Analysis of a Queueing System with Mixed Service Discipline

In this paper, we analyse a queueing model with two types of requests arriving in a marked Markov arrival process. Type-1 requests require a constant service rate, while type-2 requests admit a flexible service rate. Mixed service discipline is considered. It is defined as follows. The number of type-1 requests that can be processed by the system simultaneously is restricted. Type-2 requests receive service according to the classical processor sharing discipline and use all currently available (not occupied by type-1 requests) system bandwidth. Type-2 requests can be impatient and leave the system without receiving complete service. The system behavior is described by a multidimensional Markov chain. The infinitesimal generator of this chain is derived. The transparent ergodicity condition is obtained, and the stationary performance measures of the system are computed. A numerical example is presented, including consideration of the problem of choosing the optimal values of the system bandwidth and its share dedicated to the service of type-1 requests.