The Annals of Probability

Asymptotics of Exit Times for Markov Jump Processes. II: Applications to Jackson Networks

I. Iscoe and D. McDonald

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Abstract

We show that a Jackson network relaxes exponentially fast to its steady state by giving a lower bound on the Cheeger constant for the associated Markov process. We also give lower bounds on the mean time until some node of the network overflows.

Article information

Source
Ann. Probab., Volume 22, Number 4 (1994), 2168-2182.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176988498

Digital Object Identifier
doi:10.1214/aop/1176988498

Mathematical Reviews number (MathSciNet)
MR1331219

Zentralblatt MATH identifier
0834.60091

JSTOR
links.jstor.org

Subjects
Primary: 60J75: Jump processes
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]

Keywords
Jackson networks asymptotic exponentiality Cheeger constant

Citation

Iscoe, I.; McDonald, D. Asymptotics of Exit Times for Markov Jump Processes. II: Applications to Jackson Networks. Ann. Probab. 22 (1994), no. 4, 2168--2182. doi:10.1214/aop/1176988498. https://projecteuclid.org/euclid.aop/1176988498


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See also

  • Part I: I. Iscoe, D. McDonald. Asymptotics of Exit Times for Markov Jump Processes I. Ann. Probab., Volume 22, Number 1 (1994), 372--397.