Flexible Queueing Architectures

• 成果类型: Article
• 署名作者: Tsitsiklis, John N.; Xu, Kuang
• 署名单位: Massachusetts Institute of Technology (MIT); Stanford University
• 刊物名称: OPERATIONS RESEARCH
• ISSN/ISSBN: 0030-364X
• DOI: 10.1287/opre.2017.1620
• 发表日期: 2017
• 页码: 1398-1413
• 关键词: process flexibility; long-chain; systems; inequalities; PERSPECTIVE; expander; Servers; queues; DESIGN

摘要

We study a multiserver model with n flexible servers and n queues, connected through a bipartite graph, where the level of flexibility is captured by an upper bound on the graph's average degree, d(n). Applications in content replication in data centers, skill-based routing in call centers, and flexible supply chains are among our main motivations. We focus on the scaling regime where the system size n tends to infinity, while the overall traffic intensity stays fixed. We show that a large capacity region and an asymptotically vanishing queueing delay are simultaneously achievable even under limited flexibility (d(n) << n). Our main results demonstrate that, when d(n) >> In n, a family of expander-graph-based flexibility architectures has a capacity region that is within a constant factor of the maximum possible, while simultaneously ensuring a diminishing queueing delay for all arrival rate vectors in the capacity region. Our analysis is centered around anew class of virtual-queue-based scheduling policies that rely on dynamically constructed job-to-server assignments on the connectivity graph. For comparison, we also analyze a natural family of modular architectures, which is simpler but has provably weaker performance.