The efficiency of two groups of heterogeneous stations cared for by r operatives with a priority group

Abstract

This paper solves the machine interference problem in which a team of r operatives look after two separate groups of machines. Within each group the machines can be totally heterogeneous. Repair times are assumed to have a negative exponential distribution. Run times for the individual machines are assumed to have a general distribution. The service discipline is of service in random order (SIRO) form. Whenever there are more stopped machines than operatives, the particular r machines to be repaired are selected at random from the stopped machines. However it is always the case that stopped machines from the first group are accorded priority over those from the second group and are allocated to the operatives first. Explicit expressions for the probability that a particular set of machines from the first group and a particular set from the second group are found in the running state are derived. From this other useful measures for the system can be obtained. It is shown that these depend on the run-time distributions only through the mean run times and not on the shape of the distributions.