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A discrete-time $$Geo/G/1$$ retrial queue with starting failures and second optional service. (English) Zbl 1172.90368
Summary: We consider a discrete-time $$Geo/G/1$$ retrial queue with starting failures in which all the arriving customers require a first essential service while only some of them ask for a second optional service. We study the Markov chain underlying the considered queueing system and its ergodicity condition. Explicit formulae for the stationary distribution and some performance measures of the system in steady state are obtained. We also obtain two stochastic decomposition laws regarding the probability generating function of the system size. Finally, some numerical examples are presented to illustrate the influence of the parameters on several performance characteristics.

MSC:
 90B22 Queues and service in operations research 60K25 Queueing theory (aspects of probability theory)
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References:
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