Transient Solution of Machine Interference Problem with an Unreliable Server under Multiple Vacations Policy

Abstract

Consider the machine interference problem with an unreliable server under multiple vacations. There are M similar machines that are subject to breakdowns with a single server who is responsible for repairing the failed machines. Each machine fails completely at random with rate λ. When a machine fails, it is immediately sent to the service centre where it is attended to in order of breakdowns with a state dependent service rate. State dependent service rate is a situation where the rate of service depends on the number of customers present in the system. The machines operate independently but are subject to breakdowns. The service time distributions of the failed machines are assumed to be exponentially distributed with state dependent service rate µn. Where n is the number of failed machines. The Chapman-Kolmogorov differential equations obtained for the multiple vacations model is solved through ODE45 (Runge-Kutta algorithm of order 4 and 5) in MATLAB programming language. The transient probabilities obtained are used to compute the operational measures of performance for the systems. In the multiple vacations model the server will continue to take vacations until there is one failed machine in the system. The effects of λ, µ, α, β and θ on the machine availability under different values of t for the multiple vacations is investigate; it is observe that the machine availability decreases with increase in time t. The CPU time for obtaining the transient results for the systems and the variance of the systems are reported in this work.