Busy Periods of Poisson Arrival Queues with Loss

Authors:
Sunggon Kim;Jongho Bae;Eui Yong Lee
Affiliations:
Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea opop@postech.ac.kr;Statistical Research Center for Complex Systems, Seoul National University, Seoul, 151-742, Republic of Korea jongho@statcom.snu.ac.kr;Department of Statistics, Sookmyung Women's University, Seoul, 140-742, Republic of Korea eylee@sookmyung.ac.kr
Venue:
Queueing Systems: Theory and Applications
Year:
2001

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Abstract

We consider two queues with loss, one is the finite dam with Poisson arrivals and the other is the M/G/1 queue with impatient customers. We use the method of Kolmogorov's backward differential equation and construct a type of renewal equation to obtain the Laplace transform of busy(or wet) period in both queues. As a consequence, we provide the explicit forms of expected busy periods.