Hostname: page-component-848d4c4894-wg55d Total loading time: 0 Render date: 2024-05-02T08:33:45.977Z Has data issue: false hasContentIssue false
  • English
  • Français

Bicriterion Optimization of an M/G/1 Queue with A Removable Server

Published online by Cambridge University Press:  27 July 2009

Eugene A. Feinberg  and
Dong J. Kim
Eugene A. Feinberg
Affiliation:
W. A. Harriman School for Management and Policy, SUNY at Stony Brook, Stony Brook, New York 11794-3775
Dong J. Kim
Affiliation:
Department of Applied Mathematics and Statistics, SUNY at Stony Brook, Stony Brook, New York 11794-3600
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies bicriterion optimization of an M/G/1 queue with a server that can be switched on and off. One criterion is an average number of customers in the system, and another criterion is an average operating cost per unit time. Operating costs consist of switching and running costs. We describe the structure of Pareto optimal policies for a bicriterion problem and solve problems of optimization of one of these criteria under a constraint for another one.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 1 , January 1996 , pp. 57 - 73
Copyright
Copyright © Cambridge University Press 1996

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.Altman, E. & Nain, P. (1993). Optimal control of an M/G/1 queue with vacations. IEEE Transactions on Automatic Control 38: 1766–1775.CrossRefGoogle Scholar
2.Altman, E. & Shwartz, A. (1993). Time-sharing policies for controlled Markov chains. Operations Research 41: 1116–1124.CrossRefGoogle Scholar
3.Balachandran, K.R. (1973). Control policies for a single server system. Management Science 19: 1013–1018.CrossRefGoogle Scholar
4.Balachandran, K.R. & Tijms, H. (1975). On the D-policy for the M/G/1 queue. Management Science 21: 1073–1076.Google Scholar
5.Bell, C.E. (1971). Characterization and computation of optimal policies for operating an M/G/1 queueing system with removable server. Operations Research 19: 208–218.CrossRefGoogle Scholar
6.Boxma, O.J. (1976). Note on a control problem of Balachandran and Tijms. Management Science 22: 916–917.Google Scholar
7.Denardo, E.V., Feinberg, E.A., & Kella, O. (1995). Stochastic monotonicity for stationary recurrence times of first passage heights. Preprint.Google Scholar
8.Federgruen, A. & So, K.C. (1991). Optimality of threshold policies in singer-server queueing systems with server vacations. Advances in Applied Probability 23: 388–405.CrossRefGoogle Scholar
9.Feinberg, E.A. (1994). A generalization of ‘expectation equals reciprocal of intensity.’ Journal of Applied Probability 31: 262–267.Google Scholar
10.Feinberg, E.A. (1994). Constrained semi-Markov decision processes with average rewards. ZOR–Mathematical Methods of Operations Research 39: 257–288.Google Scholar
11.Feinberg, E.A. & Kim, D.J. (1994). Optimal switching policies for M/G/1 queues with two performance criteria. In Dengs, U., Bachem, A., & Drexi, A. (eds.), Operations research proceedings. Berlin: Springer-Verlag, pp. 227–232.Google Scholar
12.Feinberg, E.A. & Reiman, M.I. (1994). Optimality of randomized trunk reservation. Probability in the Engineering and Informational Sciences 8: 463–489.CrossRefGoogle Scholar
13.Heyman, D. (1968). Optimal operating policies for M/G/1 queueing systems. Operations Research 16: 362–383.CrossRefGoogle Scholar
14.Heyman, D. & Sobel, M. (1984). Stochastic models in operations research, Vol. 2. New York: McGraw-Hill.Google Scholar
15.Hofri, M. (1986). Queueing systems with a procrastinating server. In Performance '86 and A CM Sigmetrics 1986, Proceedings of the Joint Conference on Computer Performance Modeling, Measurement and Evaluation, Raleigh, NC, pp. 245–253, New York: Association for Computing Machinery.Google Scholar
16.Hordijk, A. & Spieksma, F. (1989). Constrained admission control to a queueing system. Advances in Applied Probability 21: 409–431.Google Scholar
17.Kella, O. (1989). The threshold policy in the M/G/1 queue with server vacations. Naval Research Logistics Quarterly 36: 111–123.3.0.CO;2-3>CrossRefGoogle Scholar
18.Lee, H.S. & Srinivasan, M.M. (1989). Control policies for the Mx/G/1 queueing system. Management Science 35: 708–721.CrossRefGoogle Scholar
19.Ma, D.-J. & Makowski, A.M. (1988). A class of steering policies under a recurrence condition. Proceedings of the 27th IEEE Conference on Decision and Control, pp. 1192–1197.Google Scholar
20.Makowski, A.M. & Shwartz, A. (1993). On constrained optimization of the Klimov network and related Markov decision processes. IEEE Transactions on Automatic Control 38: 354–359.Google Scholar
21.Nain, P. & Ross, K.W. (1986). Optimal priority assignment with hard constraint. IEEE Transactions on Automatic Control 36: 454–462.Google Scholar
22.Ross, K.W. (1989). Randomized and past-dependent policies for Markov decision processes with multiple constraints. Operations Research 37: 474–477.CrossRefGoogle Scholar
23.Sennott, L.I. (1993). Constrained average cost Markov decision chains. Probability in the Engineering and Informational Sciences 7: 69–83.CrossRefGoogle Scholar
24.Sobel, M. (1969). Optimal average cost policy for a queue with start-up and shut-down costs. Operations Research 17: 145–162.Google Scholar
25.Tijms, H. (1976). Optimal control of the workload in an M/G/1 queueing system with removable server. Math. Operalionsforsch. u. Statistik 7: 933–943.CrossRefGoogle Scholar
26.Yadin, M. & Naor, P. (1963). Queueing systems with a removable service station. Operational Research Quarterly 14: 393–405.CrossRefGoogle Scholar