Performance analysis of a Geom/Geom/1 queueing system with variable input probability

Zhanyou Ma; Wuyi Yue; Xiaoli Su

doi:10.3934/jimo.2011.7.641

Article Contents

2011, Volume 7, Issue 3: 641-653. Doi: 10.3934/jimo.2011.7.641

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Performance analysis of a Geom/Geom/1 queueing system with variable input probability

1.
Department of Applied Mathematics, College of Science, Yanshan University, Qinhuangdao 066004
2.
Department of Intelligence and Informatics, Konan University, Kobe 658-8501
3.
Department of Applied Mathematics, College of Science Yanshan University, Qinhuangdao 066004

Received: September 2010

Revised: May 2011

Published: July 2011

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Abstract

In this paper, we present a Geom/Geom/1 queueing model with variable input probability. In this queueing model, an arriving customer, who sees many customers waiting for service in the queueing system, will consider whether to enter the system or not. We consider the possibility that the customer enters the system to receive service to be a probability called the "Input Probability". We derive the transition probability matrix of the birth and death chain of the queueing model. Using a birth and death process, we gain the probability distributions of the stationary queue length and the waiting time in the queueing model. Then we derive special cases of the considered model by applying different input probability distributions, which lead to several known specific queueing models. We also derive some performance measures of these specific queueing models. Therefore, this queueing model that we present in this paper has a certain extension, extending to the existing models. Finally, we compare the effect of the parameters on the stationary queue length and waiting time by using numerical results.

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Mathematics Subject Classification: Primary: 60K25; Secondary: 90B22.

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