Shortest Path Problem with Gamma Probability Distribution Arc Length

We propose a dynamic program to find the shortest path in a network having gamma probability distributions as arc lengths. Two operators of sum and comparison need to be adapted for the proposed dynamic program. Convolution approach is used to sum two gamma probability distributions being employed in the dynamic program.

[1]  Xiaoyu Ji,et al.  Models and algorithm for stochastic shortest path problem , 2005, Appl. Math. Comput..

[2]  Yueyue Fan,et al.  Shortest paths in stochastic networks with correlated link costs , 2005 .

[3]  T. Lindvall.  ON A ROUTING PROBLEM , 2004, Probability in the Engineering and Informational Sciences.

[4]  Yen-Liang Chen,et al.  Minimum time paths in a network with mixed time constraints , 1998, Comput. Oper. Res..

[5]  L. B. Fu,et al.  Expected Shortest Paths in Dynamic and Stochastic Traf c Networks , 1998 .

[6]  Ismail Chabini,et al.  A New Algorithm for Shortest Paths in Discrete Dynamic Networks , 1997 .

[7]  Hani S. Mahmassani,et al.  A note on least time path computation considering delays and prohibitions for intersection movements , 1996 .

[8]  Sumit Sarkar,et al.  A Relaxation-Based Pruning Technique for a Class of Stochastic Shortest Path Problems , 1996, Transp. Sci..

[9]  H. Mahmassani,et al.  Path search techniques for transportation networks with time-dependent, stochastic arc costs , 1994, Proceedings of IEEE International Conference on Systems, Man and Cybernetics.

[10]  Pitu B. Mirchandani,et al.  Multiobjective routing of hazardous materials in stochastic networks , 1993 .

[11]  John N. Tsitsiklis,et al.  Dynamic Shortest Paths in Acyclic Networks with Markovian Arc Costs , 1993, Oper. Res..

[12]  Dimitris Bertsimas,et al.  Stochastic and Dynamic Vehicle Routing in the Euclidean Plane with Multiple Capacitated Vehicles , 1993, Oper. Res..

[13]  John N. Tsitsiklis,et al.  An Analysis of Stochastic Shortest Path Problems , 1991, Math. Oper. Res..

[14]  Dimitris Bertsimas,et al.  A Stochastic and Dynamic Vehicle Routing Problem in the Euclidean Plane , 1991, Oper. Res..

[15]  Ariel Orda,et al.  Shortest-path and minimum-delay algorithms in networks with time-dependent edge-length , 1990, JACM.

[16]  H. Moskowitz,et al.  Generalized dynamic programming for multicriteria optimization , 1990 .

[17]  Randolph W. Hall,et al.  The Fastest Path through a Network with Random Time-Dependent Travel Times , 1986, Transp. Sci..

[18]  Ronald Prescott Loui,et al.  Optimal paths in graphs with stochastic or multidimensional weights , 1983, Commun. ACM.

[19]  Jonathan Halpern,et al.  Shortest route with time dependent length of edges and limited delay possibilities in nodes , 1977, Math. Methods Oper. Res..

[20]  H. Frank,et al.  Shortest Paths in Probabilistic Graphs , 1969, Oper. Res..

[21]  Stuart E. Dreyfus,et al.  An Appraisal of Some Shortest-Path Algorithms , 1969, Oper. Res..

[22]  K. Cooke,et al.  The shortest route through a network with time-dependent internodal transit times , 1966 .

[23]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[24]  I. Ilic,et al.  The time-dependent vehicle routing problem , 2012 .

[25]  Robert L. Smith,et al.  Fastest Paths in Time-dependent Networks for Intelligent Vehicle-Highway Systems Application , 1993, J. Intell. Transp. Syst..

[26]  Hani S. Mahmassani,et al.  Time dependent, shortest-path algorithm for real-time intelligent vehicle highway system applications , 1993 .

[27]  David E. Kaufman,et al.  ANTICIPATORY TRAFFIC MODELING AND ROUTE GUIDANCE IN INTELLIGENT VEHICLE- HIGHWAY SYSTEMS , 1990 .

[28]  Chryssi Malandraki,et al.  Time dependent vehicle routing problems : formulations, solution algorithms and computational experiments , 1989 .