A Quick Simulation Method for Excessive Backlogs in Networks of Queues

IEEE Transactions on Automatic Control

Volumn 34, Issue 1, 1989, Pages 54-66

  Parekh, Shyam ^a   Walrand, Jean ^b  

^a LUCENT TECHNOLOGIES   (United States)

^b University of   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL TECHNIQUES--HEURISTIC; MATHEMATICAL TRANSFORMATIONS--LAPLACE TRANSFORMS; PROBABILITY--QUEUEING THEORY;

EXCESSIVE BACKLOGS; LARGE DEVIATION THEORY; MARKOVIAN ROUTING; OPEN JACKSON NETWORKS;

COMPUTER NETWORKS;

EID: 0024479530     PISSN: 00189286     EISSN: 15582523     Source Type: Journal    
DOI: 10.1109/9.8649     Document Type: Article

References (15)

1. R. Azencott and G. Ruget, “Melanges dÉequations differentielles et grands Écarts a la loi des grands nombres,” Z. Wahrscheinlichkeitstheorie verm. Gebiete, vol. 38, pp. 1–54, 1977.
2. P. Billingsley, Convergence of Probability Measures. New York: Wiley, 1968.
3. M. Cottrell, J.-C. Fort, and G. Malgouyres, “Large deviations and rare events in the study of stochastic algorithms,’’ IEEE Trans. Automat. Contr., vol. AC-28, no. 9, pp. 907–920, 1983.
4. P. Dupuis and J. Kushner, “Stochastic systems with small noise, analysis and simulation; A phase locked loop example,’’ SIAM J. Appl. Math., vol. 47, pp. 643–661, June 1987.
5. R. Ellis, Entropy, Large Deviations and Statistical Mechanics. New York: Springer-Verlag, 1986.
6. —, “Large deviations for the empirical measure of a Markov chain with an application to the multivariate empirical measure,” Dep. Math. Stat., Univ. Massachusetts, Amherst, MA, Int. Memo., 1987.
7. S. Natarajan, “Large deviation, hypotheses testing, and coding for finite Markov chains,” IEEE Trans. Inform. Theory, vol. IT-31, no. 3, pp. 360–365, 1985.
8. S. Parekh, “Rare events in networks,” Ph.D. dissertation, Dep. EECS, Univ. Calif., Berkeley, CA, 1986.
9. G. Ruget, “Quelques Occurences Des Grands Ecarts Dans La Litterature Electronique,” Asterisque, vol. 68, pp. 187–199, 1979.
10. I. Sanov, “On the probability of large deviation of random variables,” Sel. Trans. Math. Statist. Prob., vol. I, pp. 213–244, 1957.
11. S. R. S. Varadhan, “Large deviations and applications,” SIAM, 1984.
12. A. D. Ventsel, “Rough limit theorems on large deviation for Markov stochastic processes— II,” Theory Prob. Appl. (USSR), vol. 21, pp. 499–512, 1976.
13. R. Weber, “The interchangeability of /M/1 queues in series,” J. Appl. Prob., vol. 16, pp. 690–695, 1979.
14. A. Weiss, “A new technique for analyzing large traffic systems,” Adv. Appl. Prob., vol. 18, pp. 506–532, 1986.
15. —, “Large deviations for a Markov process with one boundary,” presented at Conf. Stochastic Processes and Applications, Stanford, CA, Aug. 1987.