Hostname: page-component-76fb5796d-2lccl Total loading time: 0 Render date: 2024-04-28T08:59:30.571Z Has data issue: false hasContentIssue false
  • English
  • Français

QUANTIFYING FAIRNESS IN QUEUING SYSTEMS

PRINCIPLES, APPROACHES, AND APPLICABILITY

Published online by Cambridge University Press:  25 September 2008

Benjamin Avi-Itzhak ,
Hanoch Levy  and
David Raz
Benjamin Avi-Itzhak
Affiliation:
RUTCOR, Rutgers University, New Brunswick, NJ, USA E-mail: aviitzha@rutcor.rutgers.edu
Hanoch Levy
Affiliation:
Computer Engineering and Networks Lab, ETH Zurich, Switzerland E-mail: hanoch@tik.ee.ethz.ch
David Raz
Affiliation:
Holon Institute of Technology, Holon, Israel E-mail: davidra@hit.ac.il
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article we discuss fairness in queues, view it in the context of social justice at large, and survey the recently published research work and publications dealing with the issue of measuring fairness of queues. The emphasis is placed on the underlying principles of the different measurement approaches, on reviewing their methodology, and on examining their applicability and intuitive appeal. Some quantitative results are also presented.

The article has three major parts (sections) and a short concluding discussion. In the first part we discuss fairness in queues and its importance in the broader context of the prevailing conception of social justice at large, and the distinction between fairness of the queue and fairness at large is illuminated. The second part is dedicated to explaining and discussing three main properties expected of a fairness measure: conformity to the general concept of social justice, granularity, and intuitive appeal and rationality. The third part reviews the fairness of the queue evaluating and measuring approaches proposed and studied in recent years. We describe the underlying principles of the different approaches, present some of their results, and review them in context of the three main properties expected from a measure. The short discussion that follows centers on future research issues.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 4 , October 2008 , pp. 495 - 517
Copyright
Copyright © Cambridge University Press 2008

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.Avi-Itzhak, B. & Levy, H. (2004). On measuring fairness in queues. Advances of Applied Probability 36(3): 919–936.Google Scholar
2.Avi-Itzhak, B., Levy, H. & Raz, D. (2005). Quantifying fairness in queueing systems: Principles, approaches and Applicability, Technical report RRR-25-2005, RUTCOR, Rutgers University, New Brunswick, NJ. Available from http://rutcor.rutgers.edu/pub/rrr/reports2005/25_2005.pdf.Google Scholar
3.Bansal, N. & Harchol-Balter, M. (2001). Analysis of SRPT scheduling: Investigating unfairness. In Proceedings of ACM Sigmetrics 2001 Conference on Measurement and Modeling of Computer Systems, pp. 279–290.Google Scholar
4.Bender, M., Chakrabarti, S. & Muthukrishnan, S. (1998). Flow and stretch metrics for scheduling continuous job streams. In Proceedings of the 9th Annual ACMSIAM Symposium on Discrete Algorithms, pp. 270–279.Google Scholar
5.Brosh, E., Levy, H. & Avi-Itzhak, B. (2005). The effect of service time variability on queue Fairness. Report RRR 24-2005, RUTCOR Technical, Rutgers University, New Brunswick, NJ.Google Scholar
6.Chan, M.F. & Tien, J.M. (1981). An alternative approach to police response. Wilmington Management of Demand Program, National Institute of Justice, Washington DC.Google Scholar
7.Gordon, E.S. (1987). New problems in queues: Social injustice and server production management, Ph. D. dissertation, MIT, Boston, MA.Google Scholar
8.Hassin, R. & Haviv, M. (2002). To queue or not to queue, equilibrium behavior in queueing systems. Boston: Kluwer Academic Publishers.Google Scholar
9.Kingman, J.F.C. (1962). The effect of queue discipline on waiting time variance, Proceedings of the Cambridge Philosophical Society, 58: 163–164.Google Scholar
10.Kleinrock, L. (1976). Queueing systems Vol II: Computer applications. New York: Wiley, 1976.Google Scholar
11.Larson, R.C. (1987). Perspective on queues: Social justice and the psychology of queueing, Operations Research 35(6): 895–905.Google Scholar
12.Mann, I. (1969). Queue culture: The waiting line as a social system, American Journal of Sociology 75: 340–354.Google Scholar
13.Markowitz, H.M. (1991). Portfolio selection, 2nd ed.Boston: Blackwell.Google Scholar
14.McEwen, J.T., Connors, E.F. & Cohen, M.I. (1984). Evaluation of the differential police response field test. Alexandria, VA: Research Management Associates, Inc.Google Scholar
15.Nussbaum, M. (2001). The enduring significance of John Rawls, the Chronicle of Higher Education. The Chronicle Review, July 20, 2001.Google Scholar
16.Palm, C. (1953). Methods of judging the annoyance caused by congestion, TELE 4: 189–108.Google Scholar
17.Piccard, D. (2005). Outline of an extended book review, Stanford Encyclopedia of Philosophy. Available from http://oak.cats.ohiou.edu/~piccard/entropy/rawls.html (accessed January 2005).Google Scholar
18.Pla, V., Casares-Giner, V. & Martinez, J. (2004). On a multiserver finite buffer queue with impatient customers. In Proceedings of 16th ITC Specialist Seminar on Performance Evaluation of Wireless and Mobile System.Google Scholar
19.Rafaeli, A., Barron, G. & Haber, K. (2002). The effects of queue structure on attitudes. Journal of Service Research 5(2): 125–139.Google Scholar
20.Rafaeli, A., Kedmi, E., Vashdi, D. & Barron, G. (2005). Queues and fairness: A multiple study investigation. Technical report, Technion—Israel Institute of Technology.Google Scholar
21.Rawls, J. (1971). A theory of justice. Cambridge, MA: Harvard University Press; revised edition published 1999.Google Scholar
22.Raz, D., Avi-Itzhak, B. & Levy, H. (2005). Fairness considerations of scheduling in multi-server and multi-queue systems, RUTCOR Technical report RRR-11-2005, Rutgers University, New Brunswick, NJ.CrossRefGoogle Scholar
23.Raz, D., Levy, H. & Avi-Itzhak, B. (2004). A resource-allocation queueing fairness measure. In Proceedings of Sigmetrics 2004; Performance Evaluation Review 32(1): 130–141.CrossRefGoogle Scholar
24.Avi-Itzhak, B., Levy, H. & Raz, D. (2004). A resource allocation queueing fairness measure: Propertius and bounds. Queueing Systems Theory and Application 56: 65–71.Google Scholar
25.Rothkopf, M.H. & Rech, P. (1987). Perspectives on queues: Combining queues is not always beneficial. Operations Research 35: 6.Google Scholar
26.Sandmann, W. (2005). A discrimination frequency based queueing fairness measure with regard to job seniority and service requirement. In Proceedings of the 1st Euro NGI Conference on Next Generation Internet Networks Traffic Engineering.Google Scholar
27.Zalta, E.N. (Ed.) (2005). Stanford Encyclopedia of Philosophy. Available from http://plato.stanford.edu/contents.html.Google Scholar
28.Whitt, W. (1984). The amount of overtaking in a network of queues. Networks 14(3): 411–426.Google Scholar
29.Wierman, A. & Harchol-Balter, M. (2003). Classifying scheduling policies with respect to unfairness in an M/GI/1. In Proceedings of the ACM Sigmetrics 2003 Conference on Measurement and Modeling of Computer Systems.Google Scholar