An enhanced algorithm to solve multiserver retrial queueing systems with impatient customers

• Published in: Computers & industrial engineering Vol. 65; no. 4; pp. 719 - 728
• Main Authors: Do, Tien Van, Do, Nam H., Zhang, Jie
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01-08-2013; Pergamon Press Inc
• Subjects: Algorithms; Efficient algorithm; Geometry; Homogenization; Mathematical problems; Matrix; Matrix-geometric method; Queuing theory; Retrial queues; Spectral expansion; Studies; Retrial queues; Spectral expansion; Matrix-geometric method; Efficient algorithm
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2013.04.008

•This paper derives the computation of the rate matrix, the conditional mean number of customers.•This paper provides a proof concerning the determination of a threshold.•This paper derives simple equations that allows the memory-efficient implementation of the computation of the performance measures.•This paper proposes an efficient algorithm for the stationary distribution of a multiserver retrial queue.
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.