An enhanced algorithm to solve multiserver retrial queueing systems with impatient customers |
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Authors: | Tien Van Do Nam H. Do Jie Zhang |
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Affiliation: | 1. MTA-BME Information Systems Research Group, Department of Networked Systems and Services, Budapest University of Technology and Economics, Magyar tudósok körútja 2, H-1117 Budapest, Hungary;2. Inter-University Centre for Telecommunications and Informatics, Budapest University of Technology and Economics, Kassai út 26, 4028 Debrecen, Hungary;3. Communications Group, The Department of Electronic and Electrical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD, UK |
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Abstract: | The homogenization of the state space for solving retrial queues refers to an approach, where the performance of the M/M/c retrial queue with impatient customers and c servers is approximated with a retrial queue with a maximum retrial rate restricted beyond a given number of users in the orbit. As a consequence, the stationary distribution can be obtained by the matrix-geometric method, which requires the computation of the rate matrix. In this paper, we revisit an approach based on the homogenization of the state space. We provide the exact expression for the conditional mean number of customers based on the computation of the rate matrix R with the time complexity of O(c). We develop simplified equations for the memory-efficient implementation of the computation of the performance measures. We construct an efficient algorithm for the stationary distribution with the determination of a threshold that allows the computation of performance measures with a specific accuracy. |
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Keywords: | Retrial queues Matrix-geometric method Spectral expansion Efficient algorithm |
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