Transient Solution for Single Server Machine Interference Problem with Additional Server for Long Queues under N-Policy Vacations

Abstract

We consider the transient state single server machine interference problem with additional server for long queues under N-policy vacations. There are M operating machines with two repairmen. The first repairman is always available for serving the failed machines but go on a single vacation when there are no failed machines in the system. The second repairman is always on vacation but only comes back from vacation to attend to broken down machines if there are more than or equal to N broken down machine in queue in the system (N-policy vacations). Otherwise he goes for another vacation. The number of servers available for service in this system is two. The service discipline is first in first out (FIFO). The Chapman-Kolmogorov differential equations obtained for the model is solved through ODE45 in MATLAB. The transient probabilities obtained for the model are used to compute the expected number of failed machines E[F], expected number of operating machine E[O], expected length of vacation the servers has E[V], the machine availability at time t (M.A.(t)) and variance of the number of broken down machines σ2(t) for the systems. We investigate the effect of CPU time and different parameters on the availability of the machine for the single server machine interference problem with additional server for long queues. We found that with the same service rate μ, failure rate λ and vacations length θ, as the number of failed machines that trigger repairman 2 in the system increases the variance is less than one. This is caused by the additional repairman. The additional repairman reduces the waiting time of failed machines in the system.