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Transient Behavior of Fractional Queues and Related Processes

Dexter O. Cahoy (), Federico Polito () and Vir Phoha ()
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Dexter O. Cahoy: Louisiana Tech University
Federico Polito: University of Torino
Vir Phoha: Louisiana Tech University

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 3, 739-759

Abstract: Abstract We propose a generalization of the classical M/M/1 queue process. The resulting model is derived by applying fractional derivative operators to a system of difference-differential equations. This generalization includes both non-Markovian and Markovian properties which naturally provide greater flexibility in modeling real queue systems than its classical counterpart. Algorithms to simulate M/M/1 queue process and the related linear birth-death process are provided. Closed-form expressions of the point and interval estimators of the parameters of the proposed fractional stochastic models are also presented. These methods are necessary to make these models usable in practice. The proposed fractional M/M/1 queue model and the statistical methods are illustrated using financial data.

Keywords: Transient analysis; Fractional M/M/1 queue; Mittag–Leffler function; Fractional birth-death process; Parameter estimation; Simulation; 60G55; 60K25; 26A33 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9391-2

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