englewood Cliffs, NJ
6. R. Arnott, and K. Small The economics of traffic congestion American Scientist 82 1994 446 455
7. D. Tas, N. Dellaert, T. van Woensel, and T. de Kok Vehicle routing problem with stochastic travel times including soft time windows and service costs Computers & Operations Research 40 1 2013 214 224
8. Bureau of Public Roads, Traffic Assignment Manual, Tech. Rep. 1964 US Department of Commerce
9. R. Akçelik Travel time function for transport planning purposes: Davidson's function, its time dependent form and an alternative travel time function Australian Road Research 21 3 1991 49 59
10. K.B. Davidson, A flow travel-time relationship for use in transportation planning, in: Proceedings 3rd Australian Road Research Board Conference (Part 1), Melbourne, Australia, 1966, pp. 183-194.
11. G. Rose, M.A.P. Taylor, and P. Tisato Estimating travel time functions for urban roads: options and issues Transportation Planning and Technology 14 1 1989 63 82
12. H. Spiess Conical volume delay functions Transportation Science 24 2 1990 153 158
13. R.G. Dowling, R. Singh, and W.W.-K. Cheng Accuracy and performance of improved speed-flow curves Journal Transportation Research Record: Journal of the Transportation Research Board 1646 1998 9 17
14. D. Chowdhury, L. Santen, and A. Schadschneider Statistical physics of vehicular traffic and some related systems Physics Reports 329 4-6 2000 199 329
15. D. Helbing Traffic and related self-driven many-particle systems Reviews of Modern Physics 73 2001 1067 1141
16. T. Nagatani The physics of traffic jams Reports on Progress in Physics 65 9 2002 1331
17. A.J. Horowitz Delay/Volume Relations for Travel Forecasting, Based on the 1985 Highway Capacity Manual, Report FHWA-PD-92-015 1991 FHWA, US Department of Transportation
18. M. Schónhof, and D. Helbing Criticism of three-phase traffic theory Transportation Research Part B: Methodological 43 7 2009 784 797
19. M. Treiber, A. Kesting, and D. Helbing Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts Transportation Research Part B: Methodological 44 8-9 2010 983 1000
20. B.S. Kerner Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-Phase Traffic Theory 2009 Springer Berlin
21. R. Jain, and J. MacGregor Smith Modeling vehicular traffic flow using M / G / C / C state dependent queueing models Transportation Science 31 4 1997 324 336
22. L.C. Edie Car following and steady-state theory Operations Research 9 1961 66 76
23. R.T. Underwood Speed, volume, and density relationships: quality and theory of traffic flow Yale Bureau of Highway Traffic 1961 141 188
24. B.D. Greenshields A study of traffic capacity Highway Research Board Proceedings 14 1935 448 477
25. J.S. Drake, J.L. Schofer, and A.D. May A statistical analysis of speed density hypotheses Highway Research Record 154 1967 53 87
26. Transportation Research Board, Highway Capacity Manual, Tech. Rep. 2000 National Research Council Washington, DC
27. P.R. Tregenza The Design of Interior Circulation 1976 Van Nostrand Reinhold Company New York, NY, USA
28. S.J. Yuhaski, and J. Macgregor Smith Modeling circulation systems in buildings using state dependent queueing models Queueing Systems 4 4 1989 319 338
29. A.D. May Traffic Flow Fundamentals 1990 Prentice-Hall Englewood Cliffs, NJ
30. F.R.B. Cruz, J. MacGregor Smith, and R.O. Medeiros An M / G / C / C state dependent network simulation model Computers & Operations Research 32 4 2005 919 941
31. F.R.B. Cruz, P.C. Oliveira, and L. Duczmal State-dependent stochastic mobility model in mobile communication networks Simulation Modelling Practice and Theory 18 3 2010 348 365
32. J.-Y. Cheah, and J. MacGregor Smith Generalized M / G / C / C state dependent queueing models and pedestrian traffic flows Queueing Systems 15 1 1994 365 386
33. F.R.B. Cruz, and J.M. Smith Approximate analysis of M / G / c / c state-dependent queueing networks Computers & Operations Research 34 8 2007 2332 2344
34. N. Vandaele, T.V. Woensel, and A. Verbruggen A queueing based traffic flow model Transportation Research Part D: Transport and Environment 5 2 2000 121 135
35. T. van Woensel, and F.R.B. Cruz A stochastic approach to traffic congestion costs Computers & Operations Research 36 6 2009 1731 1739
36. J.D.C. Little, and S.C. Graves Building intuition: insights from basic operations management models and principles D. Chhajed, T.J. Lowe, Little's Law 2008 Springer Science+Business Media New York, NY 81 100 (Chapter 5)
37. J.N. Prashker, and S. Bekhor Some observations on stochastic user equilibrium and system optimum of traffic assignment Transportation Research Part B 34 2000 277 291
38. M.G.H. Bell, and C. Cassir Risk-averse user equilibrium traffic assignment: an application of game theory Transportation Research Part B 36 8 2002 671 681
39. D. Braess, A. Nagurney, and T. Wakolbinger On a paradox of traffic planning (translation from the original in German, Braess (1968)) Transportation Science 39 2005 446 450
40. X. Zheng, and M. Liu Forecasting model for pedestrian distribution under emergency evacuation Reliability Engineering & System Safety 95 11 2010 1186 1192
41. R. García-Ródenas, M.L. López-García, A. Niño-Arbelaez, and D. Verastegui-Rayo A continuous whole-link travel time model with occupancy constraint European Journal of Operational Research 175 3 2006 1455 1471
42. M. Ghatee, and S.M. Hashemi Traffic assignment model with fuzzy level of travel demand: an efficient algorithm based on quasi-logit formulas European Journal of Operational Research 194 2 2009 432 451
43. F.R.B. Cruz, T. van Woensel, J.M. Smith, and K. Lieckens On the system optimum of traffic assignment in M / G / c / c state-dependent queueing networks European Journal of Operational Research 201 1 2010 183 193
44. F. Cavallini Fitting a logistic curve to data The College Mathematics Journal 24 3 1993 247 253
45. D.H. Mitchell, and J. MacGregor Smith Topological network design of pedestrian networks Transportation Research Part B 35 2001 107 135
46. B.S. Kerner, C. Demir, R.G. Herrtwich, S.L. Klenov, H. Rehborn, M. Aleksic, A. Haug, Traffic state detection with floating car data in road networks, in: Proceedings of the 8th International IEEE Conference on Intelligent Transportation Systems, Vienna, Austria, 2005, pp. 700-705. http://dx.doi.org/10.1109/ITSC.2005.1520133.
47. R. Jiang, D. Helbing, P.K. Shukla, and Q.-S. Wu Inefficient emergent oscillations in intersecting driven many-particle flows Physica A. Statistical Mechanics and its Applications 368 2 2006 567 574
48. L.C. Davis Predicting travel time to limit congestion at a highway bottleneck Physica A. Statistical Mechanics and its Applications 389 17 2010 3588 3599
49. B.S. Kerner, and S.L. Klenov A microscopic model for phase transitions in traffic flow Journal of Physics A: Mathematical and General 35 3 2002 L31 L43
50. B.S. Kerner, and S.L. Klenov Microscopic theory of spatial-temporal congested traffic patterns at highway bottlenecks Physical Review E 68 2003 036130 10.1103/PhysRevE.68.036130
51. B.S. Kerner, and S.L. Klenov Phase transitions in traffic flow on multilane roads Physical Review E 80 2009 056101
52. B.S. Kerner, and S.L. Klenov A theory of traffic congestion at moving bottlenecks Journal of Physics A: Mathematical and Theoretical 43 42 2010 425101
53. J. MacGregor Smith State dependent queueing models in emergency evacuation networks Transportation Research Part B 25 1991 373 389
54. J. MacGregor Smith Application of state-dependent queues to pedestrian/vehicular network design Operations Research 42 1994 414 427
55. J. MacGregor Smith Topological network design of state-dependent queueing networks Networks 28 1996 55 68