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

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  • In this paper, we consider the balking behavior of customers in an M/G/1 queueing system with a removable server under N-policy, where the server may be turned off when no customers are present, and be turned on when the queue length reaches size $N$. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. For the unobservable and partially observable queues, we first analyze the stationary behavior of the system; then derive the equilibrium mixed strategies and compare them to the socially optimal strategies. We take the number $N$ as a decision variable and discuss the optimal operations policy in equilibrium states. Finally, we present two examples to demonstrate some of the phenomena in the considered models.
    Mathematics Subject Classification: Primary: 60K25; Secondary: 90B22.

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