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In this paper, we provide a matrix-analytic solution for randomized loadbalancing models (also known as \emph{supermarket models}) with phase-type (PH)service times. Generalizing the service times to the phase-type distributionmakes the analysis of the supermarket models more difficult and challengingthan that of the exponential service time case which has been extensivelydiscussed in the literature. We first describe the supermarket model as asystem of differential vector equations, and provide a doubly exponentialsolution to the fixed point of the system of differential vector equations.Then we analyze the exponential convergence of the current location of thesupermarket model to its fixed point. Finally, we present numerical examples toillustrate our approach and show its effectiveness in analyzing the randomizedload balancing schemes with non-exponential service requirements.

A Matrix-Analytic Solution for Randomized Load Balancing Models with Phase-Type Service Times