Abstract
This paper presents a novel reliability-based stochastic user equilibrium traffic assignment model in view of the day-to-day demand fluctuations for multi-class transportation networks. In the model, each class of travelers has a different safety margin for on-time arrival in response to the stochastic travel times raised from demand variations. Travelers' perception errors on travel time are also considered in the model. This model is formulated as an equivalent variational inequality problem, which is solved by the proposed heuristic solution algorithm. Numerical examples are presented to illustrate the applications of the proposed model and the efficiency of solution algorithm.
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References
Abdalla M, Abdel-Aty M (2006) Modeling travel time under atis using mixed linear models. Transportation 33:63–82
Abdel-Aty M, Kitamura R, Jovanis P (1995) Investigating effect of travel time variability on route choice using repeated measurement stated preference data. Transp Res Rec 1493:39–45
Asakura Y, Kashiwadani M (1991) Road network reliability caused by daily fluctuation of traffic flow. European Transport, Highways & Planning 19:73–84
Bates J, Polak J, Jones P, Cook A (2001) The valuation of reliability for personal travel. Transp Res E 37:191–229
Bell MGH (2000) A game theory approach to measuring the performance reliability of transport networks. Transp Res B 34:533–546
Bell MGH, Cassir C (2002) Risk-averse user equilibrium traffic assignment: an application of game theory. Transp Res B 36:671–682
Bernstein D, Gabriel G (1997) Solving the nonadditive traffic equilibrium problem. In: Pardalos PM, Hearn DW, Hager WW (eds) Network optimization. Springer, Berlin Heidelberg New York, pp 72–102
Bruinsma FR, Rietveld P, van Vuuren DJ (1999) Unreliability in public transport chains. Proceedings of 8th World Conference on Transport Research, Vol. 1, pp 359–372
Chen A, Ji ZW, Recker W (2002a) Travel time reliability with risk sensitive travelers. Transp Res Rec 1783:27–33
Chen A, Yang H, Lo HK, Tang WH (2002b) Capacity reliability of a road network: an assessment methodology and numerical results. Transp Res B 36:225–252
Chen A, Subprasom K, Ji ZW (2003) Mean-variance model for the build–operate–transfer scheme under demand uncertainty. Transp Res Rec 1857:93–101
Chen A, Ji ZW (2005) Path finding under uncertainty. J Adv Transp 39:19–37
Clark S, Watling D (2005) Modeling network travel time reliability under stochastic demand. Transp Res B 39:119–140
de Palma A, Picard N (2005) Route choice decision under travel time uncertainty. Transp Res A 39:295–324
Facchinei F, Pang JS (2003) Finite-dimensional variational inequalities and complementarity problems. Springer, Berlin Heidelberg New York
Federal Highway Administration (2006) Travel time reliability: making it there on time, all the time. http://www.ops.fhwa.dot.gov/publications/tt_reliability/TTR_Report.html, Accessed on 1 March 2006
Gabay D, Mercier B (1976) A dual algorithm for the solution of nonlinear variational problems via finite element approximations. Computer and Mathematics with Applications 2:17–40
Hall R W (1983) Travel outcome and performance: the effect of uncertainty on accessibility. Transp Res B 17:275–290
He BS, Liao LZ (2002) Improvements of some projection methods for monotone nonlinear variational inequalities. J Optim Theory Appl 112:111–128
Kazimi C, Brownstone D, Ghosh A, Golob T F, van Amelsfort D (2000) Willingness-to-pay to reduce commute time and its variance: evidence from the San Diego I-15 congestion pricing project. Paper presented at the 79th Annual Meeting of the Transportation Research Board, Washington, District of Columbia
Kharoufeh JP, Gautam N (2004) Deriving link travel-time distributions via stochastic speed processes. Transp Sci 38:97–106
Lam T (2000) “The effect of variability of travel time on route and time-of-day choice.” Ph.D. Dissertation, University of California, Irvine
Lam T, Small K (2001) The value of time and reliability: measurement from a value pricing experiment. Transp Res E 37:231–251
Lo HK, Tung YK (2003) Network with degradable links: capacity analysis and design. Transp Res B 37:45–363
Lo HK, Luo XW, Siu BWY (2006) Degradable transport network: travel time budget of travelers with heterogeneous risk aversion. Transp Res B 40:792–806
National Research Council (2000) Highway capacity manual. Washington, District of Columbia USA
Polychronopoulos GH, Tsitsiklis JN (1996) Stochastic shortest path problems with recourse. Networks 27:133–143
Sheffi Y (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall, Englewood Cliff, New Jersey
Sánchez-Silva M, Daniels M, Lleras G, Patiñob D (2005) A transport network reliability model for the efficient assignment of resources. Transp Res B 39:47–63
Tam ML, Lam WHK (1999) Analysis of demand for road-based transport facilities: bi-level programming approach. Transp Res Rec 1685:73–80
Uchida T, Iida Y (1993) Risk assignment: a new traffic assignment model considering risk of travel time variation. In: Daganzo CF (ed) Proceedings of the 12th International Symposium on Transportation and Traffic Theory. Elsevier, Amsterdam, pp 89–105
Waller ST, Schofer JL, Ziliaskopoulos AK (2001) Evaluation with traffic assignment under demand uncertainty. Transp Res Rec 1771:69–74
Weisstein WE (2005) Gaussian integral. MathWorld—a Wolfram web resource. http://mathworld.wolfram.com/GaussianIntegral.html, Accessed on 15 October 2005
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Shao, H., Lam, W.H.K. & Tam, M.L. A Reliability-Based Stochastic Traffic Assignment Model for Network with Multiple User Classes under Uncertainty in Demand. Netw Spat Econ 6, 173–204 (2006). https://doi.org/10.1007/s11067-006-9279-6
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DOI: https://doi.org/10.1007/s11067-006-9279-6