State-dependent M/M/c/c + r retrial queues with Bernoulli abandonment

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July 2010, 6(3): 517-540. doi: 10.3934/jimo.2010.6.517

State-dependent M/M/c/c + r retrial queues with Bernoulli abandonment

Tuan Phung-Duc ^1, , Hiroyuki Masuyama ^1, , Shoji Kasahara ^1, and Yutaka Takahashi ^1,

1.	Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501, Japan

Received September 2009 Revised April 2010 Published June 2010

Abstract
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This paper considers a state-dependent M/M/$c$/$c+r$ retrial queue with Bernoulli abandonment, where the number of servers is equal to $c$, the capacity of the buffer is equal to $r$ and that of the virtual waiting room (called orbit) for the retrial customers is infinite. We assume that the arrival, service and retrial rates depend on the number of customers in the system (the servers and buffer). In this paper, we first present the ergodic condition for our retrial queue. Then, by a continued fraction approach, we derive analytical solutions for the stationary joint distribution of the queue lengths in the system and in the orbit, assuming that the capacity of the system is less than or equal to 4. We further show that our analytical solutions can be computed with any desired accuracy. Finally, we present some numerical results to show the impact of the parameters on the performance of the system.

Keywords: hypergeometric functions, Continued fractions., Multiserver retrial queue, Bernoulli abandonment, Three-term recurrence relations.

Mathematics Subject Classification: Primary: 68M20, 90B22; Secondary: 60K2.

Citation: Tuan Phung-Duc, Hiroyuki Masuyama, Shoji Kasahara, Yutaka Takahashi. State-dependent M/M/c/c + r retrial queues with Bernoulli abandonment. Journal of Industrial & Management Optimization, 2010, 6 (3) : 517-540. doi: 10.3934/jimo.2010.6.517

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