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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1423-1435
Number of pages13
JournalOperations Research
Volume60
Issue number6
DOIs
StatePublished - Nov 2012

Keywords

  • Capacity optimization
  • Diffusion approximation
  • Flexibility
  • Queueing network

ASJC Scopus subject areas

  • Computer Science Applications
  • Management Science and Operations Research

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