A Little Flexibility Is All You Need: On the Asymptotic Value of Flexible Capacity in Parallel Queuing Systems

• Authors: Achal Bassamboo;Ramandeep S. Randhawa;Jan A. Van Mieghem
• Venue: Operations Research
• Year: 2012

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 Oλ 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.