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TO BALANCE OR UNBALANCE LOAD IN SIZE-INTERVAL TASK ALLOCATION

Published online by Cambridge University Press:  18 March 2010

Mor Harchol-Balter  and
Rein Vesilo
Mor Harchol-Balter
Affiliation:
School of Computer Science, Carnegie Mellon University, Pittsburgh, PA E-mail: harchol@cs.cmu.edu
Rein Vesilo
Affiliation:
Department of Physics and Engineering, Macquarie UniversitySydney, Australia E-mail: rein@science.mq.edu.au
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Abstract

Server farms, consisting of a collection of hosts and a front-end router that dispatches incoming jobs to hosts, are now commonplace. It is well known that when job service requirements (job sizes) are highly variable, then the Size-Interval task assignment policy is an excellent rule for assigning jobs to hosts, since it provides isolation for short jobs by directing short jobs to one host's queue and long jobs to another host's queue. What is not understood is how to classify a “short” job versus a “long” job. For a long time it was believed that the size cutoff separating “short” jobs from “long” ones should be chosen to balance the load at the hosts in the server farm. However, recent literature has provided empirical evidence that load balancing is not always optimal for minimizing mean response time. This article provides the first analytical criteria for when it is preferable to unbalance load between two hosts using Size-Interval task assignment and in which direction the load should be unbalanced. Some very simple sufficient criteria are provided under which we prove that the short job host should be underloaded, and likewise for the long job host. These criteria are then used to prove that the direction of load imbalance depends on moment index properties related to the job size distribution. For example, under the Bounded Pareto (BP) job size distribution with parameter α and a sufficiently high upper bound (the BP is well known to be a good model of empirical computer system workloads), we show that α determines the direction of load imbalance. For α<1, the short job host should be underloaded; for α=1, load should be balanced; and for α>1, the long job host should be underloaded. Many other job size distributions are considered as well. We end by showing that load unbalancing can have a dramatic impact on performance, reducing mean response time by an order of magnitude compared to load balancing in many common cases.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 24 , Issue 2 , April 2010 , pp. 219 - 244
Copyright
Copyright © Cambridge University Press 2010

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References

1.Bachmat, E. & Sarfati, H. (2008). Analysis of size interval task assignment policies. In ACM SIGMETRICS Performance Evaluation Review. New York: ACM, pp. 107–109.Google Scholar
2.Bachmat, E. & Sarfati, H. (2010). Analysis of SITA policies. Performance Evaluation 67(1): 102–120.CrossRefGoogle Scholar
3.Cardellini, V., Colajanni, M. & Yu, P.S. (1999). Dynamic load balancing on web-server systems. IEEE Internet Computing 3(3): 28–39.CrossRefGoogle Scholar
4.Ciardo, G., Riska, A. & Smirni, E. (2001). EQUILOAD: A load balancing policy for clustered web servers. Performance Evaluation 46(2–3): 101–124.CrossRefGoogle Scholar
5.Crovella, M.E. & Bestavros, A. (1997). Self-similarity in World Wide Web traffic: Evidence and possible causes. IEEE/ACM Transactions on Networking 5(6): 835–846.CrossRefGoogle Scholar
6.Crovella, M., Harchol-Balter, M. & Murta, C. (1998). Task assignment in a distributed system: Improving performance by unbalancing load. In Proceedings of ACM Sigmetrics ’98 Conference on Measurement and Modeling of Computer Systems Poster Session, Madison, WI.Google Scholar
7.Crovella, M.E., Taqqu, M.S. & Bestavros, A. (1998). Heavy-tailed probability distributions in the world wide web. In Adler, R., Feldman, R. & Taqqu, M. (eds.) A Practical Guide to Heavy Tails. New York: Chapman & Hall, pp. 1–23.Google Scholar
8.Daley, D.J. (2001). The moment index of minima. Journal of Applied Probability 38A: 33–36.CrossRefGoogle Scholar
9.Embrechts, P., Kluppelberg, C. & Mikosch, T. (1997). Modelling extremal events. Berlin: Springer.CrossRefGoogle Scholar
10.Feng, H., Misra, V. & Rubenstein, D. (2005). Optimal state-free, size-aware dispatching for heterogeneous M/G/-type systems. Performance Evaluation 62: 475–492.CrossRefGoogle Scholar
11.Harchol-Balter, M. (2002). Task assignment with unknown duration. Journal of the ACM 49(2): 260–288.Google Scholar
12.Harchol-Balter, M., Crovella, M. & Murta, C. (1999). On choosing a task assignment policy for a distributed server system. Journal of Parallel and Distributed Computing 59(2): 204–228.CrossRefGoogle Scholar
13.Harchol-Balter, M. & Downey, A. (1997). Exploiting process lifetime distributions for dynamic load balancing. ACM Transactions on Computer Systems 15(3): 253–285.CrossRefGoogle Scholar
14.Harchol-Balter, M. & Vesilo, R.A. (2009). Limit properties of probability densities characterized by moment indexes. Carnegie Mellon University Computer Science Technical Report CMU-CS-09-118. Pittsburgh, PA: Carnegie Mellon University.Google Scholar
15.Hwang, S. & Jung, N. (2002). Dynamic scheduling of web server cluster. In Proceedings of the Ninth International Conference on Parallel and Distributed Systems (ICPADS’02), pp. 563–568.CrossRefGoogle Scholar
16.Paxson, V. & Floyd, S. (1995). Wide-area traffic: The failure of Poisson modeling. IEEE/ACM Transactions on Networking 3(3): 226–244.CrossRefGoogle Scholar
17.Riska, A., Smirni, E. & Ciardo, G. (2000). Analytic modelling of load balancing policies for tasks with heavy-tailed distributions. In Workshop on Software and Performance, pp. 147–157.CrossRefGoogle Scholar
18.Samorodnitsky, G. & Taqqu, M.S. (1994). Stable non-Gaussian random processes. New York: Chapman & Hall.Google Scholar
19.Schroeder, B. & Harchol-Balter, M. (2000). Evaluation of task assignment policies for supercomputer servers: The case for load unbalancing and fairness, In Proceedings of the 9th IEEE Symposium on High Performance Distributed Computing, pp. 211–220.CrossRefGoogle Scholar
20.Shin, K.G. & Hou, C.J. (1994). Design and evaluation of effective load sharing in distributed real-time systems. IEEE Transactions on Parallel and Distributed Systems 5(7): 704–719.CrossRefGoogle Scholar
21.Tari, Z., Broberg, J., Zomaya, A. & Baldoni, R. (2005). A least flow-time first load sharing approach for distributed server farm. Journal of Parallel and Distributed Computing 65(7): 832–842.CrossRefGoogle Scholar
22.Ungureanu, V., Bradford, P.G., Katehakis, M. & Melamed, B. (2006). Deferred assignment scheduling in clustered web servers. Cluster Computing 9(1): 57–65.CrossRefGoogle Scholar
23.Vesilo, R. (2008). Asymptotic analysis of load distribution for size-interval task allocation with bounded Pareto job sizes, In Proceedings of the 14th IEEE International Conference on Parallel and Distributed Systems (ICPADS’08), 8–10 December, Melbourne, Australia, pp. 129–137.Google Scholar
24.Zolotarev, V.M. (1986). One-dimensional stable distributions. Translations of Mathematical Monographs Volume 65. Providence, RI: American Mathematical Society.CrossRefGoogle Scholar