Retrial queueing model with time-phased batch arrivals

Abstract

A novel retrial multi-server queueing model with batch arrival of customers is considered. In contrast to the standard batch arrival when a whole batch arrives into the system at one epoch, we assume that the customers of a batch arrive one-by one in exponentially distributed times. Service time is exponentially distributed. Flow of batches is the stationary Poisson arrival process. Batch size distribution is geometric. The number of batches, which can be admitted into the system simultaneously, is subject of control. Analysis of the joint distribution of the number batches and customers in the system is implemented using the tool of the multi-dimensional asymptotically quasi-Toeplitz Markov chains.