A Solution Algorithm for Elastic Demand Traffic Assignment Model Based on Dynamic Process

동적과정을 이용한 가변수요 통행배정모형의 알고리듬 개발

  • Published : 2006.04.30

Abstract

Traffic assignment has been used both for predicting travel demands and for evaluating the tools for alleviating congestion on road network in advance. Some assignment models have been proposed such as equivalent mathematical minimization method, variational inequality problem, nonlinear complementary problem and fixed point method, in following the principle of Wardrop (1952) that no driver can not Improve his travel cost by unilaterally changing his route. Recently Jin(2005a) presented a traffic assignment model based on dynamic process. This paper proposes a solution algorithm for the model of Jin and assesses the performances. Compared to the Frank-Wolfe method, which has been wildly used for solving the existing assignment models, the proposed algorithm is expected to be more efficient because it does not need to evaluate the objective function. Two numerical examples are used for assessing the algorithm, and they show that the algorithm converges to user equilibrium of Wardrop.

References

  1. Beckmann P.L., McGuire C.B. and Winsten C.B. (1956) Studies in the economics of transportation, Yale University Press
  2. Ben-Akiva, M., De Palma, A. Kanaroglou, P. (1986) Dynamic model of peak period traffic congestion with elastic arrival rates. Transportation Science 20(2), pp.164-181 https://doi.org/10.1287/trsc.20.3.164
  3. Cantarella, G.E., Cascetta, E.(1995) Dynamic processes and equilibrium in transportation networks: towards a unifying theory. Transportation Science 29(4), pp.305-329 https://doi.org/10.1287/trsc.29.4.305
  4. Cascetta E.(1989) A stochastic process approach to the analysis of temporal dynamics in transportation networks, Transportation Research(23B) No.1, pp.1-17
  5. Emmerink, R.H.M., Axhausen,K.W., Nijkamp,P., Rietveld,P.,(1995) Effects of information in road transport networks with recurrent congestion, Transportation 22(1), pp.21-53 https://doi.org/10.1007/BF01151617
  6. Horowitz J. L.(1984) The Stability of Stochastic Equilibrium in a two-link Transportation Network, Transportation Research(18B), pp.13 -28
  7. Jin, W.L.,(2005a) The dynamic system of the traffic assignment problem : Part 1. Theory, Working paper UCI-ITS-TS-WP-05-01, ITS, University of California, Irvine
  8. Jin, W.L.,(2005b) The dynamic system of the traffic assignment problem : Part 2. Computation, Working paper UCI-ITS-TS-WP-05-02, ITS, University of California, Irvine
  9. Peeta,S., Yang,T.H. (2003) Stability issues for dynamic traffic assignment, Automatica 39, pp.21-34 https://doi.org/10.1016/S0005-1098(02)00179-6
  10. Sheffi,Y.(1985) Urban transportation networks, Equilibrium analysis with mathematical programming method, Prentice-Hall
  11. Smith, M.J.(1979) Existence, uniqueness and stability of traffic equilibria, Transportation Research 13B, pp.295-304
  12. Smith, M.J.(1984) The stability of a dynamic model of traffic assignment - an application of a method of Lyapunov. Transportation Science 18(3), pp.245-252 https://doi.org/10.1287/trsc.18.3.245
  13. Vythoulkas, P.C.,(1990) A dynamic stochastic assignment model for the analysis of general networks. Transportation Research(24B) No.6, pp.453-469
  14. Wardrop J. G.,(1952), 'Some theoretical aspects of road traffic research', Proc. Inst. Civil Engineer, Part II, pp.325-378