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.
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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