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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.

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