Analytically simple and computationally efficient results for the \(GI^X/ Geo /c\) queues (Q2175386)

Summary: A simple solution to determine the distributions of queue-lengths at different observation epochs for the model \(GI^X/ Geo /c\) is presented. In the past, various discrete-time queueing models, particularly the multiserver bulk-arrival queues, have been solved using complicated methods that lead to incomplete results. The purpose of this paper is to use the roots method to solve the model \(GI^X/ Geo /c\) that leads to a result that is analytically elegant and computationally efficient. This method works well even for the case when the inter-batch-arrival times follow heavy-tailed distributions. The roots of the underlying characteristic equation form the basis for all distributions of queue-lengths at different time epochs.