Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T09:28:24.410Z Has data issue: false hasContentIssue false
  • English
  • Français

On the optimal allocation of service to impatient tasks

Part of: Computer system organization Operations research and management science

Published online by Cambridge University Press:  14 July 2016

K. D. Glazebrook ,
P. S. Ansell ,
R. T. Dunn  and
R. R. Lumley
K. D. Glazebrook*
Affiliation:
University of Edinburgh
P. S. Ansell*
Affiliation:
University of Newcastle upon Tyne
R. T. Dunn*
Affiliation:
University of Edinburgh
R. R. Lumley*
Affiliation:
University of Edinburgh
*
∗ Postal address: School of Management, University of Edinburgh, Edinburgh EH8 9JY, UK.
∗∗∗ Postal address: School of Mathematics and Statistics, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU, UK.
∗ Postal address: School of Management, University of Edinburgh, Edinburgh EH8 9JY, UK.
∗ Postal address: School of Management, University of Edinburgh, Edinburgh EH8 9JY, UK.
Get access Rights & Permissions [Opens in a new window]

Abstract

Service is often provided in contexts where tasks or customers are impatient or perishable in that they have natural lifetimes of availability for useful service. Moreover, these lifetimes are usually unknown to the service provider. The question of how service might best be allocated to the currently waiting tasks or customers in such a context has been neglected and we propose three simple models. For each model, an index heuristic is developed and is assessed numerically. In all cases studied the heuristic comes close to optimality.

Keywords

Dynamic programmingindex policyMarkov decision processmulticlass queuerestless bandit

MSC classification

Primary: 90B36: Scheduling theory, stochastic
Secondary: 68M20: Performance evaluation; queueing; scheduling
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 1 , March 2004 , pp. 51 - 72
Copyright
Copyright © Applied Probability Trust 2004 

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

Ansell, P. S., Glazebrook, K. D., Niño-Mora, J., and O'Keeffe, M. (2003). Whittle's index policy for a multi-class queueing system with convex holding costs. Math. Meth. Operat. Res. 57, 21–39.Google Scholar
Bertsimas, D. and Niño Mora, J. (1996). Conservation laws, extended polymatroids and multi-armed bandit problems: a polyhedral approach to indexable systems. Math. Operat. Res. 21, 257–306.CrossRefGoogle Scholar
Boots, N. K., and Tjims, H. (1999). A multi-server queueing system with impatient customers. Manag. Sci. 45, 444–448.Google Scholar
Brouns, G. A. and, J. F. van der Wal, J. (2003). Optimal threshold policies in a workload model with a variable number of service phases per job. To appear in Math. Meth. Operat. Res.Google Scholar
Doytchinov, B., Lehoczky, J., and Shreve, S. (2001). Real-time queues in heavy traffic with earliest-deadline-first queue discipline. Ann. Appl. Prob. 2, 332–378.Google Scholar
Gaver, D. P., and Jacobs, P. A. (2000). Servicing impatient tasks that have uncertain outcomes. Tech. Rep., Naval Postgraduate School, Monterey, CA.Google Scholar
Gittins, J. C. (1979). Bandit processes and dynamic allocation indices (with discussion). J. R. Statist. Soc. B 41, 148–177.Google Scholar
Gittins, J. C. (1989). Multi-armed Bandit Allocation Indices. John Wiley, New York.Google Scholar
Glazebrook, K. D. (1983). Stochastic scheduling with due dates. Internat. J. Systems Sci. 14, 1259–1271.Google Scholar
Glazebrook, K. D., Niño Mora, J., and Ansell, P. S. (2002). Index policies for a class of discounted restless bandits. Adv. Appl. Prob. 34, 754–774.Google Scholar
Jiang, Z., Lewis, T. G., and Colin, J.-Y. (1996). Scheduling hard real-time constrained periodic tasks on multiple processors. J. Systems Software 19, 102–118.Google Scholar
Johansen, S. G., and Larsen, C. (2001). Computation of a near-optimal service policy for a single-server queue with homogeneous jobs. Europ. J. Operat. Res. 134, 648–663.Google Scholar
Katehakis, M. N., and Veinott, A. F. (1987). The multi-armed bandit problem: decomposition and computation. Math. Operat. Res. 12, 262–268.Google Scholar
Krishnan, K. R. (1987). Joining the right queue: a Markov decision rule. In Proc. 28th IEEE Conf. Decision Control, pp. 1863–1868.CrossRefGoogle Scholar
Lehoczky, J. P. (1996). Real-time queueing theory. In Proc. 17th IEEE Real-Time Systems Symp., Washington, DC, pp. 186–195.Google Scholar
Lehoczky, J. P. (1997a). Real-time queueing network theory. In Proc. 18th IEEE Real-Time Systems Symp., San Francisco, CA, pp. 58–67.CrossRefGoogle Scholar
Lehoczky, J. P. (1997b). Using real-time queueing theory to control lateness in real-time systems. Performance Evaluation Rev. 25, 158–168.CrossRefGoogle Scholar
Liu, C. L., and Layland, J. W. (1973). Scheduling algorithms for multiprogramming in a hard real-time environment. J. Automatic Comput. Mach. 20, 40–61.Google Scholar
Niño-Mora, J. (2001). Restless bandits, partial conservation laws and indexability. Adv. Appl. Prob. 33, 76–98.CrossRefGoogle Scholar
Niño-Mora, J. (2002). Dynamic allocation indices for restless projects and queueing admission control: a polyhedral approach. Math. Prog. 93, 361–413.CrossRefGoogle Scholar
Puterman, M. L. (1994). Markov Decision Processes: Discrete Stochastic Dynamic Programming. John Wiley, New York.Google Scholar
Righter, R. (2000). Expulsion and scheduling control for multiclass queues with heterogeneous servers. Queueing Systems 34, 289–300.Google Scholar
Weber, R. R., and Weiss, G. (1990). On an index policy for restless bandits. J. Appl. Prob. 27, 637–648.Google Scholar
Weber, R. R., and Weiss, G. (1991). Addendum to ‘On an index policy for restless bandits’. Adv. Appl. Prob. 23, 429–430.Google Scholar
Whitt, W. (1999). Improving service by informing customers about anticipated delays. Manag. Sci. 45, 192–207.Google Scholar
Whittle, P. (1988). Restless bandits: activity allocation in a changing world. In A Celebration of Applied Probability (J. Appl. Prob. Spec. Vol. 25A), ed. Gani, J., Applied Probability Trust, Sheffield, pp. 287–298.Google Scholar
Xu, S. H. (1994). A duality approach to admission and scheduling control of queues. Queueing Systems 18, 273–300.Google Scholar
Xu, S. H., and Shanthikumar, J. G. (1993). Optimal expulsion control—a dual approach to admission control of an ordered-entry system. Operat. Res. 41, 1137–1152.Google Scholar