A queueing system with Markov arrival process, several customer types, generalized foreground-background processor sharing discipline with minimal served length, and an in♀nite bu♂er for all types of customers is studied. The joint stationary distribution of the number of customers of all types and the stationary distribution of time of sojourn of customers of every type are determined in terms of generating functions and Laplace{Stieltjes transforms.

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