Multiserver systems with rejections and the equiprobable distribution of customers

Abstract

The queueing systems with rejections, arbitrary service time distributions, and two ways of the distributions of customers over heterogeneous servers (the equiprobable customer distribution over all (idle and busy) servers and the equiprobable customer distribution over idle servers) are discussed and used to find the stationary distributions of the number of customers. Their invariance with respect to service time distribution functions is proved. For an MX/M/n/0 system with homogeneous servers and the equiprobable customer distribution over all servers, the algorithm is proposed for determining the stationary distributions of the number of customers when their number in the batch is less than six. MX/M/2/0 and MX/M/3/0 systems with the equiprobable customer distribution over all servers and the arbitrary distribution of the number of arriving customers are studied. The results are checked using simulation models based on GPSS World software.