ANALYSIS OF MULTI-SERVER PRIORITY QUEUEING SYSTEM WITH SERVERS RESERVATION AND DISASTERS

A multi-server queueing system with an infinite buffer and two types of customers is considered. The flow of customers is described by two Markovian arrival processes (MAPs). Type-1 (or HPT) customers have the preemptive priority over type-2 (or LPT) customers. To avoid frequent interruption of service of LPT customers, reservation of a certain number of servers for HPT customers is assumed. LPT customers, who are not accepted for service upon arrival or service of which is interrupted, may decide to go to the buffer of an infinite capacity or abandon the system. An HPT customer who meets all servers busy by HPT customers is lost. The MAP flow of disasters arrives. An arrival of a disaster causes instantaneous departure of all customers from the buffer. The behavior of the system is described by the multi-dimensional continuous time Markov chain. The form of the generator of this chain is highlighted and the way for computation of the stationary distribution of this chain is outlined.