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Analysis of the Mx/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
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

[1] Burke, P. J. (1975) Delays in single-server queues with batch input. Operat. Res. 23, 830–833.CrossRefGoogle Scholar
[2] Doshi, B. T. (1986) Queueing systems with vacations: a survey. QUESTA 1, 29–66.Google Scholar
[3] Fuhmann, S. W. and Cooper, R. B. (1985) Stochastic decompositions in the M/G/1 queue with generalized vacations. Operat. Res. 33, 1117–1129.CrossRefGoogle Scholar
[4] Hofri, M. (1986) Queueing systems with a procrastinating server. Performance' 86 and ACMSIGMETRICS 1980. Perform. Eval. Rev. 14, 245–253.CrossRefGoogle Scholar
[5] Kella, O. (1989) The threshold policy in the M/G/1 queue with server vacations. Naval Res. Logis. 36, 111–123.3.0.CO;2-3>CrossRefGoogle Scholar
[6] Lee, H. S. and Srinivasan, M. M. (1989) Control policies for the Mx /G/1 queueing system. Management Sci. 35, 708–721.CrossRefGoogle Scholar
[7] Lee, H. S. (1991) Steady-state probabilities for the server vacation model with group arrivals and under control operation policy (in Korean). J. Korean OR/MS Soc 16, 36–48.Google Scholar
[8] Lee, H. W., Lee, S. S. and Chae, K. C. (1993) Operating characteristics of Mx /G/1 queue with N-policy. QUESTA. To appear.CrossRefGoogle Scholar
[9] Lee, S. S., Lee, H. W. and Chae, K. C. (1993) On a batch arrival queue with N-policy and single vacation. Research Report. Dept of Industrial Engineering, Sung Kyun Kwan University, Su Won, Korea.Google Scholar
[10] Lee, H. W. and Lee, S. S. (1993) Corrected distribution of idle period in M/G/1 queue with multiple vacations. Research Report, Dept. of Industrial Engineering, Sung Kyun Kwan University, Su Won, Korea.Google Scholar
[11] Levy, Y. and Yechiali, Y. (1975) Utilization of idle time in an M/G/1 queueing system. Management Sci. 22, 202–211.Google Scholar
[12] Takagi, H. (1991) Queueing Analysis: A Foundation of Performance Evaluation, Vol. 1, Vacation and Priority Systems, Part 1. North-Holland, Amsterdam.Google Scholar