Saturday, 14 August 2021

A Computational Approach for Evaluating the Transient Behaviour of M/M (a, b)/1 Bulk Service Queueing System with Working Vacation | Chapter 4| Current Topics on Mathematics and Computer Science Vol. 6

 The transient behaviour of a single server bulk service queuing system with working vacation is evaluated using a new computational technique with an arrival rate that follows a Poisson process and a bulk service. The server under this approach offers two sorts of services: normal service and lower service. The normal service time follows a one-parameter exponential distribution. The reduced service rate follows a two-parameter exponential distribution. The vacation time is distributed exponentially with parameter. According to Neuts, the server only starts serving consumers when there are at least ‘a' customers in the queue. The letter ‘b' stands for a waiting room and a maximum service capacity. For each transition, an infinitesimal generator matrix is created. The Cayley Hamilton theorem is used to find time dependent and steady state solutions. For various values of t, 1, 2, a, and b, numerical studies have been conducted for time dependent average number of customers in the queue, transient probability of server in vacation, and server busy. We've included a transient probability distribution of the number of consumers in the line at time t, as well as time-dependent system measures in this model.

Author (S) Details

Mrs. S. Shanthi
Department of Mathematics, Kanchi Mamunivar Government Institute for Post Graduate Studies and Research, Pondicherry, India.

Dr. A. Muthu Ganapathi Subramanian
Department of Mathematics, Kanchi Mamunivar Government Institute for Post Graduate Studies and Research, Pondicherry, India.

Dr. Gopal Sekar
Department of Mathematics, Kanchi Mamunivar Government Institute for Post Graduate Studies and Research, Pondicherry, India.

View Book :- https://stm.bookpi.org/CTMCS-V6/article/view/2584

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