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Strong stability of queues with multiple vacation of the server. (English) Zbl 1139.60341
Summary: The main purpose of this article is to use the strong stability method to approximate the characteristics of the \(M/G/1//N\) queue with server vacation by those of the classical \(M/G/1//N\) queue, when the rate of the vacations is sufficiently small. This last queue is simpler and more exploitable in practice. For this, we proof the stability conditions and next obtain quantitative stability estimates with an exact computation of constants. From these theoretical results, we can develop an algorithm in order to check the conditions of approximation. These results of approximation have a great practical and economic interest in reliability systems and maintenance optimization policy, when we consider elements with constant failure rate.

MSC:
60K25 Queueing theory (aspects of probability theory)
60J25 Continuous-time Markov processes on general state spaces
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