Document Type
Article
Publication Date
9-30-2022
Publication Title
Mathematics
Abstract
Queueing models have proven to be very useful in real-life applications to enable the practitioners to optimize the limited resources to conduct their businesses as well as offer services efficiently. In general, we can group such applications into two sectors: manufacturing and service. These two sectors cover everything we deal with on a day-to-day basis. Queues in which the services are offered in blocks (or groups or batches) are well established in the literature and have a wide variety of applications in practice. In this paper, we look at one such queueing model in which the arrivals occur according to a Markovian arrival process and the services are offered in batches of varying sizes from 1 to a finite pre-determined constant, say, b. The service times are assumed to be of phase type with representation depending on the size of the group. Thus, the distributions considered are heterogeneous from both the representation and rate points of view. The model can be studied as a G I/M/1-type queue or as a QBD-model. The model is analyzed in steady state by establishing results including on the rate matrix and the waiting time distribution and providing a number of illustrative examples.
Volume
10
Issue
3575
First Page
1
Last Page
30
DOI
10.3390/math10193575
ISSN
2227-7390
Rights
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).
Recommended Citation
Chakravarthy, Srinivas R., "Analysis of a Queueing Model with MAP Arrivals and Heterogeneous Phase-Type Group Services" (2022). Industrial & Manufacturing Engineering Publications. 133.
https://digitalcommons.kettering.edu/industrialmanuf_eng_facultypubs/133