Machine Interference Problem with Reliable Server under Multiple Vacations Policy

Abstract

The machine interference problem with reliable server under multiple vacations policy is considered. There are M similar machines that are subject to breaks down with a single server who is responsible for repairing the failed machines under multiples vacations. The failed machines arrive for service according to Poisson distribution with rate λ. 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 differential difference equations obtained for the reliable server is solved through in MATLAB to obtain transient probability for the system. The transient probabilities are used to compute the operational measures of performance for the systems. The effects of failure rate, service rate and vacation length for the system were studied. We show that with the same service rate μ , failure rate λ and vacation length θ, as the number of operating machine in the system increases the variance also increases. We also found that the variance under multiple vacations system is slightly less than that of single vacation. This means that the multiple vacations models may be preferred to the single vacation. The result also shows that the CPU time for the machine interference problem with reliable server under single vacation is slightly lower than that of machine interference problem with an unreliable server under single vacation policy.