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Maintenance in single-server queues: a game-theoretic approach. (English) Zbl 1190.90048
Summary: We use antagonistic stochastic games and fluctuation analysis to examine a single-server queue with bulk input and secondary work during server’s multiple vacations. When the buffer contents become exhausted the server leaves the system to perform some diagnostic service of a minimum of $$L$$ jobs clustered in packets of random sizes (event A). The server is not supposed to stay longer than $$T$$ units of time (event B). The server returns to the system when A or B occurs, whichever comes first. On the other hand, he may not break service of a packet in a middle even if A or B occurs. Furthermore, the server waits for batches of customers to arrive if upon his return the queue is still empty. We obtain a compact and explicit form functional for the queueing process in equilibrium.

##### MSC:
 90B22 Queues and service in operations research 90B25 Reliability, availability, maintenance, inspection in operations research 91A80 Applications of game theory
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