Abstract

In this research paper, we considered a transient behaviour of finite source retrial model with multiple vacations and orbital search in which the primary arrival rate λ which follows a Poisson distribution and the service time μ follows an exponential distribution. We have assumed that the finite calling population size being M. The vacation time follows an exponential distribution with parameter α. All transitions are assembled by using an infinitesimal generator matrix. Fundamental Matrix method is used to obtain the time dependent and steady state solutions. Numerical studies have been done for time dependent mean number of customers in the orbit, transient probabilities of server free/busy/vacation for various values of M, λ, μ, σ, α, p and t.

Author: J. Indhumathi, A. Muthu Ganapathi Subramanian, Gopal Sekar

Received on: January, 2022

Accepted on: August, 2024