Computational approach for transient behaviour of M/M (a, b)/1 bulk service queueing system with working vacation
Abstract
A new computational technique is used to evaluate the Transient behaviour of Single Server Bulk Service Queueing System with Working Vacation with arrival rate λ which follows a Poisson process and the service will be in bulk. In this model the server provides two types of services namely normal service and lower service. The normal service time follows an exponential distribution with parameter μ1. The lower service rate follows an exponential distribution with parameter μ2. The vacation time follows an exponential distribution with parameter α. According to Neuts, the server begins service only when a minimum of ‘a’ customers in the waiting room and a maximum service capacity is ‘b’. An infinitesimal generator matrix is formed for all transitions. Time dependent solutions and Steady state solutions are acquired by using Cayley Hamilton theorem. Numerical studies have been done for Time dependent average number of customers in the queue, Transient probabilities of server in vacation and server busy for several values of t, λ, µ1, μ2, α, a and b.
Copyright © 2020 S. Shanthi, A. Muthu Ganapathi Subramanian, A. Muthu Ganapathi Subramanian, Gopal Sekar, Gopal Sekar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. Shanthi, A. M. G. Subramanian, A. M. G. Subramanian, G. Sekar, G. Sekar, Computational approach for transient behaviour of M/M (a, b)/1 bulk service queueing system with working vacation, J. Math. Comput. Sci. 10 (2020), 2557–2578. https://doi.org/10.28919/jmcs/4940
BibTeX
@article{Shanthi2020,
author = {Shanthi, S. and Subramanian, A. Muthu Ganapathi and Subramanian, A. Muthu Ganapathi and Sekar, Gopal and Sekar, Gopal},
title = {Computational approach for transient behaviour of M/M (a, b)/1 bulk service queueing system with working vacation},
journal = {J. Math. Comput. Sci.},
volume = {10},
year = {2020},
pages = {2557--2578},
doi = {10.28919/jmcs/4940}
}