STABILITY OF JOIN THE SHORTEST QUEUE NETWORKS

• 成果类型: Article
• 署名作者: Bramson, Maury
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP726
• 发表日期: 2011
• 页码: 1568-1625
• 关键词: 2 choices; POWER

摘要

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.