Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-05T16:39:09.236Z Has data issue: false hasContentIssue false
  • English
  • Français

Three management policies for a resource with partition constraints

Part of: Stochastic systems and control Operations research and management science Special processes Computer system organization

Published online by Cambridge University Press:  01 July 2016

Murat Alanyali
Murat Alanyali*
Affiliation:
Bilkent University
*
∗ Postal address: Department of Electrical and Electronic Engineering, Bilkent University, Bilkent TR-06533, Ankara, Turkey. Email address: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Management of a bufferless resource is considered under non-homogeneous demand consisting of one-unit and two-unit requests. Two-unit requests can be served only by a given partition of the resource. Three simple admission policies are evaluated with regard to revenue generation. One policy involves no admission control and two policies involve trunk reservation. A limiting regime in which demand and capacity increase in proportion is considered. It is shown that each policy is asymptotically optimal for a certain range of parameters. Limiting dynamical behavior is obtained via a theory developed by Hunt and Kurtz. The results also point out the remarkable effect of partition constraints.

Keywords

Resource managementpartition constraintsloss networksmultirate networksadmission controltrunk reservationheavy traffictime-scale separation

MSC classification

Primary: 60K30: Applications (congestion, allocation, storage, traffic, etc.)
Secondary: 90B22: Queues and service 68M20: Performance evaluation; queueing; scheduling 93E20: Optimal stochastic control
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 31 , Issue 3 , September 1999 , pp. 795 - 818
Copyright
Copyright © Applied Probability Trust 1999 

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.)

Footnotes

This work was supported in part by the US National Science Foundation under contract NSF NCR 93-14253.

References

Alanyali, M. and Hajek, B. (1997). Analysis of simple algorithms for dynamic load balancing. Math. Operat. Res. 22, 840–871.Google Scholar
Asmussen, S. (1987). Applied Probability and Queues. Wiley, Chichester.Google Scholar
Bean, N. G., Gibbens, R. J. and Zachary, S. (1995). Asymptotic analysis of single resource loss systems in heavy traffic, with applications to integrated networks. Adv. Appl. Prob. 27, 273–292.CrossRefGoogle Scholar
Bean, N. G., Gibbens, R. J. and Zachary, S. (1997). Dynamic and equilibrium behaviour of controlled loss networks. Ann. Appl. Prob. 7, 873–885.Google Scholar
Ethier, S. N. and Kurtz, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York.CrossRefGoogle Scholar
Fayolle, G., Malyshev, V. A. and Menshikov, M. V. (1995). Topics in the Constructive Theory of Countable Markov Chains. Cambridge University Press, Cambridge.Google Scholar
Hunt, P. J. (1995). Pathological behaviour in loss networks. J. Appl. Prob. 32, 519–533.CrossRefGoogle Scholar
Hunt, P. J. and Kurtz, T. G. (1994). Large loss networks. Stoch. Proc. Appl. 53, 363–378.Google Scholar
Hunt, P. J. and Laws, C. N. (1997). Optimization via trunk reservation in single resource loss systems under heavy traffic. Ann. Appl. Prob. 7, 1058–1079.CrossRefGoogle Scholar
Kelly, F. P. (1986). Blocking probabilities in large circuit switched networks. Adv. Appl. Prob. 18, 473–505.CrossRefGoogle Scholar
Miller, B. (1969). A queueing reward system with several customer classes. Management Sci. 16, 234–245.CrossRefGoogle Scholar
Ramaswami, V. and Rao, K. A. (1985). Flexible time-slot assignment: a performance study for the integrated services digital network. Proc. ITC-11. Elsevier, New York, 2:2.1A-3-1–2.1A.3.7.Google Scholar
Reiman, M. I. and Schmitt, J. A. (1994). Performance models of multirate traffic in various network implementations. In Proc. ITC-14. Elsevier, New York, pp. 1217–1228.Google Scholar
Ross, K. W. and Tsang, D. H. K. (1989). Optimal circuit access policies in an ISDN environment: a Markov decision approach. IEEE Trans. Commun. 37, 934–939.CrossRefGoogle Scholar
Royden, H. L. (1988). Real Analysis. Macmillan, New York.Google Scholar
Zachary, S. (1995). On two-dimensional Markov chains in the positive quadrant with partial spatial homogeneity. Markov Proc. Rel. Fields. 1, 267–280.Google Scholar