Optimum departure times for commuters in congested networks
- 51 Downloads
We propose an algorithm to compute the optimum departure time and path for a commuter in a congested network. Constant costs for use of arcs, cost functions of travel time depending on exogenous congestion and schedule delay are taken into account. A best path for a given departure time is computed with a previous algorithm for the generalized shortest path problem. The globally optimal departure time and an optimal path are determined by adapting Piyavskii's algorithm to the case of one-sided Lipschitz functions.
KeywordsCost Function Travel Time Short Path Departure Time Optimal Path
Unable to display preview. Download preview PDF.
- R. Arnott, A. de Palma and R. Lindsey, Economics of a Bottleneck, J. of Urban Econ. 27 (1990) 111–130.Google Scholar
- M.D. Atkinson, J.-R. Sack, N. Santoro and Th. Strotholte. Min-max heaps and generalized priority queues, Commun. ACM 29 (1986) 996–1000.Google Scholar
- A. de Palma, P. Hansen and M. Labbé, Commuters' paths with penalties for early or late arrival time, Transp. Sci. (1990) forthcoming.Google Scholar
- P. Hansen, Bicriterion path problems, in:Multiple Criteria Decision-Making: Theory and Applications, G. Fandel and T. Gall (eds.) (Springer, Berlin, 1980) pp. 109–127.Google Scholar
- P. Hansen, B. Jaumard and S.H. Lu, Global optimization of univariate Lipschitz functions. I. Survey and properties, RUTCOR Research Report 18-89 (1989), to appear in Math. Progr.Google Scholar
- P. Hansen, B. Jaumard and S.H. Lu, Global optimization of univariate Lipschitz functions. II. New algorithms and computational comparison, RUTCOR Research Report 23-89 (1989), to appear in Math. Progr.Google Scholar
- C. Hendrickson and G. Kocur, Schedule delay and departure time decisions in a deterministic model, Transp. Sci. 15 (1981) 62–77.Google Scholar
- S.A. Piyavskii, An algorithm for finding the absolute minimum of a function, Theory of Optimal Solutions, No. 2, Kiev, IK AN USSR (in Russian) (1967) 13–24.Google Scholar
- S.A. Piyavskii, An algorithm for finding the absolute extremum of a function, USSR Comput. Maths. Math. Phys. 12 (1972) 57–67; (Zh. vychisl. Mat. mat. Fiz. 12 (1972) 888–896).Google Scholar
- B.O. Shubert, A sequential method seeking the global maximum of a function, SIAM J. Num. Anal. 9 (1972) 379–388.Google Scholar
- W.S. Vickrey, Congestion theory and transport investment, Amer. Econ. Rev. 59 (1969) 251–261.Google Scholar