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In this paper, the authors 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 the 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. The first describe the supermarket model as a system of differential vector equations, and provide a doubly exponential solution to the fixed point of the system of differential vector equations.
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