A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems
Achal Bassamboo, Ramandeep S. Randhawa, Jan A. Van Mieghem
Operations Research · 2012 · Volume 60 · Issue 6
Abstract
We analytically study optimal capacity and flexible technology selection in parallel queuing systems. We consider N stochastic arrival streams that may wait in N queues before being processed by one of many resources (technologies) that differ in their flexibility. A resource's ability to process k different arrival types or classes is referred to as level- k flexibility. We determine the capacity portfolio (consisting of all resources at all levels of flexibility) that minimizes linear capacity and linear holding costs in high-volume systems where the arrival rate λ → ∞. We prove that “a little flexibility is all you need”: the optimal portfolio invests O (λ) in specialized resources and only O (√λ) in flexible resources and these optimal capacity choices bring the system into heavy traffic. Further, considering symmetric systems (with type-independent parameters), a novel “folding” methodology allows the specification of the asymptotic queue count process for any capacity portfolio under longest-queue scheduling in closed form that is amenable to optimization. This allows us to sharpen “a little flexibility is all you need”: the asymptotically optimal flexibility configuration for symmetric systems with mild economies of scope invests a lot in specialized resources but only a little in flexible resources and only in level-2 flexibility, but effectively nothing ( o (√λ)) in level- k > 2 flexibility. We characterize “tailored pairing” as the theoretical benchmark configuration that maximizes the value of flexibility when demand and service uncertainty are the main concerns.
Keywords
flexibility, capacity optimization, queueing network, diffusion approximation
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