Analytically Simple and Computationally Efficient Results for the GIX/Geo/c Queues

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.

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