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

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Abstract

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.

About the authors

Amina Angelika Bouchentouf

Djillali Liabes University of Sidi Bel Abbes

Author for correspondence.
Email: bouchentouf_amina@yahoo.fr
ORCID iD: 0000-0001-8972-4221

Full Professor, Professor of Mathematics

22000, Algeria

Latifa Medjahri

University of Tlemcen

Email: l.medjahri@yahoo.fr

Faculty Member at Abou Bekr Belkaid University of Tlemcen

B.P. 119, 13000, Algeria

Mohamed Boualem

University of Bejaia

Email: robertt15dz@yahoo.fr
ORCID iD: 0000-0001-9414-714X

Full Professor, Professor of Applied Mathematics at the Department of Technology

06000, Algeria

Amit Kumar

Chandigarh University, Mohali (Punjab)

Email: amitk251@gmail.com
ORCID iD: 0000-0001-5347-1808

Assistant Professor at the Department of Mathematics

Pin No-140413, India

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