Hostname: page-component-cb9f654ff-rkzlw Total loading time: 0 Render date: 2025-08-21T14:37:14.025Z Has data issue: false hasContentIssue false
  • English
  • Français

Heavy Tails in Queueing Systems: Impact of Parallelism on Tail Performance

Part of: Computer system organization Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Bo Jiang ,
Jian Tan ,
Wei Wei ,
Ness Shroff  and
Don Towsley
Bo Jiang*
Affiliation:
University of Massachusetts
Jian Tan*
Affiliation:
The Ohio State University and IBM T. J. Watson Research
Wei Wei*
Affiliation:
University of Massachusetts
Ness Shroff*
Affiliation:
The Ohio State University
Don Towsley*
Affiliation:
University of Massachusetts
*
∗ Postal address: School of Computer Science, University of Massachusetts, 140 Governors Drive, Amherst, MA 01003, USA.
∗∗∗ Postal address: IBM T. J. Watson Research, Yorktown Heights, NY 10598, USA. Email address: tanji@us.ibm.com
∗ Postal address: School of Computer Science, University of Massachusetts, 140 Governors Drive, Amherst, MA 01003, USA.
∗∗∗∗∗ Postal address: Department of Electrical Engineering, The Ohio State University, 2015 Neil Avenue, Columbus, OH 43210, USA. Email address: shroff@ece.osu.edu
∗ Postal address: School of Computer Science, University of Massachusetts, 140 Governors Drive, Amherst, MA 01003, USA.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we quantify the efficiency of parallelism in systems that are prone to failures and exhibit power law processing delays. We characterize the performance of two prototype schemes of parallelism, redundant and split, in terms of both the power law exponent and exact asymptotics of the delay distribution tail. We also develop the optimal splitting scheme which ensures that split always outperforms redundant.

Keywords

Multipathpower lawparallelism

MSC classification

Primary: 68M20: Performance evaluation; queueing; scheduling
Secondary: 60G99: None of the above, but in this section

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 127 - 150
Copyright
Copyright © Applied Probability Trust 2013 

References

Andersen, L. N. and Asmussen, S. (2008). Parallel computing, failure recovery, and extreme values. J. Statist. Theory Appl. 2, 279–292.Google Scholar
Asmussen, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.Google Scholar
Asmussen, S. et al. (2008). Asymptotic behavior of total times for Jobs that must start over if a failure occurs. Math. Operat. Res. 33, 932–944.Google Scholar
Bingham, N. H., Goldie, C. M. and Teugels, J. L. (1987). Regular Variation (Encyclopedia Math. Appl. 27). Cambridge University Press.CrossRefGoogle Scholar
Cantor, D. G. and Gerla, M. (1974). Optimal routing in a packet-switched computer network. IEEE Trans. Comput. 23, 1062–1069.Google Scholar
Gallager, R. G. (1977). A minimum delay routing algorithm using distributed computation. IEEE Trans. Commun. 25, 73–85.Google Scholar
Hoekstra, G., Mei, R., Nazarathy, Y. and Zwart, B. (2009). Optimal file splitting for wireless networks with concurrent access. In NET-COOP '09: Proc. 3rd Euro-NF Conf. on Network Control and Optimization (Lecture Notes Comput. Sci. 5894), Springer, Berlin, pp. 189–203.Google Scholar
Jelenković, P. and Momčilović, P. (2003). Large deviation analysis of subexponential waiting times in a processor-sharing queue. Math. Operat. Res. 28, 587–608.Google Scholar
Jelenković, P. R. and Tan, J. (2007). Is ALOHA causing power law delays? In Proc. 20th Internat. Teletraffic Congress (Lecture Notes Comput. Sci. 4516), Springer, Berlin, pp. 1149–1160.Google Scholar
Jelenković, P. R. and Tan, J. (2007). Can retransmissions of superexponential documents cause subexponential delays? In Proc. IEEE INFOCOM '07, pp. 892–900.Google Scholar
Jelenković, P. R. and Tan, J. (2007). Characterizing heavy-tailed distributions induced by retransmissions. Tech. Rep. EE2007-09-07, Department of Electrical Engineering, Columbia University. Available at http://arxiv.org/abs/0709.1138v2.Google Scholar
Kleinrock, L. (1964). Communication Nets: Stocastic Message Flow and Delay. McGraw-Hill, New York.Google Scholar
Nagaev, S. V. (1979). Large deviations of sums of independent random variables. Ann. Prob. 7, 745–789.Google Scholar
Sheahan, R., Lipsky, L., Fiorini, P. and Asmussen, S. (2006). On the completion time distribution for tasks that must restart from the beginning if a failure occurs. In ACM SIGMETRICS Performance Evaluation Review, Association for Computing Machinery, New York, pp. 24–26.Google Scholar
Tan, J. and Shroff, N. (2010). Transition from heavy to light tails in retransmission durations. In Proc. INFOCOM '10 (San Diego, California), IEEE Press, Piscataway, NJ, pp. 1334–1342.Google Scholar
Tan, J., Yang, Y., Shroff, N. B. and Gamal, H. E. (2011). Delay asymptotics with retransmissions and fixed rate codes over erasure channels. In Proc. INFOCOM '11, IEEE Press, Piscataway, NJ, pp. 1260–1268.Google Scholar