Day-to-day dynamic congestion pricing schemes have been recently proposed to force the traffic system to evolve from the status quo to a stationary state of system optimum instead of user equilibrium, considering drivers’ day-to-day behavior adjustments. From the perspective of traffic management, it may be desirable to expedite the evolution process such that the total travel cost across the process can be reduced. A novel steepest descent dynamic toll scheme is proposed that minimizes the derivative of the total system cost with regard to day t or reduces the total system cost the most for each day. The problem of finding the steepest descent scheme is first formulated as a piecewise linear nonsmooth optimization problem and then transformed into a standard linear programming problem. Its mathematical properties are discussed further and a solution procedure is proposed for specifying the steepest descent pricing scheme. A numerical study of the well-known Braess network and the Sioux Falls, South Dakota, network is conducted to compare the performance of different dynamic pricing schemes.
Get full access to this article
View all access options for this article.
References
1.
National Strategy to Reduce Congestion on America's Transportation Network.U.S. Department of Transportation, 2006.
2.
PigouA. C.The Economics of Welfare.Macmillan, London, 1920.
3.
KnightF. H.Some Fallacies in the Interpretation of Social Cost. Quarterly Journal of Economics, Vol. 38, 1924, pp. 582–606.
4.
BeckmannM. J., McGuireC. B., and WinstenC. B.Studies in the Economics of Transportation.Yale University Press, New Haven, Conn., 1956.
5.
FrieszT. L., BernsteinD., and KydesN.Dynamic Congestion Pricing in Disequilibrium. Networks and Spatial Economics, Vol. 4, 2004, pp. 181–202.
6.
YangF., and SzetoW. Y.Day-to-Day Dynamic Congestion Pricing Policies Towards System Optimal. Proc., First International Symposium on Dynamic Traffic Assignment, Leeds, United Kingdom, 2006, pp. 266–275.
7.
SmithM. J.The Stability of a Dynamic Model of Traffic Assignment: An Application of a Method of Lyapunov. Transportation Science, Vol. 18, 1984, pp. 259–304.
8.
FrieszT. L., BersteinD. H., MehtaN. J., TobinR. L., and GanjalizadehS.Day-to-Day Dynamic Network Disequilibrium and Idealized Traveler Information Systems. Operations Research, Vol. 42, 1994, pp. 1120–1136.
9.
NagurneyA., and ZhangD.Projected Dynamical Systems and Variational Inequalities with Applications.Kluwer, Boston, Mass., 1996.
10.
YangF.An Evolutionary Game Theory Approach to the Day-to-day Traffic Dynamics. PhD dissertation. University of Wisconsin, Madison, 2005.
BergendorffP., HearnD., and RamanaM.Congestion Toll Pricing of Traffic Networks. In Network Optimization, Lecture Notes in Economics and Mathematical Systems (PardalosP. M., HearnD. W., and HagerW. W., eds.), Springer-Verlag, 1997, pp. 51–71.
13.
CascettaE.A Stochastic Process Approach to the Analysis of Temporal Dynamics in Transportation Networks. Transportation Research, Vol. 23B, No. 1, 1989, pp. 1–17.
14.
PeetaS.Perception Updating and Day-to-Day Travel Choice Dynamics in Traffic Networks with Information Provision. Transportation Research, Vol. 6C, No. 3, 1998, pp. 189–212.
15.
JinW. L.2006. A Dynamical System Model of the Traffic Assignment Problem. Transportation Research, Vol. 41B, 2006, pp. 32–48.
16.
DavisG. A., and NihanN. L.Large Population Approximations of a General Stochastic Traffic Assignment Model. Operations Research, Vol. 41, No. 1, 1993, pp. 169–178.
17.
HazeltonM. L., and WatlingD. P.Computation of Equilibrium Distributions of Markov Traffic Assignment Models. Transportation Science, Vol. 38, 2004, pp. 331–342.
18.
ChangG.-L., and MahmassaniH. S.Travel Time Prediction and Departure Time Adjustment Behavior Dynamics in a Congested Traffic System. Transportation Research, Vol. 22B, No. 3, 1988, pp. 217–232.
19.
ArentzeT. A., and TimmermansH. J. P.A Learning-Based Transportation Oriented Simulation System. Transportation Research, Vol. 38B, 2004, pp. 613–633.
20.
ArentzeT. A., and TimmermansH. J. P.Modeling Learning and Adaptation in Transportation Contexts. Transportmetrica, Vol. 1, No. 1, 2005, pp. 13–22.
21.
SmithM. J., and WistenM. B.A Continuous Day-to-Day Traffic Assignment Model and the Existence of a Continuous Dynamic User Equilibrium. Annals of Operations Research, Vol. 60, 1995, pp. 59–79.
22.
SandholmW. H.Potential Games with Continuous Player Sets. Journal of Economic Theory, Vol. 97, 2001, pp. 81–108.
23.
YangF., and ZhangD.Day-to-day Stationary Link Flow Pattern. Submitted to Transportation Research, Part B (in review, 2007).
24.
ZhangD., NagurneyA., and WuJ.On the Equivalence Between Stationary Link Flow Patterns and Traffic Network Equilibria. Transportation Research, Vol. 35B, No. 8, 2001, pp. 731–748.
25.
HuangH. J., and LamW.Modeling and Solving the Dynamic User Equilibrium Route and Departure Time Choice Problem in Network with Queues. Transportation Research, Vol. 36B, No. 3, 2002, pp. 253–273.
26.
PeetaS., and YangT. H.Stability Issues for Dynamic Traffic Assignment. Automatica, Vol. 39, 2003, pp. 21–34.
27.
JayakrishnanR., TsaiW. K., PrashkerJ. N., and RajadhyakshaS.Faster Path-Based Algorithm for Traffic Assignment. In Transportation Research Record 1443, TRB, National Research Council, Washington, D.C., 1994, pp. 75–83.
28.
ChenA., LeeD., and JayakrishnanR.Computational Study of State-of-the-Art Path-Based Traffic Assignment Algorithms. Mathematics and Computers in Simulation, Vol. 59, 2002, pp. 509–518.
29.
LeBlancL. J., MorlokE. K., and PierskallaW. P.An Efficient Approach to Solving the Road Network Equilibrium Traffic Assignment Problem. Transportation Research, Vol. 9, 1975, pp. 309–318.
