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

Mohan L. Chaudhry, James J. Kim and Abhijit D. Banik

Journal of Probability and Statistics, 2019, vol. 2019, 1-18

Abstract:

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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljps:6480139

DOI: 10.1155/2019/6480139

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