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A study of \(M_1,M_2/G/1/K\) queueing system. (English) Zbl 1166.60058

This paper deals with a finite capacity single server queueing model, with two types of customers each arriving in a Poisson manner. The second type of customers may balk or renege, when either the server is on vacation or when the number of customers for each type exceeds their respective threshold levels. The system operates under \(N\)-policy and service times are assumed to have a common general distribution. For this model, using the supplementary variable method, difference-differential equations are set up for the distribution of the number of customers, from which steady state equations, that can be solved using recursive method, are derived.

MSC:

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