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

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 → . We prove that "a little flexibility is all you need": the optimal portfolio invests O in specialized resources and only O √ 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 √ ) 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.

On the Power of (Even a Little) Resource Pooling

“…Some recent work in this area [19] that studies limited pooling in a large-system limit is closer to our work in spirit, but still differs significantly in terms of critical modeling assumptions and dynamics. The notion of limited flexibility has also been studied in manufacturing systems, such as the celebrated Long Chain design [9,10] and its variants [11][12][13][14].…”

“…By applying the Foster-Lyapunov stability criterion, one should be able to prove positive recurrence of V N and give an explicit upper-bound on the expected value of V N 1 in steady state. 19 If this expectation is bounded as N → ∞, we will have obtained the desirable result by the Markov inequality. We do not pursue this direction in this paper, because we believe that the stochastic dominance approach adopted here provides more insight by exploiting the monotonicity in p of the steady-state queue length distribution.…”

Modelling of accounting information system for military medical institutions

“…In case of servicing the requests i type, the system receives revenue C i . The task consists in finding the optimal management of resource allocation [14], which maximizes the expected usefulness of accounting information [15] from servicing requests during a given time interval T.…”

Queueing system topologies with limited flexibility

“…Simulations in [15] show empirically that limited cross-training can be highly effective in a large call center under a skill-based routing algorithm. Using a very different set of modeling assumptions, [16] proposes a specific chaining structure with limited flexibility, which is shown to perform well under heavy traffic. Closer to the spirit of the current work is [17], which studies a partially flexible system where a fraction p > 0 of all processing resources are fully flexible, while the remaining fraction, 1 − p, is dedicated to specific demand types, and shows an exponential improvement in delay scaling under heavy-traffic.…”

“…Closer to the spirit of the current work is [17], which studies a partially flexible system where a fraction p > 0 of all processing resources are fully flexible, while the remaining fraction, 1 − p, is dedicated to specific demand types, and shows an exponential improvement in delay scaling under heavy-traffic. However, both [16] and [17] focus on the heavy-traffic regime, which is different from the current setting where traffic intensity is assumed to be fixed while the system size tends to infinity, and provide analytical results for the special case of uniform demand rates. Furthermore, with a constant fraction of fully flexible resources, the average degree in [17] scales linearly with the system size n, whereas we are interested in the case of a much slower degree scaling.…”