The machine interference problem with reliable server under single vacation is considered here. There are M similar machines that are subject to fail or breaks down with a single server who is responsible for repairin...The machine interference problem with reliable server under single vacation is considered here. There are M similar machines that are subject to fail or breaks down with a single server who is responsible for repairing or maintaining the failed machines. The machine fails completely at random with rate 2 and they are serviced in order of breaks down. More so, the machines operate independently but are subject to fail or break down. The service time distributions of the failed machines are assumed to be exponentially distributed with state dependent service rate #n, where n is the number of failed machines. By state dependent service rate we mean a situation where the rate of service depends on the number of failed machines present in the system. The Chapman-Kolmogorov differential equations obtained for the reliable server under single vacation 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. The following time dependent operational measures of performance for the system are obtained： expected number of failed machines, expected number of operating machines, machine availability, expected idle period, expected busy period, operational utilization of the machine, the variance of the expected number of failed machine and variance of expected number of operating machine in the system. The effects of failure rate of machines, service rate of failed machines and the number of operating machines are investigated; it is observe that the rate at which machine fails and is serviced, affect the expected number of failed and operating machines in the system. The CPU time for obtaining the transient results for the systems and the variance of the systems are reported in this work.展开更多
文摘The machine interference problem with reliable server under single vacation is considered here. There are M similar machines that are subject to fail or breaks down with a single server who is responsible for repairing or maintaining the failed machines. The machine fails completely at random with rate 2 and they are serviced in order of breaks down. More so, the machines operate independently but are subject to fail or break down. The service time distributions of the failed machines are assumed to be exponentially distributed with state dependent service rate #n, where n is the number of failed machines. By state dependent service rate we mean a situation where the rate of service depends on the number of failed machines present in the system. The Chapman-Kolmogorov differential equations obtained for the reliable server under single vacation 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. The following time dependent operational measures of performance for the system are obtained： expected number of failed machines, expected number of operating machines, machine availability, expected idle period, expected busy period, operational utilization of the machine, the variance of the expected number of failed machine and variance of expected number of operating machine in the system. The effects of failure rate of machines, service rate of failed machines and the number of operating machines are investigated; it is observe that the rate at which machine fails and is serviced, affect the expected number of failed and operating machines in the system. The CPU time for obtaining the transient results for the systems and the variance of the systems are reported in this work.
