A queueing system with a batch Markovian arrival process and varying priorities

We consider herein a single-server queueing system with finite buffer and batch Markovian arrival process. Customers staying in the may have lower or higher priority. Immediately after each of customer is assigned lowest priority timer set for it, which defined as random variable distributed according to phase law having two absorbing states. After enters one states, leave forever (get lost) change its highest. When another state, lost some probability again an additional probability. If completely full system, it lost. Systems this type can serve mathematical models many real-life medical care systems, contact centers, perishable food storage etc. The operation described terms multidimensional Markov chain, stationary distribution number performance characteristics are calculated.