A gradient projection method is presented to solve the problem with dynamic traffic assignment. The gradient projection scheme is a feasible direction algorithm that operates directly in the space of path flows. The algorithm was applied to a simulation-based model for dynamic traffic assignment that used microscopic simulation for supply-side modeling. The formulation used link cost functions that were separate for moving and queuing vehicles on each link, so that the formulation could effectively capture the effects of traffic dynamic characteristics on each group, especially in arterial networks. The model and solution algorithm were applied to a small real-world network, and the performance was studied. The gradient projection algorithm avoided the problem of convergence to nonoptimal conditions shown by the prevalent method of successive averages and demonstrated significantly faster convergence.
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References
1.
PeetaS., and ZiliaskopoulosA. K.Foundations of Dynamic Traffic Assignment: The Past, the Present, and the Future. Networks and Spatial Economics, Vol. 1, No. 3, 2001, pp. 233–265.
2.
PeetaS.System Optimal Dynamic Traffic Assignment in Congested Networks with Advanced Information Systems.PhD dissertation. University of Texas at Austin, 1994.
3.
MerchantD.K., and NemhauserG. L.A Model and an Algorithm for the Dynamic Traffic Assignment Problems. Transportation Science, Vol. 12, No. 3, 1978, pp. 183–199.
4.
MerchantD.K., and NemhauserG. L.Optimality Conditions for a Dynamic Traffic Assignment Model. Transportation Science, Vol. 12, No. 3, 1978, pp. 200–207.
5.
CareyM.Optimal Time-Varying Flows on Congested Networks. Operations Research, Vol. 35, No. 1, 1987, pp. 58–69.
6.
JansonB. N.Convergent Algorithm for Dynamic Traffic Assignment. In Transportation Research Record 1328, TRB, National Research Council, Washington, D.C., 1991, pp. 69–80.
7.
FrieszT.L., LuqueJ., TobinR.L., and WieB.-W.Dynamic Network Traffic Assignment Considered as a Continuous Time Optimal Control Problem. Operations Research, Vol. 37, No. 6, 1989, pp. 893–901.
8.
RanB., and ShimazakiT.A General Model and Algorithm for the Dynamic Traffic Assignment Problems. Proc., Fifth World Conference on Transport Research, Yokohama, Japan, World Conference on Transport Research Society, Karlsruhe, Germany1989.
9.
BoyceD.E., RanB., and LeblancL. J.Solving an Instantaneous Dynamic User-Optimal Route Choice Model. Transportation Science, Vol. 29, No. 2, 1995, pp. 128–142.
10.
FrieszT.L., BernsteinD., SmithT.E., TobinR.L., and WieB. W.A Variational Inequality Formulation of the Dynamic Network User Equilibrium Problem. Operations Research, Vol. 41, 1993, pp. 179–191.
11.
RanB., HallR.W., and BoyceD. E.A Link-Based Variational Inequality Model for Dynamic Departure Time/Route Choice. Transportation Research Part B: Methodological, Vol. 30, No. 1, 1996, pp. 31–46.
12.
JayakrishnanR., TsaiW.K., and ChenA.A Dynamic Traffic Assignment Model with Traffic-Flow Relationships. Transportation Research Part C: Emerging Technologies, Vol. 3, No. 1, 1995, pp. 51–72.
13.
GhaliM.O., and SmithM. J.A Model for the Dynamic System Optimum Traffic Assignment Problem. Transportation Research Part B: Methodological, Vol. 29, No. 3, 1995, pp. 155–170.
14.
LeonardD., GrowerP., and TaylorN.CONTRAM: Structure of the Model.Technical report 178. Transport and Road Research Laboratory, Crowthorne, United Kingdom, 1989.
15.
PeetaS., and MahmassaniH. S.System Optimal and User Equilibrium Time-Dependent Traffic Assignment in Congested Networks. Annals of Operations Research, Vol. 60, No. 1, 1995, pp. 81–113.
16.
JayakrishnanR., MahmassaniH.S., and HuT.-Y.An Evaluation Tool for Advanced Traffic Information and Management Systems in Urban Networks. Transportation Research Part C: Emerging Technologies, Vol. 2, No. 3, 1994, pp. 129–147.
17.
BarceloJ., and CasasJ.Heuristic Dynamic Assignment Based on Microscopic Simulation. Proc., 9th Meeting of the Euro Working Group on Transportation, Bari, Italy, 2002.
18.
LiuH.X., MaW., BanJ.X., and MirchandaniP.Dynamic Equilibrium Assignment with Microscopic Traffic Simulation. Proc., Intelligent Transportation Systems, IEEE, New York, 2005, pp. 676–681.
19.
SmithM., DuncanG., and DruittS.PARAMICS: Microscopic Traffic Simulation for Congestion Management. Proc., Colloquium on Dynamic Control of Strategic Inter-Urban Road Networks, London, 1995.
20.
WardropJ. G.Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institute of Civil Engineers, Part II, Vol. 1, 1952, pp. 325–378.
21.
RickertM., and NagelK.Dynamic Traffic Assignment on Parallel Computers in TRANSIMS. Future Generation Computer Systems, Vol. 17, No. 5, 2001, pp. 637–648.
22.
JeihaniM., SheraliH.D., and HobeikaA. G.Computing Dynamic User Equilibria for Large-Scale Transportation Networks. Transportation, Vol. 33, No. 1, 2006, pp. 589–604.
23.
FlorianM., MahutM., and TremblayN.Application of a Simulation-Based Dynamic Traffic Assignment Model. European Journal of Operational Research, Vol. 189, No. 3, 2008, pp. 1381–1392.
24.
LuC.-C.MahmassaniH.S., and ZhouX.Equivalent Gap Function-Based Reformulation and Solution Algorithm for the Dynamic User Equilibrium Problem. Transportation Research Part B: Methodological, Vol. 43, No. 3, 2009, pp. 345–364.
25.
JayakrishnanR., ChenA., and TsaiW. K.Freeway and Arterial Traffic Flow Simulation Analytically Embedded in Dynamic Assignment. In Transportation Research Record: Journal of the Transportation Research Board, No. 1678, TRB, National Research Council, Washington, D.C., 1999, pp. 242–250.
26.
BertsekasD.On the Goldstein-Levitin-Polyak Gradient Projection Method. IEEE Transactions on Automatic Control, Vol. 21, No. 2, 1976, pp. 174–184.
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.
ZiliaskopoulosA., and MahmassaniH.Time-Dependent, Shortest-Path Algorithm for Real-Time Intelligent Vehicle Highway System Applications. In Transportation Research Record 1408, TRB, National Research Council, Washington, D.C., 1993, pp. 94–100.
29.
ZiliaskopoulosA., and MahmassaniH.A Note on Least Time Path Computation Considering Delays and Prohibitions for Intersection Movements. Transportation Research Part B: Methodological, Vol. 30, No. 5, 1996, pp. 359–367.
30.
AbdelfatahA.S., and MahmassaniH. S.System Optimal Time-Dependent Path Assignment and Signal Timing in Traffic Network. In Transportation Research Record 1645, TRB, National Research Council, Washington, D.C., 1998, pp. 185–193.
31.
SbaytiH., LuC.-C., and MahmassaniH. S.Efficient Implementation of Method of Successive Averages in Simulation-Based Dynamic Traffic Assignment Models for Large-Scale Network Applications. In Transportation Research Record: Journal of the Transportation Research Board, No. 2029, Transportation Research Board of the National Academies, Washington, D.C., 2007, pp. 22–30.
32.
ChenA., ZhouZ., and XuX.A Self-Adaptive Gradient Projection Algorithm for the Nonadditive Traffic Equilibrium Problem. Computers and Operations Research, Vol. 39, No. 2, 2012, pp. 127–138.
