EXPLICIT SOLUTION FOR QUEUE LENGTH DISTRIBUTION OF M/T-SPH/1 QUEUE

Hongbo Zhang (), Dinghua Shi () and Zhenting Hou ()
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Hongbo Zhang: School of Mathematics, Central South University, Changsha, 410075, P. R. China;
Dinghua Shi: Department of Mathematics, Shanghai University, Shanghai, 200444, P. R. China
Zhenting Hou: School of Mathematics, Central South University, Changsha, 410075, P. R. China

Asia-Pacific Journal of Operational Research (APJOR), 2014, vol. 31, issue 01, 1-19

Abstract: In this paper we study an M/T-SPH/1 queue system, where T-SPH denotes the continuous time phase type distribution defined on a birth and death process with countably many states. The queue model can be described by a quasi-birth-and-death (QBD) process with countable phases. For the QBD process, we give the computation scheme of the joint stationary distribution. Furthermore, the obtained results enable us to give the stationary queue length distribution for the M/T-SPH/1 queue.

Keywords: M/T-SPH/1 queue; QBD process; joint stationary distribution; stationary queue length (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1142/S0217595914500018

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