Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-27T07:23:08.959Z Has data issue: false hasContentIssue false
  • English
  • Français

ASYMPTOTIC PROPERTIES OF SOJOURN TIMES IN MULTICLASS TIME-SHARED SYSTEMS

Published online by Cambridge University Press:  19 March 2008

Arzad A. Kherani
Arzad A. Kherani
Affiliation:
General Motors India Science LabBangalore, India E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider two multiclass discriminatory process sharing (DPS)-like time-shared M/G/1 queuing systems in which the weight assigned to a customer is a function of its class as well as (1) the attained service of the customer in the first system and (2) the residual processing time of the customer in the second system. We study the asymptotic slowdown, the ratio of expected sojourn time to the service requirement, of customers with very large service requirements. We also provide various results dealing with ordering of conditional mean sojourn times of any two given classes. We also show that the sojourn time of an arbitrary customer of a particular class in the standard DPS system (static weights) with heavy-tailed service requirements has a tail behavior similar to that of a customer from the same class that starts a busy period.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 22 , Issue 2 , March 2008 , pp. 231 - 259
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.Avrachenkov, K., Ayesta, U., Brown, P., & Nunez-Queija, R. (2005). Discriminatory processor sharing revisited. In IEEE INFOCOM 2005.CrossRefGoogle Scholar
2.Bansal, N. & Harchol-Balter, M. (2001). Analysis of SRPT scheduling: Investigating unfairness. In Proceedings of ACM Sigmetrics 2001 Conference.CrossRefGoogle Scholar
3.Borst, S.C., Boxma, O.J., Nunez-Queija, R., & Zwart, A.P. (2003). The impact of the service discipline on delay asymptotics. Performance Evaluation 54: 175–206.CrossRefGoogle Scholar
4.Borst, S.C., van Ooteghem, D., & Zwart, B. (2005). Tail asymptotics for discriminatory processor sharing queues with heavy-tailed service sequirements. Performance Evaluation 61: 281–298.CrossRefGoogle Scholar
5.Fayolle, G., Mitrani, I., & Iasnogorodski, R. (1980). Sharing a processor among many job classes. Journal of the ACM 27: 519–532.CrossRefGoogle Scholar
6.Floyd, S. (2003). RFC 3649: HighSpeed TCP for large congestion windows. Internet Request for Comments, RFC 3649, Experimental. December 2003. Available at http://www.ietf.org/rfc.html.Google Scholar
7.Harchol-Balter, M., Schroeder, B., Bansal, N., & Agrawal, M. (2003). Size-based scheduling to improve Web performance. ACM Transactions Compon Systems 21: 207–233.CrossRefGoogle Scholar
8.Harchol-Balter, M., Sigman, K., & Wierman, A. (2002). Asymptotic convergence of scheduling policies with respect to slowdown. Performance Evaluation 49: 241–256.CrossRefGoogle Scholar
9.Kelly, T. (2003). Scalable TCP: Improving performance in highspeed wide area networks. Computer Communication Review 33: 83–91.CrossRefGoogle Scholar
10.Kherani, A.A. & Kumar, A. (2002). Stochastic models for throughput analysis of randomly arriving elastic flows in the internet. In IEEE Infocom 2002.Google Scholar
11.Kherani, A.A. & Nunez-Queija, R. (2006). TCP as an implementation of age-based scheduling: fairness and performance. In IEEE Infocom 2006.Google Scholar
12.Kleinrock, L. (1967). Time-shared systems: A theoretical treatment. Journal of the ACM 14: 242–261.CrossRefGoogle Scholar
13.Mandjes, M. & Zwart, B. (2006). Large deviations for sojourn times in processor sharing queues. Queueing Systems 52: 237–250.CrossRefGoogle Scholar
14.Padhy, S. & Kherani, A.A. (2006). Tail equivalence for some time-shared systems. In Proceedings of Valuetools 2006 Conference.CrossRefGoogle Scholar
15.Queija, R.N. (2002). Queues with equally heavy sojourn time and service requirement distributions. Annals of Operations Research 113: 101–117.CrossRefGoogle Scholar
16.Rai, I.A., Urvoy-Keller, G., Vernon, M., & Biersack, E.W. (2004). Performance analysis of LAS-based scheduling disciplines in a packet switched network. In Sigmetrics 2004.Google ScholarPubMed
17.Schrage, L.E. (1968). A proof of the optimality of the shortest remaining processing time discipline. Operations Research 16: 687–690.CrossRefGoogle Scholar
18.Wolff, R.W. (1989). Stochastic modeling and the theory of queues. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar