Journal of Optimization Theory and Applications

, Volume 127, Issue 3, pp 497–513 | Cite as

Arriving on Time

  • Y. Y. Fan
  • R. E. Kalaba
  • J. E. MooreII


This research proposes a procedure for identifying dynamic routing policies in stochastic transportation networks. It addresses the problem of maximizing the probability of arriving on time. Given a current location (node), the goal is to identify the next node to visit so that the probability of arriving at the destination by time t or sooner is maximized, given the probability density functions for the link travel times. The Bellman principle of optimality is applied to formulate the mathematical model of this problem. The unknown functions describing the maximum probability of arriving on time are estimated accurately for a few sample networks by using the Picard method of successive approximations. The maximum probabilities can be evaluated without enumerating the network paths. The Laplace transform and its numerical inversion are introduced to reduce the computational cost of evaluating the convolution integrals that result from the successive approximation procedure.


Optimal routing stochastic shortest path problems dynamic programming convolution integrals 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Y. Y. Fan
    • 1
  • R. E. Kalaba
    • 2
  • J. E. MooreII
    • 3
  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaDavis
  2. 2.Departments of Biomedical, Economics, and Electrical EngineeringUniversity of Southern CaliforniaLos Angeles
  3. 3.Daniel J. Epstein Department of Industrial and System Engineering, Department of Civil and Environmental Engineering, and School of Policy, Planning, and DevelopmentUniversity of Southern CaliforniaLos Angeles

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