Tail asymptotics for discrete event systems

ACM International Conference Proceeding Series

Volumn 180, Issue , 2006, Pages

  Lelarge, Marc ^a  

^a UNIVERSITY COLLEGE CORK   (Ireland)

Author keywords

Performance; Theory

Indexed keywords

ASYMPTOTIC ANALYSIS; GRAPH THEORY; QUEUEING NETWORKS; RANDOM PROCESSES; RESPONSE TIME (COMPUTER SYSTEMS); TELECOMMUNICATION NETWORKS;

LOGARITHMIC TAIL ASYMPTOTICS; NON-TRIVIAL EFFECTS; STATIONARY RESPONSE TIME; STOCHASTIC EVENT GRAPHS;

DISCRETE EVENT SIMULATION;

EID: 34748883702     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1190095.1190141     Document Type: Conference Paper

References (25)

1. V. ANANTHARAM, HOW large delays build up in a GI/G/1 queue, Queueing Systems Theory Appl., 5 (1989), pp. 345-367.
2. F. BACCELLI, G. COHEN, G. J. OLSDER, AND J.-P. QUADRAT, Synchronization and Linearity, Wiley, 1992. Available at http://www-rocq.inria.fr/metalau/cohen/SED/book-online.html.
3. F. BACCELLI AND S. FOSS, On the saturation rule for the stability of queues, Journal of Applied Probability, 32 (1995), pp. 494-507.
4. F. BACCELLI, S. FOSS, AND M. LELARGE, Asymptotics of subexponential max plus networks: the stochastic event graph case, Queueing Systems, 46 (2004), pp. 75-96.
5. F. BACCELLI AND A. MAKOWSKI, Queueing models for systems with synchronization constraints, Proceedings of the IEEE, 77 (1989), pp. 138-161.
6. D. BERTSIMAS, I. C. PASCHALIDIS, AND J. N. TSITSIKLIS, On the large deviations behavior of acyclic networks of G/G/1 queues, Ann. Appl. Probab., 8 (1998), pp. 1027-1069.
7. V. D. BLONDEL, S. GAUBERT, AND J. N. TSITSIKLIS, Approximating the spectral radius of sets of matrices in the max-algebra is NP-hard, IEEE Trans. Automat. Control, 45 (2000), pp. 1762-1765.
8. C. S. CHANG, Sample path large deviations and intree networks, Queueing Systems Theory Appl., 20 (1995), pp. 7-36.
9. H. CRAMÉR, Sur un nouveau théorème limite de la théorie des probabilités, Actualités Scientifiques et Industrielles, 736 (1938), pp. 5-23.
10. A. DEMBO AND O. ZEITOUNI, Large Deviations Techniques and Applications, Springer-Verlag, 1998.
11. K. DUFFY, J. T. LEWIS, AND W. G. SULLIVAN, Logarithmic asymptotics for the supremum of a stochastic process, Ann. Appl. Probab., 13 (2003), pp. 430-445.
12. P. DUPUIS AND R. S. ELLIS, The large deviation principle for a general class of queueing systems. I, Trans. Amer. Math. Soc., 347 (1995), pp. 2689-2751.
13. P. DUPUIS, R. S. ELLIS, AND A. WEISS, Large deviations for Markov processes with discontinuous statistics. I. General upper bounds, Ann. Probab., 19 (1991), pp. 1280-1297.
14. A. GANESH, Large deviations of the sojourn time for queues in series, Annals of Operations Research, 79 (1998), pp. 3-26.
15. A. GANESH AND V. ANANTHARAM, Stationary tail probabilities in exponential server tandems with renewal arrivals, Queueing Systems Theory Appl., 22 (1996), pp. 203-247.
16. R. HAJI AND G. F. NEWELL, A relation between stationary queue and waiting time distributions, J. Appl. Probability, 8 (1971), pp. 617-620.
17. Y. HAN AND A. M. MAKOWSKI, Resequencing delays under multipath routing - asymptotics in a simple queueing model, IEEE INFOCOM Proceedings, (2006).
18. D. L. IGLEHART, Extreme values in the GI/G/1 queue, Ann. Math. Statist., 43 (1972), pp. 627-635.
19. I. IGNATIOUK-ROBERT, Large deviations of Jackson networks, Annals of Applied Probability, 3 (2000), pp. 962-1001.
20. I. IGNATIOUK-ROBERT, Large deviations for processes with discontinuous statistics, Ann. Probab., 33 (2005), pp. 1479-1508.
21. A. JEAN-MARIE AND L. GUN, Parallel queues with resequencing, J. Assoc. Comput. Mach., 40 (1993), pp. 1188-1208.
22. M. LELARGE, Tail asymptotics for monotone-separable networks, arxiv/math.PR/0510117. Available at http://www.proba.ucc.ie/~lm4/.
23. M. LELARGE, Rare Events in Networks, PhD thesis, Ecole polytechnique, 2005. Available at http://www.proba.ucc.ie/~lm4/.
24. A. PAKES, On the tails of waiting-time distributions, Journal of Applied Probability, 12 (1975), pp. 555-564.
25. F. TOOMEY, Large deviations of products of random topical operators, The Annals of Applied Probability, 12 (2002), pp. 317-333.