• Management Science and Financial Engineering
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• v.9 no.2
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• pp.1-12
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• 2003

For a stationary queue with BMAP arrivals, Takine and Takahashi [8] present a relationship between the queue length distributions at a random epoch and at a departure epoch by using the rate conservation law of Miyazawa [6]. In this note, we derive the same relationship by using the elementary balance equation, ‘rate-in = rate-out’. Along the same lines, we additionally derive relationships between the queue length distributions at a random epoch and at an arrival epoch. All these relationships hold for a broad class of finite-as well as infinite-capacity queues with BMAP arrivals.

• Journal of Korean Institute of Industrial Engineers
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• v.28 no.3
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• pp.319-330
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• 2002

We consider BMAP/G/1 queueing system with N-policy and multiple vacations. We derive the vector generating functions of the queue length in a factorized form and interpret the factorization. We also derive the mean queue length.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.2
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• pp.16-23
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• 2007

Tandem queueing systems well suit for modeling many telecommunication systems. Recently, very general $BMAP/G/1/N/1{\to}{\bullet}/PH/1/M-1$ type tandem queues were constructively studied. In this paper we illustrate application of the obtained results for optimization of a buffer pool design.