A FINITE-CAPACITY MULTISERVER MULTI-QUEUING PRIORITY MODEL WITH NONRENEWAL INPUT

We consider a non-preemptive head-of-the-line multi-server multi-queue ing priority model with finite buffer capacity for each priority class . As an 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. The model is de scribed by a homogeneous continuous-time Markov chain (CTMC). From the steady-state distribution of the CTMC, which is calculated by matrix- geometric methods, we derive the steady-state distributions immediatel y after arrival instants of the different priority classes. Applying m atrix-analytic methods, we calculate the Laplace-Stieltjes Transform ( LST) of the actual waiting times for the different priority classes.