Open AccessMathematical analysis of a Markovian multi-server feedback queue with a variant of multiple vacations, balking and reneging
Author(s) -
Amina Angelika Bouchentouf,
Latifa Medjahri,
Mohamed Boualem,
Amit Kumar
Publication year - 2022
Publication title -
discrete and continuous models and applied computational science
Language(s) - English
Resource type - Journals
eISSN - 2658-7149
pISSN - 2658-4670
DOI - 10.22363/2658-4670-2022-30-1-21-38
Subject(s) - computer science , queue , server , markov process , queueing theory , bernoulli's principle , service (business) , retrial queue , probability generating function , function (biology) , real time computing , computer network , mathematical optimization , queueing system , mathematics , probability distribution , statistics , engineering , economy , evolutionary biology , economics , biology , aerospace engineering , moment generating function
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.