Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-01-14T04:51:18.215Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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