Asymptotics of stochastic networks with subexponential service times

Queueing Systems

Volumn 33, Issue 1-3, 1999, Pages 205-232

  Baccelli, François ^a   Schlegel, Sabine ^b   Schmidt, Volker ^b  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b UNIVERSITY OF ULM   (Germany)

Author keywords

Response times; Stationary distribution; Stochastic networks; Subexponential service times; Tail asymptotics; Tandem queues

Indexed keywords

LINEAR SYSTEMS; LYAPUNOV METHODS; MATRIX ALGEBRA; PETRI NETS; QUEUEING THEORY; RESPONSE TIME (COMPUTER SYSTEMS);

RESPONSE TIMES; SERVICE TIME; STATIONARY DISTRIBUTION; STOCHASTIC NETWORKS; TAIL ASYMPTOTICS; TANDEM QUEUE;

STOCHASTIC SYSTEMS;

EID: 0033236512     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019176129224     Document Type: Article

References (23)

1. V. Anantharam, Networks of queues with long-range dependent traffic streams, in: Stochastic Networks: Stability and Rare Events, Lecture Notes in Statistics, Vol. 117 (Springer, Berlin, 1996) pp. 237-256.
2. S. Asmussen, C. Klüppelberg and K. Sigman, Sampling at subexponential times, with queueing applications, Stochastic Process. Appl. 79 (1999) 265-286.
3. S. Asmussen, H. Schmidli and V. Schmidt, Tail probabilities for nonstandard risk and queueing processes with subexponential jumps, Adv. in Appl. Probab. 31 (to appear 1999).
4. F. Baccelli, G. Cohen, G.J. Olsder and J.P. Quadrat, Synchronization and Linearity (Wiley, Chichester, UK, 1992).
5. F. Baccelli, S. Schlegel and V. Schmidt, Asymptotics of tandem queues with subexponential service times, in: Proc. of the Workshop on Stochastic Modelling of High-Speed Networks, Technical University of Munich (18 June 1998) (CS Press, Munich, 1999) pp. 25-41.
6. F. Baccelli and V. Schmidt, Taylor series expansions for Poisson-driven (max, +)-linear systems, Ann. Appl. Probab. 6 (1996) 138-185.
7. D. Bertsimas, I. Paschalides and J. Tsitsiklis, On the large deviations behaviour of acyclic networks of G/G/1 queues, Ann. Appl. Probab. 8 (1998) 1027-1069.
8. O.J. Boxma and Q. Deng, Asymptotic properties in the tandem queueing system with identical service times at both queues, Working paper (1998).
9. V.P. Chistyakov, A theorem on sums of independent, positive random variables and its applications to branching processes, Theory Probab. Appl. 9 (1964) 640-648.
10. D.B.H. Cline, Convolution tails, product tails and domains of attraction, Probab. Theory Related Fields 72 (1986) 529-557.
11. J.W. Cohen, Some results on regular variation for distributions in queueing and fluctuation theory, J. Appl. Probab. 10 (1973) 343-353.
12. P. Embrechts and C.M. Goldie, On closure and factorization theorems for subexponential and related distributions, J. Austral. Math. Soc. Ser. A 29 (1980) 243-256.
13. P. Embrechts and C.M. Goldie, On convolution tails, Stochastic Process. Appl. 13 (1982) 263-278.
14. P. Embrechts and N. Veraverbeke, Estimates for the probability of ruin with special emphasis on the possibility of large claims, Insurance Math. Econom. 1 (1982) 55-72.
15. A. Ganesh and V. Anantharam, Stationary tail probabilities in exponential server tandems with renewal arrivals, Queueing Systems 22 (1996) 203-248.
16. B. Gaujal, Parallélisme et simulation des systèmes à événements discrets, Thèse de Doctorat, Université de Nice Sophia Antipolis (1994).
17. T. Huang and K. Sigman, Steady-state asymptotics for tandem, split-match and other feedforward queues with heavy tailed service, Queueing Systems (this issue) 33 (1999) 233-259.
18. C. Klüppelberg, Subexponential distributions and integrated tails, J. Appl. Probab. 25 (1988) 132-141.
19. A.G. Pakes, On the tails of waiting-time distributions, J. Appl. Probab. 12 (1975) 555-564.
20. E.J.G. Pitman, Subexponential distribution functions, J. Austral. Math. Soc. Ser. A 29 (1980) 337-347.
21. T. Rolski, H. Schmidli, V. Schmidt and J.L. Teugels, Stochastic Processes for Insurance and Finance (Wiley, Chichester, UK, 1999).
22. J.L. Teugels and N. Veraverbeke, Cramér-type estimates for the probability of ruin, CORE Discussion Paper No. 7316 (1973).
23. N. Veraverbeke, Asymptotic behavior of Wiener - Hopf factors of a random walk, Stochastic Process. Appl. 5 (1977) 27-37.