Mathematical Problems in Engineering
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 jobs clustered in packets of random sizes (event A). The server is not supposed to stay longer than 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.
Al-Matar, N., & Dshalalow, J. H. (2009). Maintenance in single server queues: A game theoretic approach, Mathematical Problems in Engineering, 2009.