Comparisons of customer balking behavior in observable queues with N policies and geometric abandonments

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ABSTRACT This paper studies and compares customer balking behavior in some single-server observable queues with N policies and geometric abandonments. We focus on two types of N policies: the classic one and the modified one. Under the classic N policy, the server begins to take a vacation period as soon as the system becomes empty until there are N customers in the queue. On the other hand, under the modified N policy, the server takes multiple vacations until at least N customers are waiting in the queue when a vacation time ends. Abandonment opportunities occur during a whole vacation period, and customers decide independently and sequentially whether to renege. Comparing the two types of N policies, we realize that the residual time of the server's last vacation under the modified N policy indeed inhibits customers joining, whereas it may be more economic in practice if we take the whole system cost into consideration. As for the optimal N, under which the server is free of compensation, we observe that he should choose the modified N policy when the abandonment probability is much close to 1. Otherwise, he should choose the classic N policy.