Closed queueing networks under congestion: non-bottleneck independence and bottleneck convergence

Jonatha Anselmi, Bernardo D'Auria and Neil Walton

DES - Working Papers. Statistics and Econometrics. WS from Universidad Carlos III de Madrid. Departamento de Estadística

Abstract: We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.

Keywords: Fluid; limit; Closed; queueing; networks; Product-form; Asymptotic; independence; Large; population (search for similar items in EconPapers)
Date: 2012-06
New Economics Papers: this item is included in nep-net and nep-tre
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Persistent link: https://EconPapers.repec.org/RePEc:cte:wsrepe:ws121711

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