Moments of the queue size distribution in the MAP/G/1 retrial queue

Authors:
Jeongsim Kim;Bara Kim;Jerim Kim
Affiliations:
Department of Mathematics Education, Chungbuk National University, 12, Gaeshin-dong, Heungduk-ku, Cheongju, Chungbuk 361-763, Republic of Korea;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea;Department of Mathematics and Telecommunication Mathematics Research Center, Korea University, 1, Anam-dong, Sungbuk-ku, Seoul 136-701, Republic of Korea
Venue:
Computers and Operations Research
Year:
2010

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Abstract

We consider an MAP/G/1 retrial queue. A necessary and sufficient condition is obtained for the existence of the moments of the queue size distribution. The condition is expressed in terms of the moment condition for a service time distribution. In addition, we provide recursive formulas for the moments of the queue size distribution. Numerical examples are given to illustrate our results.