Finding the shortest path in stochastic networks

Computers and Mathematics with Applications

Volumn 53, Issue 5, 2007, Pages 729-740

  Peer, S K ^a   Sharma, Dinesh K ^b  

^a Kandula Sreenivasa Reddy Memorial College Of Engineering   (India)

^b UNIVERSITY OF MARYLAND EASTERN SHORE   (United States)

Author keywords

Arc length; Incomplete network; Linear programming; Minimum expected length; Random variable; Stochastic networks

Indexed keywords

LINEAR PROGRAMMING; PROBABILITY; PROBLEM SOLVING; RANDOM VARIABLES;

ARC LENGTH; INCOMPLETE NETWORK; MINIMUM EXPECTED LENGTH; STOCHASTIC NETWORKS;

RANDOM PROCESSES;

EID: 34248185608     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2007.01.012     Document Type: Article

References (14)

1. Kulkarni V.G. Shortest paths in networks with exponentially distributed arc lengths. Networks 16 (1986) 255-274
2. Bellman R.E. On a routing problem. Quarterly of Applied Mathematics 16 (1958) 87-90
3. Dijkstra E.W. A note on two problems on connexion with graphs. Numerische Mathematik 1 (1959) 269-271
4. Dreyfus S.E. An appraisal of some shortest-path algorithm. Operations Research 17 (1969) 395-412
5. Fan Y., Kalaba R., and Moore J. Shortest paths in stochastic networks with correlated link costs. Computers and Mathematics with Applications 49 (2005) 1549-1564
6. Snyder T.L., and Steele J.M. Probabilistic networks and network algorithms. Handbooks in Operations Research and Management Science vol. 7 (1995), North-Holland Publishing, Amsterdam 401-424
7. Martin J.J. Distribution of time through a directed acyclic network. Operations Research 13 (1965) 46-66
8. Bereanu B. On stochastic linear programming. The Laplace transform of the distribution of the optimum and applications. Journal of Mathematical Analysis and Applications 15 (1966) 280-294
9. Grimmett G.R., and Welsh D.J. Flow in networks with random capacities. Stochastics 7 (1982) 205-229
10. Frieze A., and Grimmett G. The shortest-path problem for graphs with random arc-lengths. Discrete Applied Mathematics 10 (1985) 57-77
11. G. Andretta, F. Ricaldone, L. Romeo, Exploring stochastic shortest path problems, ATTI Giomale di Lavaro, Tecnoprint, Bologna, Italy, 1985
12. Jaillet P. Shortest path problems with node failures. Networks 22 (1992) 589-605
13. Frank H. Shortest paths in probabilistic graphs. Operations Research 17 (1969) 583-599
14. Taha H.A. Operations Research-An Introduction. sixth ed. (1997), Prentice-Hall, New Jersey