Design heuristic for parallel many server systems

Adan, I.J.B.F.; Boon, Marko; Weiss, Gideon

doi:10.1016/j.ejor.2018.08.042

Cited by 44 publications

(9 citation statements)

References 32 publications

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“…To complete this review of previous work, let us mention another conjectural connection between the bipartite matching model and the parallel server queueing model. In [1,2], it is conjectured that in a parallel server queueing model, stabilized by abandonments, and operated under FCFS-ALIS, matching rates of the queueing system under many server scaling equal the matching rates of the FCFS infinite bipartite matching model. This conjecture is as yet not proved, but simulations indicate that it may be correct, and that it can be used to evaluate performance and assist in design of such systems.…”

Section: Introductionmentioning

confidence: 99%

Reversibility and Further Properties of FCFS Infinite Bipartite Matching

et al. 2018

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The model of FCFS infinite bipartite matching was introduced in Caldentey, Kaplan, & Weiss Adv. Appl. Probab., 2009. In this model, there is a sequence of items that are chosen i.i.d. from a finite set C and an independent sequence of items that are chosen i.i.d. from a finite set S, and a bipartite compatibility graph G between C and S. Items of the two sequences are matched according to the compatibility graph, and the matching is FCFS, meaning that each item in the one sequence is matched to the earliest compatible unmatched item in the other sequence. In Adan & Weiss, Operations Research, 2012, a Markov chain associated with the matching was analyzed, a condition for stability was derived, and a product form stationary distribution was obtained. In the current paper, we present several new results that unveil the fundamental structure of the model. First, we provide a pathwise Loynes' type construction which enables to prove the existence of a unique matching for the model defined over all the integers. Second, we prove that the model is dynamically reversible: we define an exchange transformation in which we interchange the positions of each matched pair, and show that the items in the resulting permuted sequences are again independent and i.i.d., and the matching between them is FCFS in reversed time. Third, we obtain product form stationary distributions of several new Markov chains associated with the model. As a by product, we compute useful performance measures, for instance the link lengths between matched items.

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Section: Introductionmentioning

confidence: 99%

Reversibility and Further Properties of FCFS Infinite Bipartite Matching

et al. 2018

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“…where ∼ means the ratio of the two sides converges to 1 when n → ∞, m 1 and m 2 are defined in (4). Note that the definition in (4) does not require a specific case.…”

Section: Proof Of Theoremmentioning

confidence: 99%

“…In Sect. 4 we verify the heuristic guess and obtain the stationary behavior under many-server scaling. In Sect.…”

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confidence: 99%

“…The following conjecture was made in [4]. If the system is stable and has complete resource pooling for given λ, n, and we let both become large together, the behavior of the system simplifies: there will exist β j such that servers of type j perform a fraction β j of the services, and the matching rates r i, j will converge to the rates for the FCFS infinite matching model with G, α, β, as calculated in [1] (see also [5]).…”

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confidence: 99%

“…The N-system is one of the simplest special cases of skill-based routing in parallel server systems, as defined in [9,15] and further studied in [4,6,7,[12][13][14]17,19,20,22,23]. The general model has customers of types i = 1, .…”

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Many-server scaling of the N-system under FCFS–ALIS

Zhan

Weiss

2017

Queueing Syst

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The N-system with independent Poisson arrivals and exponential serverdependent service times under the first come first served and assign to the longest idle server policy has an explicit steady-state distribution. We scale the arrival rate and the number of servers simultaneously, and obtain the fluid and central limit approximation for the steady state. This is the first step toward exploring the many-server scaling limit behavior of general parallel service systems.

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