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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Kim, Jerim¹  Kim, Jeongsim²  Kim, Bara¹ 

[1] Korea Univ, Dept Math, Seoul 136701, South Korea

[2] Chungbuk Natl Univ, Dept Math Educ, Cheongju 361763, Chungbuk, South Korea

关键词: M/M/m retrial queue;    Queue size distribution;    Censored Markov process;    Tail asymptotics;    Karamata Tauberian theorem;    Riemann-Lebesgue lemma;   

DOI  :  10.1016/j.cam.2012.03.027

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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