Analysis of Retrial Queuing System with Limited Processor Sharing Discipline and Changing Effective Bandwidth

In this paper, a queueing system with a flexible limited processor sharing discipline according to which a limited number of requests can receive service simultaneously is considered. Each request has the required service rate and when the number of requests in service is such that the bandwidth of the server is sufficient for providing this rate for all requests, the requests receive this service rate. We suggest that the requests on service can disturb (interfere) each other and the effective bandwidth of the server decreases with increase of the number of servicing requests. In the situation when the effective bandwidth is not enough, all requests receive service at a proportionally reduced rate. The arrival flow is defined by a Markovian arrival process. A request, which cannot enter the service immediately upon arrival due to a limitation on the number of requests that can receive service simultaneously, will make retrials according to the classical retrial strategy. The process of the system states is defined as the level-dependent multidimensional Markov process. The infinitesimal generator of this process is derived. The main performance measures of the system are obtained. Numerical illustrations are presented. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.