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Analysis of the M x/G/1 queue by N-policy and multiple vacations

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Ho Woo Lee ,
Soon Seok Lee ,
Jeong Ok Park  and
K. C. Chae
Ho Woo Lee*
Affiliation:
Sung Kyun Kwan University
Soon Seok Lee*
Affiliation:
ETRI
Jeong Ok Park*
Affiliation:
Korea Telecom Research Center
K. C. Chae*
Affiliation:
KAIST
*
∗ Postal address: Department of Industrial Engineering, Sung Kyun Kwan University, Su Won, Korea 440–746.
∗∗ Postal address: Switching Methods Section, ETRI, Tae Jeon, Korea 305–606.
∗∗∗ Postal address: Telecommunication Network Research Lab., Korea Telecom Research Center, Seoul, Korea 137–792.
∗∗∗∗ Postal address: Department of Management Science, KAIST, Tae Jon, Korea 305–701.
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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.

Keywords

SYSTEM SIZEQUEUE WAITING TIMEOPTIMAL OPERATING POLICY

MSC classification

Primary: 60K25: Queueing theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 476 - 496
Copyright
Copyright © Applied Probability Trust 1994 

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References

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