Notes of M/G/1 system under the $${\langle p, T \rangle}$$ policy with second optional service

Jau-Chuan Ke () and Yunn-Kuang Chu ()

Central European Journal of Operations Research, 2009, vol. 17, issue 4, 425-431

Abstract: We optimize the operating cost of the $${\langle p, T \rangle}$$ 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 $${\langle p, T \rangle}$$ 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. Copyright Springer-Verlag 2009

Keywords: Control; Cost; Optimization; Optional service (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s10100-009-0101-7

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