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A computational approach to steady-state convergence of fluid limits for Coxian queuing networks with abandonment

Tschaikowski, Max and Tribastone, Mirco A computational approach to steady-state convergence of fluid limits for Coxian queuing networks with abandonment. Annals of Operations Research, 252 (1). pp. 102-120. ISSN 0254-5330 (2017)

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Many-server queuing networks with general service and abandonment times have proven to be a realistic model for scenarios such as call centers and health-care systems. The presence of abandonment makes analytical treatment difficult for general topologies. Hence, such networks are usually studied by means of fluid limits. The current state of the art, however, suffers from two drawbacks. First, convergence to a fluid limit has been established only for the transient, but not for the steady state regime. Second, in the case of general distributed service and abandonment times, convergence to a fluid limit has been either established only for a single queue, or has been given by means of a system of coupled integral equations which does not allow for a numerical solution. By making the mild assumption of Coxian-distributed service and abandonment times, in this paper we address both drawbacks by establishing convergence in probability to a system of coupled ordinary differential equations (ODEs) using the theory of Kurtz. The presence of abandonments leads in many cases to ODE systems with a global attractor, which is known to be a sufficient condition for the fluid and the stochastic steady state to coincide in the limiting regime. The fact that our ODE systems are piecewise affine enables a computational method for establishing the presence of a global attractor, based on a solution of a system of linear matrix inequalities.

Item Type: Article
Identification Number: 10.1007/s10479-016-2193-5
Additional Information: SCOPUS ID: 2-s2.0-84964262324
Projects: EU project QUANTICOL, 600708
Subjects: Q Science > QA Mathematics > QA76 Computer software
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 06 Oct 2016 15:03
Last Modified: 08 Aug 2017 09:10
URI: http://eprints.imtlucca.it/id/eprint/3575

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