The Annals of Applied Probability

Stability of join the shortest queue networks

Maury Bramson

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Abstract

Join the shortest queue (JSQ) refers to networks whose incoming jobs are assigned to the shortest queue from among a randomly chosen subset of the queues in the system. After completion of service at the queue, a job leaves the network. We show that, for all nonidling service disciplines and for general interarrival and service time distributions, such networks are stable when they are subcritical. We then obtain uniform bounds on the tails of the marginal distributions of the equilibria for families of such networks; these bounds are employed to show relative compactness of the marginal distributions. We also present a family of subcritical JSQ networks whose workloads in equilibrium are much larger than for the corresponding networks where each incoming job is assigned randomly to a queue. Part of this work generalizes results in [Queueing Syst. 29 (1998) 55–73], which applied fluid limits to study networks with the FIFO discipline. Here, we apply an appropriate Lyapunov function.

Article information

Source
Ann. Appl. Probab., Volume 21, Number 4 (2011), 1568-1625.

Dates
First available in Project Euclid: 8 August 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1312818845

Digital Object Identifier
doi:10.1214/10-AAP726

Mathematical Reviews number (MathSciNet)
MR2857457

Zentralblatt MATH identifier
1236.60088

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B15: Network models, stochastic

Keywords
Join the shortest queue stability

Citation

Bramson, Maury. Stability of join the shortest queue networks. Ann. Appl. Probab. 21 (2011), no. 4, 1568--1625. doi:10.1214/10-AAP726. https://projecteuclid.org/euclid.aoap/1312818845


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