Distribution function of the shortest path in networks of queues

OR Spectrum

Volumn 27, Issue 1, 2005, Pages 123-144

  Azaron, Amir ^a   Modarres, Mohammad ^b  

^a BU ALI SINA UNIVERSITY   (Iran)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Graph theory; Queueing; Shortest path; Stochastic processes

Indexed keywords

EID: 15244342527     PISSN: 01716468     EISSN: 14366304     Source Type: Journal    
DOI: 10.1007/s00291-004-0169-3     Document Type: Article

References (22)

1. Azaron A, Fatemi Ghomi SMT (2003) Optimal control of service rates and arrivals in jackson networks. European Journal of Operational Research 147: 17-31
2. Azaron A, Kianfar F (2003) Dynamic shortest path in stochastic dynamic networks: ship routing problem. European Journal of Operational Research 144: 138-156
3. Bondy J, Murty U (1976) Graph theory with applications. Elsevier, Amsterdam
4. Burt J, Garman M (1971) Conditional Monte Carlo: a simulation technique for stochastic network analysis. Management Science 18: 207-217
5. Corea GA, Kulkarni VG (1993) Shortest paths in stochastic networks with ARC lengths having discrete distributions. Networks 23: 175-183.
6. Fishman GS (1985) Estimating network characteristics in stochastic activity networks. Management Science 31: 579-593
7. Frank H (1969) Shortest paths in probabilistic graphs. Operations Research 17: 583-599
8. Gross D, Harris M (1985) Fundamentals of queueing theory, 2nd Wiley, New York
9. Hall R (1986) The fastest path through a network with random time-dependent travel times. Transportation Science 20: 182-188
10. Hassin R, Zemel E (1985) On shortest paths in graphs with random weights. Mathematics of Operations Research 10: 557-564
11. Hayhurst KJ, Shier DR (1991) A factoring approach for the stochastic shortest path problem. Operations Research Letters 10: 329-334
12. Kleindorfer GB (1971) Bounding distributions for a stochastic acyclic network. Operations Research 19: 1586-1601
13. Kleinrock L (1975) Queueing systems, 2 Computer applications. Wiley, New York
14. Kulkarni VG (1986) Shortest paths in networks with exponentially distributed arc lengths. Networks 16: 255-274
15. Luenberger D (1979) Introduction to dynamic systems. Wiley, New York
16. Lyons R, Pemantle R, Peres Y (1999) Resistance bounds for first-passage percolation and maximum flow. Journal of Combinatorial Theory Ser A 86: 158-168
17. Martin J (1965) Distribution of time through a directed acyclic network. Operations Research 13: 46-66
18. Mirchandani P (1976) Shortest distance and reliability of probabilistic networks. Computers and Operations Research 3: 347-355
19. Preiditis A, Davis R (1993) The expected length of a shortest path. Information Processing Letters 46: 135-141
20. Psaraftis H, Tsitsiklis J (1993) Dynamic shortest paths in acyclic networks with markovian arc costs. Operations Research 41: 91-101
21. Sigal C, Pritsker A, Solberg J (1979) The use of cut sets in monte carlo analysis of stochastic networks. Mathematics and Computer Simulation 21: 376-384
22. Sigal C, Pritsker A, Solberg J (1980) The stochastic shortest route problem. Operations Research 28: 1122-1129