Multiserver retrial queues with after-call work

Tuan Phung-Duc; Ken’ichi Kawanishi

doi:10.3934/naco.2011.1.639

Article Contents

2011, Volume 1, Issue 4: 639-656. Doi: 10.3934/naco.2011.1.639

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Multiserver retrial queues with after-call work

Tuan Phung-Duc^1, and
Ken’ichi Kawanishi^2,

1.
Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501
2.
Department of Computer Science, Gunma University, Kiryu-City, 376-8515

Received: May 31, 2011

Revised: July 31, 2011

Published: October 2011

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Abstract

This paper considers a multiserver queueing system with finite capacity. Customers that find the service facility being fully occupied are blocked and enter a virtual waiting room (called orbit). Blocked customers stay in the orbit for an exponentially distributed time and retry to occupy an idle server again. After completing a service, the server starts an additional job that we call an after-call work. We formulate the queueing system using a continuous-time level-dependent quasi-birth-and-death process, for which a sufficient condition for the ergodicity is derived. We obtain an approximation to the stationary distribution by a direct truncation method whose truncation point is simply determined using an asymptotic analysis of a single server retrial queue. Some numerical examples are presented in order to show the influence of parameters on the performance of the system.

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Mathematics Subject Classification: Primary: 60K25, 68M20; Secondary: 90B22.

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