Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-23T13:29:49.808Z Has data issue: false hasContentIssue false
  • English
  • Français

From FIFO to LIFO: a functional ordering of service delay via arrival discipline

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Jingwen Li
Jingwen Li*
Affiliation:
National University of Singapore
*
∗Postal address: Department of Decision Sciences, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260.
Get access Rights & Permissions [Opens in a new window]

Abstract

Vasicek (1977) proved that among all queueing disciplines that do not change the departure process of the queue, FIFO and LIFO yield, respectively, the smallest and the largest expectation of any given convex function of the service delay. In this note we further show that, if arriving customers join the queue stochastically ‘closer' to the server(s), then the expected value of any convex function of service delay is larger. As a more interesting result, we also show that if the function under consideration is concave, then the conclusion will be exactly the opposite. This result indicates that LIFO will be the best discipline if the delay cost is an increasing function but at a diminishing rate.

Keywords

FIFOLIFOARRIVAL DISCIPLINECONVEXITYCONCAVITYSTOCHASTIC ORDERING

MSC classification

Primary: 90B22: Queues and service
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 33 , Issue 2 , September 1996 , pp. 507 - 512
Copyright
Copyright © Applied Probability Trust 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

Fuhrmann, S. W. (1991) Second moment relationships for waiting times in queueing systems with Poisson input. Queueing Systems 8, 397–406.CrossRefGoogle Scholar
Heyman, D. P. and Stidham, S. Jr. (1980) The relation between customer and time average in queues. Operat. Res. 28, 983–994.CrossRefGoogle Scholar
Kingman, J. F. C. (1962) The effect of queue discipline on waiting time variance. Proc. Cambridge Phil. Soc. 58, 163–164.CrossRefGoogle Scholar
Larson, R. C. (1987) Perspectives on queues: social justice and the psychology of queueing. Operat. Res. 35, 895–905.Google Scholar
Özekici, S., Li, J. and Chou, F. S. (1994) Queues with impolite customers. Queueing Systems 15, 267–277.Google Scholar
Özekici, S., Li, J. and Chou, F. S. (1995) Waiting time in M/G/1 queues with impolite arrival disciplines. Prob. Eng. Inf. Sci. 9, 255–267.CrossRefGoogle Scholar
Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
Shanthikumar, J. G. and Sumita, U. (1987) Convex ordering of sojourn times in single-server queues: extremal properties of FIFO and LIFO service disciplines. J. Appl. Prob. 24, 734–748.CrossRefGoogle Scholar
Tambouratzis, D. G. (1968) On a property of the variance of the waiting time of a queue. J. Appl. Prob. 5, 702–703.CrossRefGoogle Scholar
Vasicek, O. A. (1977) An inequality for the variance of waiting time under a general queueing discipline. Operat. Res. 25, 879–844.Google Scholar
Whitt, W. (1984) The amount of overtaking in a network of queues. Networks 14, 411–426.CrossRefGoogle Scholar