Maintenance in Single-Server Queues: A Game-Theoretic Approach

We use antagonistic stochastic games and fluctuation analysis toexamine 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