Optimal balking strategies in an M/G/1 queueing system with a removable server under N-policy

Abstract

In this paper, we consider the balking behavior of customers in anM/G/1 queueing system with a removable server under N-policy, wherethe server may be turned off when no customers are present, and beturned on when the queue length reaches size $N$. Arriving customersdecide whether to join the system or balk, based on a linearreward-cost structure that incorporates their desire for service, aswell as their unwillingness for waiting. For the unobservable andpartially observable queues, we first analyze the stationarybehavior of the system; then derive the equilibrium mixed strategiesand compare them to the socially optimal strategies. We take thenumber $N$ as a decision variable and discuss the optimal operationspolicy in equilibrium states. Finally, we present two examples todemonstrate some of the phenomena in the considered models.

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