A matrix-analytic solution for randomized load balancing models with PH service times

Authors:
Quan-Lin Li;John C. S. Lui;Yang Wang
Affiliations:
School of Economics and Management Sciences, Yanshan University, China;Department of Computer Science & Engineering, The Chinese University of Hong Kong, China;Department of Computer Science and Technology, Peking University, China
Venue:
PERFORM'10 Proceedings of the 2010 IFIP WG 6.3/7.3 international conference on Performance Evaluation of Computer and Communication Systems: milestones and future challenges
Year:
2010

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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.