Abstract
Abstract We consider a non-preemptive head of the line multi-server priority model. As arrival process a generalized Markovian arrival process with marked transitions is used. The service-time distribution is of phase-type and identical for the different priority classes. Applying matrix-geometric methods we compute the time-stationary distribution of a single-class system which is derived from the priority system. Furthermore we compute the stationary distribution of the different priority classes immediately after arrival instants. Using first passage time analysis and Little's formula the mean actual waiting times and the mean queue lengths of the different priority classes are calculated.
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