Skip to main content Accessibility help
×
Home

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

  • Ho Woo Lee (a1), Soon Seok Lee (a2), Jeong Ok Park (a3) and K. C. Chae (a4)

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.

Copyright

Corresponding author

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.

References

Hide All
[1] Burke, P. J. (1975) Delays in single-server queues with batch input. Operat. Res. 23, 830833.
[2] Doshi, B. T. (1986) Queueing systems with vacations: a survey. QUESTA 1, 2966.
[3] Fuhmann, S. W. and Cooper, R. B. (1985) Stochastic decompositions in the M/G/1 queue with generalized vacations. Operat. Res. 33, 11171129.
[4] Hofri, M. (1986) Queueing systems with a procrastinating server. Performance' 86 and ACMSIGMETRICS 1980. Perform. Eval. Rev. 14, 245253.
[5] Kella, O. (1989) The threshold policy in the M/G/1 queue with server vacations. Naval Res. Logis. 36, 111123.
[6] Lee, H. S. and Srinivasan, M. M. (1989) Control policies for the Mx /G/1 queueing system. Management Sci. 35, 708721.
[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, 3648.
[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.
[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.
[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.
[11] Levy, Y. and Yechiali, Y. (1975) Utilization of idle time in an M/G/1 queueing system. Management Sci. 22, 202211.
[12] Takagi, H. (1991) Queueing Analysis: A Foundation of Performance Evaluation, Vol. 1, Vacation and Priority Systems, Part 1. North-Holland, Amsterdam.

Keywords

MSC classification

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

  • Ho Woo Lee (a1), Soon Seok Lee (a2), Jeong Ok Park (a3) and K. C. Chae (a4)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed