Heavy tails in multi-server queue

Queueing Systems

Volumn 52, Issue 1, 2006, Pages 31-48

  Foss, Serguei ^a   Korshunov, Dmitry ^b  

^a HERIOT WATT UNIVERSITY   (United Kingdom)

^b SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

Author keywords

FCFS multi server queue; Large deviations; Long tailed distribution; Stationary waiting time; Subexponential distribution

Indexed keywords

QUEUEING THEORY;

FCFS MULTI-SERVER QUEUES; LARGE DEVIATIONS; LONG-TAILED DISTRIBUTIONS; STATIONARY WAITING TIME; SUBEXPONENTIAL DISTRIBUTIONS;

PROBABILITY DISTRIBUTIONS;

EID: 31144450512     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/s11134-006-3613-z     Document Type: Article

References (19)

1. S. Asmussen, Applied Probability and Queues, 2nd ed. (Springer, New York, 2003).
2. S. Asmussen, C. Kluppelberg and K. Sigman, Sampling at subexponential times, with queueing applications, Stoch. Process. Appl 79 (1999) 265-286.
3. F. Baccelli and S. Foss, Moments and tails in monotone-separable stochastic networks, Ann. Appl. Probab 14 (2004) 612-650.
4. A.A. Borovkov and A.A. Mogul'skii, Large deviations for Markov chains in the positive quadrant, Russ. Math. Surv 56 (2001) 803-916.
5. S. Borst, M. Mandjes and A.P. Zwart, Exact asymptotics for fluid queues fed by heavy-tailed On-Off flows, Ann. Appl. Probab 14 (2004) 903-957.
6. O.J. Boxma, S.G. Foss, J.-M. Lasgouttes and R. Nunez Queija, Waiting time asymptotics in the single server queue with service in random order, Queueing Systems 46 (2004) 35-73.
7. O.J. Boxma, Q. Deng and A.P. Zwart, Waiting-time asymptotics for the M/G/2 queue with heterogeneous servers, Queueing Systems 40 (2002) 5-31.
8. H. Cramér, Collective Risk Theory (Esselte, Stockholm, 1955).
9. D. Denisov, S. Foss and D. Korshunov, Tail asymptotics for the supremum of a random walk when the mean is not finite, Queueing Systems 46 (2004) 15-33.
10. S.G. Foss and N.I. Chernova, On optimality of FCFS discipline in multi-channel queueing systems and networks, Siberian Math. J 42 (2001) 372-385.
11. S. Foss and D. Korshunov, Sampling at a random time with a heavy-tailed distribution, Markov Processes and Related Fields 6 (2000) 643-658.
12. I.A. Ignatyuk, V. Malyshev and V. Scherbakov, Boundary effects in large deviation problems, Russ. Math. Surv 49 (1994) 41-99.
13. J. Kiefer and J. Wolfowitz, On the theory of queues with many servers, Tran. Amer. Math. Soc 78 (1955) 1-18.
14. D. Korshunov, On distribution tail of the maximum of a random walk, Stochastic Process. Appl 72 (1997) 97-103.
15. A.G. Pakes, On the tails of waiting-time distribution, J. Appl. Probab 12 (1975) 555-564.
16. A. Scheller-Wolf, Further delay moment results for FIFO multiserver queues, Queueing Systems 34 (2000) 387-400.
17. A. Scheller-Wolf and K. Sigman, Delay moments for FIFO GI/GI/s queues, Queueing Systems 25 (1997) 77-95.
18. N. Veraverbeke, Asymptotic behavior of Wiener-Hopf factors of a random walk, Stochastic Process. Appl 5 (1977) 27-37.
19. W. Whitt, The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution, Queueing Systems 36 (2000) 71-87.