Discrete-Time Approximation Of The Machine Interference Problem With Generally Distributed Failure, Repair, And Walking Times

this paper we present an approximate discrete-time analysis of the machine interference problem with generally distributed working, failure, and walking times. We analyze the corresponding asymmetric polling system consisting of N separate closed queuing stations (buffer and server), each of which contains a single customer. These queuing stations are attended to by a common server in a cyclic manner. The walking times between the stations are non-zero. Upon service completion of the common server a customer requires service by its dedicated server. Then it is routed back to its corresponding buffer where it has to wait for service by the common server once again.The analysis is exact except for the assumption that the contributions of the queuing stations to the cycle time of the common server are mutually independent. We first calculate the stationary state probabilities using an iterative procedure and then derive the cycle time and waiting time distributions and their first and second moments. Several numerical examples comparing approximate results to simulations illustrate the accuracy of our method