Steady state analysis of a bulk queue with multiple vacations,setup times with N-policy and closedown times |
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Affiliation: | 1. Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore, Tamilnadu 641 004, India;2. Department of Mathematics, Amrita Institute of Technology, Coimbatore Tamilnadu 641 105, India |
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Abstract: | In this paper a MX/G (a, b)/1 queueing system with multiple vacations, setup time with N-policy and closedown times is considered. On completion of a service, if the queue length is ξ, where ξ < a, then the server performs closedown work. Following closedown the server leaves for multiple vacations of random length irrespective of queue length. When the server returns from a vacation and if the queue length is still less than ‘N’, he leaves for another vacation and so on, until he finds ‘N’ (N > b) customers in the queue. That is, if the server finds at least ‘N’ customers waiting for service, then he requires a setup time ‘R’ to start the service. After the setup he serves a batch of ‘b’ customers, where b ⩾ a. Various characteristics of the queueing system and a cost model with the numerical solution for a particular case of the model are presented. |
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