Abstract
In many real-world systems incoming tasks split into subtasks which are processed by a set of parallel servers. In such systems two metrics are of potential interest: response time and subtask dispersion. Previous research has been focused on the minimisation of one, but not both, of these metrics. In particular, in our previous work, we showed how the processing of selected subtasks can be delayed in order to minimise expected subtask dispersion and percentiles of subtask dispersion in the context of split-merge systems. However, the introduction of subtask delays obviously impacts adversely on task response time and maximum sustainable system throughput. In the present work, we describe a methodology for managing the trade off between subtask dispersion and task response time. The objective function of the minimisation is based on the product of expected subtask dispersion and expected task response time. Compared with our previous methodology, we show how our new technique can achieve comparable subtask dispersion with substantial improvements in expected task response time.
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References
Armijo, L.: Minimization of functions having Lipschitz continuous first partial derivatives. Pacific Journal of Mathematics 16(1), 1–3 (1966)
Baccelli, F., Makowski, A.M., Shwartz, A.: The fork-join queue and related systems with synchronization constraints: Stochastic ordering and computable bounds. Advances in Applied Probability 21(3), 629–660 (1989)
Baccelli, F., Massey, W.A., Towsley, D.: Acyclic fork-join queuing networks. J. ACM 36(3), 615–642 (1989)
David, H.A., Nagaraja, H.N.: The non-IID case. In: Order Statistics, 3rd edn., ch. 5, pp. 95–120. J. Wiley & Sons, Inc. (2003)
David, H.A., Nagaraja, H.N.: Order Statistics, 3rd edn. Wiley Series in Probability and Mathematical Statistics. John Wiley (2003)
Flatto, L., Hahn, S.: Two parallel queues created by arrivals with two demands I. SIAM Journal on Applied Mathematics 44(5), 1041–1053 (1984)
Flatto, L.: Two parallel queues created by arrivals with two demands ii. SIAM Journal on Applied Mathematics 45(5), 861–878 (1985)
Gandhi, A., Gupta, V., Harchol-Balter, M., Kozuch, M.A.: Optimality analysis of energy-performance trade-off for server farm management. Performance Evaluation 67(11), 1155–1171 (2010)
Harrison, P.G., Zertal, S.: Queueing models of RAID systems with maxima of waiting times. Perf. Evaluation 64(7-8), 664–689 (2007)
Heidelberger, P., Trivedi, K.S.: Analytic queueing models for programs with internal concurrency. IEEE Transactions on Computers C-32(1), 73–82 (1983)
Kim, C., Agrawala, A.K.: Analysis of the fork-join queue. IEEE Transactions on Computers 38(2), 250–255 (1989)
Knottenbelt, W.J., Tsimashenka, I., Harrison, P.G.: Reducing subtask dispersion in parallel systems. In: Trends in Parallel, Distributed, Grid and Cloud Computing for Engineering. Saxe-Coburg Publications (2013)
Lebrecht, A., Knottenbelt, W.J.: Response Time Approximations in Fork-Join Queues. In: 23rd Annual UK Performance Engineering Workshop, UKPEW (July 2007)
Lui, J.C.S., Muntz, R.R., Towsley, D.: Computing performance bounds of fork-join parallel programs under a multiprocessing environment. IEEE Transactions on Parallel and Distributed Systems 9(3), 295–311 (1998)
Timothy Marler, R., Arora, J.S.: Survey of multi-objective optimization methods for engineering. Structural and Multidisciplinary Optimization 26(6), 369–395 (2004)
Nelson, R., Tantawi, A.N.: Approximate analysis of fork/join synchronization in parallel queues. IEEE Transactions on Computers 37(6), 739–743 (1988)
Nocedal, J., Wright, S.J.: Numerical optimization. Springer (1999)
Towsley, D., Rommel, C.G., Stankovic, J.A.: Analysis of fork-join program response times on multiprocessors. IEEE Transactions on Parallel and Distributed Systems 1(3), 286–303 (1990)
Tsimashenka, I., Knottenbelt, W.J.: Reduction of Variability in Split-Merge Systems. In: Imperial College Computing Student Workshop (ICCSW 2011), pp. 101–107 (2011)
Tsimashenka, I., Knottenbelt, W.J., Harrison, P.: Controlling variability in split-merge systems. In: Al-Begain, K., Fiems, D., Vincent, J.-M. (eds.) ASMTA 2012. LNCS, vol. 7314, pp. 165–177. Springer, Heidelberg (2012)
Varki, E.: Response time analysis of parallel computer and storage systems. IEEE Transactions on Parallel and Distributed Systems 12(11), 1146–1161 (2001)
Varma, S., Makowski, A.M.: Interpolation approximations for symmetric fork-join queues. Performance Evaluation 20(13), 245–265 (1994)
Wolfe, P.: Convergence conditions for ascent methods. SIAM Review 11(2), 226–235 (1969)
Wolfe, P.: Convergence conditions for ascent methods. II: Some corrections. SIAM Review 13(2), 185–188 (1971)
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Tsimashenka, I., Knottenbelt, W.J. (2013). Trading Off Subtask Dispersion and Response Time in Split-Merge Systems. In: Dudin, A., De Turck, K. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2013. Lecture Notes in Computer Science, vol 7984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39408-9_30
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DOI: https://doi.org/10.1007/978-3-642-39408-9_30
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