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Stability of $MAP/PH/c/K$ queue with customer retrials and server vacations

Yang Woo Shin
대한수학회 (The Korean Mathematical Society)|2016.07|대한수학회보 (Bulletin of the KMS)|제53권 제4호|pp. 985-1004

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참고문헌

키워드

retrial queuevacation queueMarkovian arrival process (MAP)PH-distributionpositive recurrent
주제분류수학

초록

We consider the $MAP/PH/c/K$ queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.

Abstract

We consider the $MAP/PH/c/K$ queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.

참고문헌 (24)

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