Tail asymptotics of the queue size distribution in the M/M/m retrial queue

Authors:
Jerim Kim;Jeongsim Kim;Bara Kim
Affiliations:
Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, Republic of Korea;Department of Mathematics Education, Chungbuk National University, 52 Naesudong-ro, Heungdeok-gu, Cheongju, Chungbuk, 361-763, Republic of Korea;Department of Mathematics, Korea University, 145, Anam-ro, Seongbuk-gu, Seoul, 136-701, Republic of Korea
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

We consider an M/M/m retrial queue and investigate the tail asymptotics for the joint distribution of the queue size and the number of busy servers in the steady state. The stationary queue size distribution with the number of busy servers being fixed is asymptotically given by a geometric function multiplied by a power function. The decay rate of the geometric function is the offered load and independent of the number of busy servers, whereas the exponent of the power function depends on the number of busy servers. Numerical examples are presented to illustrate the result.