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Analysis of the MX/G/1 Queue with N-Policy and Multiple Vacations

Ho Woo Lee, Soon Seok Lee, Jeong Ok Park and K. C. Chae
Journal of Applied Probability
Vol. 31, No. 2 (Jun., 1994), pp. 476-496
DOI: 10.2307/3215040
Stable URL: http://www.jstor.org/stable/3215040
Page Count: 21
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Analysis of the MX/G/1 Queue with N-Policy and Multiple Vacations
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Abstract

We consider an MX/G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary MX/G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.

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