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

Achal Bassamboo (), Ramandeep S. Randhawa () and Jan A. Van Mieghem ()
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Achal Bassamboo: Kellogg School of Management, Northwestern University, Evanston, Illinois 60203
Ramandeep S. Randhawa: Marshall School of Business, University of Southern California, Los Angeles, California 90089
Jan A. Van Mieghem: Kellogg School of Management, Northwestern University, Evanston, Illinois 60203

Operations Research, 2012, vol. 60, issue 6, 1423-1435

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 (lambda) (rightarrow) (infinity). We prove that “a little flexibility is all you need”: the optimal portfolio invests O ((lambda)) in specialized resources and only O ((sqrt)(lambda)) 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 ((sqrt)(lambda))) 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 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (13)

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