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Arriving on Time

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Abstract

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.

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References

  1. R.E. Bellman (1958) ArticleTitleOn a Routing Problem Quarterly of Applied Mathematics 16 87–90 Occurrence Handle0081.14403 Occurrence Handle102435

    MATH  MathSciNet  Google Scholar 

  2. S.E. Dreyfus (1969) ArticleTitleAn Appraisal of Some Shortest-Path Algorithms Operations Research 17 395–412 Occurrence Handle0172.44202

    MATH  Google Scholar 

  3. R.A. Howard (1971) Dynamic Probabilistic Systems NumberInSeriesVol. 2 John Wiley and Sons New York, NY

    Google Scholar 

  4. R.W. Hall (1986) ArticleTitleThe Fastest Path through a Network with Random Time-Dependent Travel Times Transportation Science 20 182–188

    Google Scholar 

  5. L. Fu L.R. Rilett (1998) ArticleTitleExpected Shortest Paths in Dynamic Stochastic Traffic Networks Transportation Research 32B 499–516

    Google Scholar 

  6. S.T. Waller A.K. Ziliaskopoulos (2002) ArticleTitleOn the Online Shortest Path Problem with Limited Arc Cost Dependencies Networks 40 216–227 Occurrence Handle10.1002/net.10049 Occurrence Handle1938787 Occurrence Handle1026.90088

    Article  MathSciNet  MATH  Google Scholar 

  7. E.D. Miller-Hooks H.S. Mahmassani (2000) ArticleTitleLeast Expected Time Paths in Stochastic, Time-Varying Transportation Networks Transportation Science 34 198–215 Occurrence Handle10.1287/trsc.34.2.198.12304 Occurrence Handle0990.90011

    Article  MATH  Google Scholar 

  8. P. Loui (1983) ArticleTitleOptimal Paths in Graphs with Stochastic or Multidimentional Weights Communications of the ACM 26 670–676 Occurrence Handle10.1145/358172.358406 Occurrence Handle0526.90085 Occurrence Handle784117

    Article  MATH  MathSciNet  Google Scholar 

  9. H. Frank (1969) ArticleTitleShortest Paths in Probabilistic Graphs Operations Research 17 583–599 Occurrence Handle0176.48301 Occurrence Handle243931

    MATH  MathSciNet  Google Scholar 

  10. C.E. Sigal A.A.B. Pritsker J.J. Solberg (1980) ArticleTitleThe Stochastic Shortest Route Problem Operations Research 28 1122–1129 Occurrence Handle589675 Occurrence Handle10.1287/opre.28.5.1122 Occurrence Handle0451.90091

    Article  MathSciNet  MATH  Google Scholar 

  11. R.E. Bellman R.E. Kalaba (1965) Dynamic Programming and Modern Control Theory McGraw-Hill New York, NY

    Google Scholar 

  12. D.J. White (1993) ArticleTitleMinimizing a Threshold Probability in Discounted Markov Decision Processes Journal of Mathematical Analysis and Applications 173 634–646 Occurrence Handle10.1006/jmaa.1993.1093 Occurrence Handle0810.90134 Occurrence Handle1209345

    Article  MATH  MathSciNet  Google Scholar 

  13. C. Wu Y. Lin (1999) ArticleTitleMinimizing Risk Models in Markovian Decision Processes with Policies Depending on Target Values Journal of Mathematical Analysis and Applications 231 47–67 Occurrence Handle1676741 Occurrence Handle0917.90285

    MathSciNet  MATH  Google Scholar 

  14. H.M. Srivastava R.G. Buschman (1992) Theory and Applications of Convolution Integral Equations Kluwer Academic Publishers Dordrecht, Netherlands Occurrence Handle0755.45002

    MATH  Google Scholar 

  15. R.E. Bellman R.E. Kalaba (1966) Numerical Inversion of the Laplace Transform American Elsevier Publishing Company New York, NY Occurrence Handle0147.14003

    MATH  Google Scholar 

  16. Y.Y. Fan R.E. Kalaba (2003) ArticleTitleDynamic Programming and Pseudo-Inverses Applied Mathematics and Computation 139 323–342 Occurrence Handle1948644 Occurrence Handle1027.65046

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of California, Davis, California

    Y. Y. Fan (Assistant Professor)

  2. Departments of Biomedical, Economics, and Electrical Engineering, University of Southern California, Los Angeles, California

    R. E. Kalaba (Professor)

  3. Daniel J. Epstein Department of Industrial and System Engineering, Department of Civil and Environmental Engineering, and School of Policy, Planning, and Development, University of Southern California, Los Angeles, California

    J. E. Moore II (Professor)

Authors
  1. Y. Y. Fan
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  2. R. E. Kalaba
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  3. J. E. Moore II
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Additional information

We are grateful to the colleagues who responded to this work with questions and comments during the Transportation Science Section session on Urban Transportation Planning Models II at the 2002 Meeting of the Institute for Operations Research and Management Science (INFORMS) in San José, California.

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Fan, Y.Y., Kalaba, R.E. & Moore, J.E. Arriving on Time. J Optim Theory Appl 127, 497–513 (2005). https://doi.org/10.1007/s10957-005-7498-5

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  • DOI: https://doi.org/10.1007/s10957-005-7498-5

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