Q.L. Li and J.C.S. Lui (2010). Doubly exponential solution for randomized load balancing models with Markovian arrival processes and PH service times. arXiv:1009.4970, Pages 1–39.

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In this paper, we provide a novel matrix-analytic approach for studying doubly exponential solutions of randomized load balancing models (also known as supermarket models) with Markovian arrival processes (MAPs) and phase-type (PH) service times. We describe the supermarket model as a system of differential vector equations by means of density dependent jump Markov processes, and obtain a closed-form solution with a doubly exponential structure to the fixed point of the system of differentia

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Q.L. Li and J.C.S. Lui (2010). Doubly exponential solution for randomized load balancing models with Markovian arrival processes and PH service times. arXiv:1009.4970, Pages 1–39