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Heterogeneous finite-source retrial queues. (English) Zbl 1070.60078
The paper considers a system with \(K\) different sources of primary calls, each consisting of a single request. When source \(i\) is free at time \(t\) (i.e., is not being served and not waiting for serving), it may generate a primary call during interval \((t,t + dt)\) with probability \(\lambda _i dt + o(dt)\). If the server is idle at the time of its arrival, then the service starts. The service is finished during interval \((t,t + dt)\) with probability \(\mu _i dt + o(dt)\). During the service time the source cannot generate a new primary request. After service the source moves into a free state and can generate a new call. If the server is busy at the time of arrival of a request from the source \(i\), then the source starts generating a Poisson flow of repeated calls with rate \(\nu _i \) until if finds the server free. As before, after service the source becomes free and can generate a new primary call. The objective is to give the main usual performance measures of the system and to show the effect of different parameters on them. To achieve this goal a tool called MOSEL is used.

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