Notes of M/G/1 system under the {\langle p, T \rangle} policy with second optional service |
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Authors: | Jau-Chuan Ke Yunn-Kuang Chu |
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Institution: | (1) Statistical Science & Operations Research, Southern Methodist University, Dallas, TX 75275-0332, USA |
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Abstract: | We optimize the operating cost of the ${\langle p, T \rangle}We optimize the operating cost of the áp, T ?{\langle p, T \rangle} policy for an M/G/1 queueing system with second optional service, where the customer may depart from the system either after
the first essential service with probability 1 − r or at the end of the first service may immediately go for a second service with probability r. Moreover, the server takes a vacation of fixed length T if the system becomes empty. If customers are found in the queue after T time units have elapsed since the end of the busy period, the server reactivates with probability p or leaves for a vacation of the same length T with probability 1 − p. Alternatively, if no customers present in the queue upon returning from the vacation, the server leaves for another a vacation
of the same length. We call this áp, T ?{\langle p, T \rangle} policy. The total expected cost function per unit time is developed to determine the optimal thresholds of p and T at a minimum cost. Based on the optimal cost the explicit form for joint optimum values of p and T are obtained. |
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