TY - JOUR

T1 - Tail asymptotics of the queue size distribution in the MMm retrial queue

AU - Kim, Jerim

AU - Kim, Jeongsim

AU - Kim, Bara

N1 - Funding Information:
The second author’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) ( 2009-0076674 ). The third author’s research was supported by the Korea Research Foundation (KRF) grant funded by the Korea government (MEST) ( 2009-0076600 ).

PY - 2012/8

Y1 - 2012/8

N2 - We consider an MMm 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.

AB - We consider an MMm 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.

KW - Censored Markov process

KW - Karamata Tauberian theorem

KW - MMm retrial queue

KW - Queue size distribution

KW - Riemann-Lebesgue lemma

KW - Tail asymptotics

UR - http://www.scopus.com/inward/record.url?scp=84860358195&partnerID=8YFLogxK

U2 - 10.1016/j.cam.2012.03.027

DO - 10.1016/j.cam.2012.03.027

M3 - Article

AN - SCOPUS:84860358195

VL - 236

SP - 3445

EP - 3460

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 14

ER -