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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.

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