2015/05/28 by John N. Tsitsiklis, Tsitsiklis, John N., Kuang Xu +1
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Networking and Internet Architecture (cs.NI) #Performance (cs.PF) #Probability (math.PR) #cs.NI #cs.PF #math.PR
paper · pdf · doi:10.48550/arxiv.1505.07648
Revised October 2016. A preliminary version of this paper appeared at the 2013 ACM Sigmetrics conference; the performance of the architectures proposed in the current paper is significantly better than the one in the conference version
arxiv created 2017/02/06 · arxiv updated 2017/02/07
We study a multi-server model with n flexible servers and n queues, connected through a bipartite graph, where the level of flexibility is captured by the graph's average degree, dn. 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 (dn ≪ n). Our main results demonstrate that, when dn≫ ln 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 a new 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.