Demand-Driven Traffic Assignment Problem Based on Travel Time Reliability

Abstract

A novel user equilibrium traffic assignment model based on travel time reliability is presented in view of day-to-day demand fluctuation. Because of daily demand variations, path travel times are not constants, and so they can be viewed as random variables. Assuming that travelers are able to learn the variation of path travel time from experience, a demand-driven user equilibrium principle based on travel time reliability is proposed to characterize travelers’ path choice behavior under uncertainty in travel times caused by demand variation. This principle can be formulated as a variational inequality (VI) problem in terms of path flows. The existence of at least one solution for the VI problem, for which a heuristic solution algorithm is adopted, is rigorously proved. Numerical examples are used to illustrate the applications of the proposed model and the solution algorithm.

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References

H. K.

and Tung

Y. K.

. Network with Degradable Links: Capacity Analysis and Design. Transportation Research, Vol. 37B, 2003, pp. 345–363.

H. K.

and Luo

. Travel Time Budget in Transport Network with Stochastic Degradations. Presented at 83rd Annual Meeting of the Transportation Research Board, Washington, D.C., 2004.

Chen

Yang

H. K.

and Tang

W. H.

. Capacity Reliability of a Road Network: An Assessment Methodology and Numerical Results. Transportation Research, Vol. 36B, 2002, pp. 225–252.

Asakura

and Kashiwadani

. Road Network Reliability Caused by Daily Fluctuation of Traffic Flow. European Transport, Highways & Planning, Vol. 19, 1991, pp. 73–84.

Clark

and Watling

. Modeling Network Travel Time Reliability Under Stochastic Demand. Transportation Research, Vol. 39B, 2005, pp. 119–140.

Abdel-Aty

M. A.

Kitamura

and Jovanis

P. P.

. Investigating Effect of Travel Time Variability on Route Choice Using Repeated-Measurement Stated Preference Data. In Transportation Research Record 1493, TRB, National Research Council, Washington, D.C., 1995, pp. 39–45.

Kazimi

Brownstone

Ghosh

Golob

T. F.

and Van Amelsfort

. Willingness To Pay to Reduce Commute Time and Its Variance: Evidence from the San Diego I-15 Congestion Pricing Project. Presented at 79th Annual Meeting of the Transportation Research Board, Washington, D.C., 2000.

Lam

The Effect of Variability of Travel Time on Path and Time-of-Day Choice. Ph.D. dissertation. University of California, Irvine, 2000.

Lam

and Small

K. A.

. The Value of Time and Reliability: Measurement from a Value Pricing Experiment. Transportation Research, Vol. 37E, 2001, pp. 231–251.

10.

Small

K. A.

Noland

Chu

and Lewis

. NCHRP Report 431: Valuation of Travel-Time Savings and Predictability in Congested Conditions for Highway User-Cost Estimation. TRB, National Research Council, Washington, D.C., 1999.

11.

Hall

R. W.

Travel Outcome and Performance: The Effect of Uncertainty on Accessibility. Transportation Research, Vol. 17B, 1983, pp. 275–290.

12.

Uchida

and Iida

. Risk Assignment: A New Traffic Assignment Model Considering Risk of Travel Time Variation. In Proceedings of the 12th International Symposium on Transportation and Traffic Theory ( Daganzo

C. F.

, ed.), Elsevier, Amsterdam, Netherlands, 1993.

13.

Chen

and Recker

. Travel Time Reliability with Risk-Sensitive Travelers. In Transportation Research Record: Journal of the Transportation Research Board, No. 1783, Transportation Research Board of the National Academies, Washington, D.C., 2002, pp. 27–33.

14.

Sheffi

Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods. Prentice Hall, Englewood Cliffs, N.J., 1985.

15.

Weisstein

W. E.

Gaussian Integral. MathWorld—A Wolfram Web Resource. mathworld.wolfram.com/GaussianIntegral.html. Accessed Oct. 15, 2005.

16.

Bruinsma

F. R.

Rietveld

and D. J. Van Vuuren, Unreliability in Public Transport Chains. Proc., 8th World Conference on Transport Research, Vol. 1, 1999, pp. 359–372.

17.

Bates

Polak

Jones

and Cook

. The Valuation of Reliability for Personal Travel. Transportation Research, Vol. 37E, 2001, pp. 191–229.

18.

De Palma

and Picard

. Path Choice Decision Under Travel Time Uncertainty. Transportation Research, Vol. 39A, 2005, pp. 295–324.

19.

Facchinei

and Pang

J. S.

. Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York, 2003.

20.

Dafermos

The General Multimodal Network Equilibrium Problem with Elastic Demand. Networks, Vol. 12, 1982, pp. 57–72.

21.

Bernstein

and Gabriel

. Solving the Nonadditive Traffic Equilibrium Problem. In Network Optimization ( Pardalos

P. M.

Hearn

D. W.

and Hager

W. W.

, eds.), Springer, New York, 1997.

22.

Chen

and Ji

Z. W.

. Path Finding Under Uncertainty. Journal of Advanced Transportation, Vol. 39, 2005, pp. 19–37.

23.

Highway Capacity Manual. TRB, National Research Council, Washington, D.C., 2000.

24.

Tam

M.-L.

and Lam

W. H. K.

. Analysis of Demand for Road-Based Transport Facilities: A Bi-Level Programming Approach. In Transportation Research Record: Journal of the Transportation Research Board, No. 1685, TRB, National Research Council, Washington, D.C., 1999, pp. 73–80.

25.

Waller

S. T.

and Ziliaskopoulos

A. K.

. Stochastic Dynamic Network Design Problem. In Transportation Research Record: Journal of the Transportation Research Board, No. 1771, TRB, National Research Council, Washington, D.C., 2001, pp. 106–113.