Mathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging

In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed t...

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Bibliographic Details
Published in:Discrete and continuous models and applied computational science Vol. 30; no. 1; pp. 21 - 38
Main Authors: Bouchentouf, Amina Angelika, Medjahri, Latifa, Boualem, Mohamed, Kumar, Amit
Format: Journal Article
Language:English
Published: Peoples’ Friendship University of Russia (RUDN University) 01.04.2022
Subjects:
bernoulli feedback
impatient phenomena
markovian multi-server queue
probability generating function
server vacations
ISSN:2658-4670, 2658-7149
Online Access:Get full text
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Summary:In this paper, we analyze a multi-server queue with customers impatience and Bernoulli feedback under a variant of multiple vacations. On arrival, a customer decides whether to join or balk the system, based on the observation of the system size as well as the status of the servers. It is supposed that customer impatience can arise both during busy and vacation period because of the long wait already experienced in the system. The latter can be retained via certain mechanism used by the system. The feedback occurs as returning a part of serviced customers to get a new service. The queue under consideration can be used to model the processes of information transmission in telecommunication networks. We develop the Chapman-Kolmogorov equations for the steady-state probabilities and solve the differential equations by using the probability generating function method. In addition, we obtain explicit expressions of some important system characteristics. Different queueing indices are derived such as the probabilities when the servers are in different states, the mean number of customers served per unit of time, and the average rates of balking and reneging.
ISSN:2658-4670
2658-7149
DOI:10.22363/2658-4670-2022-30-1-21-38