Abstract
In this paper, we provide a matrix-analytic solution for randomized load balancing models (also known as supermarket models) with phase-type (PH) service times. Generalizing the service times to the phase-type distribution makes analysis of the supermarket models more difficult and challenging than that of the exponential service time case which has been extensively discussed in the literature. We describe the supermarket model as a system of differential vector equations, provide a doubly exponential solution to the fixed point of the system of differential vector equations, and analyze the exponential convergence of the current location of the supermarket model to its fixed point.
Chapter PDF
Similar content being viewed by others
References
Bramson, M., Lu, Y., Prabhakar, B.: Randomized load balancing with general service time distributions. In: Proceedings of the ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, pp. 275–286 (2010)
Dahlin, M.: Interpreting stale load information. IEEE Transactions on Parallel and Distributed Systems 11, 1033–1047 (1999)
Harchol-Balter, M., Downey, A.B.: Exploiting process lifetime distributions for dynamic load balancing. ACM Transactions on Computer Systems 15, 253–285 (1997)
Luczak, M., McDiarmid, C.: On the maximum queue length in the supermarket model. The Annals of Probability 34, 493–527 (2006)
Martin, J.B.: Point processes in fast Jackson networks. The Annals of Applied Probability 11, 650–663 (2001)
Martin, J.B., Suhov, Y.M.: Fast Jackson networks. The Annals of Applied Probability 9, 854–870 (1999)
Mitzenmacher, M.D.: The power of two choices in randomized load balancing. PhD thesis, University of California at Berkeley, Department of Computer Science, Berkeley, CA (1996)
Mitzenmacher, M.D.: Analyses of load stealing models using differential equations. In: Proceedings of the Tenth ACM Symposium on Parallel Algorithms and Architectures, pp. 212–221 (1998)
Mitzenmacher, M.D.: On the analysis of randomized load balancing schemes. Theory of Computing Systems 32, 361–386 (1999)
Mitzenmacher, M.D.: How useful is old information? IEEE Transactions on Parallel and Distributed Systems 11, 6–20 (2000)
Mitzenmacher, M.D., Richa, A., Sitaraman, R.: The power of two random choices: a survey of techniques and results. In: Pardalos, P., Rajasekaran, S., Rolim, J. (eds.) Handbook of Randomized Computing, vol. 1, pp. 255–312 (2001)
Suhov, Y.M., Vvedenskaya, N.D.: Fast Jackson Networks with Dynamic Routing. Problems of Information Transmission 38, 136–153 (2002)
Telek, M., Heindl, A.: Matching moments for acyclic discrete and continuous phase-type distributions of second order. International Journal of Simulation: Systems, Science & Technology 3, 47–57 (2002)
Vvedenskaya, N.D., Dobrushin, R.L., Karpelevich, F.I.: Queueing system with selection of the shortest of two queues: An asymptotic approach. Problems of Information Transmissions 32, 20–34 (1996)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 IFIP International Federation for Information Processing
About this chapter
Cite this chapter
Li, QL., Lui, J.C.S., Wang, Y. (2011). A Matrix-Analytic Solution for Randomized Load Balancing Models with PH Service Times. In: Hummel, K.A., Hlavacs, H., Gansterer, W. (eds) Performance Evaluation of Computer and Communication Systems. Milestones and Future Challenges. PERFORM 2010. Lecture Notes in Computer Science, vol 6821. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25575-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-25575-5_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-25574-8
Online ISBN: 978-3-642-25575-5
eBook Packages: Computer ScienceComputer Science (R0)