Title: Queueing System Topologies with Limited Flexibility
Abstract: We study a multi-server model with n flexible servers and rn queues, connected through a fixed bipartite graph, where the level of flexibility is captured by the average degree, d(n), of the queues. 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 (robustness) and diminishing queueing delay (performance) are jointly achievable even under very limited flexibility (d(n) << n). In particular, when d(n) >> ln(n), a family of random-graph-based interconnection topologies is (with high probability) capable of stabilizing all admissible arrival rate vectors (under a bounded support assumption), while simultaneously ensuring a diminishing queueing delay, of order ln(n)/d(n), as n tends to infinity. Our analysis is centered around a new class of virtual-queue-based scheduling policies that rely on dynamically constructed partial matchings on the connectivity graph. We also compare different architectures in terms of to what extend the joint objective of capacity and delay is possible.
Based on joint work with John N. Tsitsiklis.