Optimal control of a removable server in an M/G/1 queue with finite capacity |
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Affiliation: | 1. Department of Chemical and Materials Engineering, Tamkang University, Tamsui, New Taipei City 25137, Taiwan;2. Energy and Opto-Electronic Materials Research Center, Tamkang University, Tamsui, New Taipei City 25137, Taiwan;3. Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan |
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Abstract: | We consider an M/G/1 system with finite capacity L in which the removable server applies a (ν, N) policy; a classical cost structure is imposed and the total expected cost per unit time in the steady state is considered. For the M/M/1 situation, Hersh and Brosh [3] analysed the policies with 0⩾ν<N⩽L and established that the best of them is characterized either by ν = 0 or by N = L. By a different and quite easy way and for a general service time distribution, we prove that an optimal policy has the form (ν = 0, 0 ⩽ N ⩽ L + 1), where the (0, 0) and (0, L + 1) policies consist in never closing or never opening the station respectively. Moreover, we describe a precise technique to analyse the policy space and to determine easily the optimal policy. |
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