An MMAP/G/1 queueing system with repeated calls and with absolute priority

Abstract

In this paper, a single-channel queueing system without an input buffer and with two types of requests is considered. At the input of the system, a marked Markov flow of requests arrives. Requests of the first type have absolute priority over requests of the second type; i.e., if a server is busy with servicing a request of the second type, an incoming request of the first type interrupts this servicing. Interrupted requests of the second type, as well as requests of this type that find the server busy on their arrival, become repeated requests and retry to get servicing later. An incoming first type request that finds the server busy with servicing a request of the same type is lost. The time of servicing requests has an arbitrary distribution dependent on the type of request. A nontrivial existence condition of the stationary operation of the system is obtained. A stationary probability distribution of system’s states at nested and random instants is found. Formulas for the main performance characteristics are obtained. The result of the numerical experiment is presented.