A mean value analysis of the travelling repairman problem

We consider the machine repairman problem where the machines are spatially distributed and repaired by a travelling serviceman. We assume identical machines with exponential up times and general repair times. We also assume that the travel times between pairs of locations have identical, but arbitrary distributions. Assuming a work-conserving, non-preemptive service discipline, a semi-Markov model is developed and various performance measures are evaluated. Some applications of the model are discussed. The model developed here, is used elsewhere to develop approximations for a more realistic situation where machines are non-identical and travel time distributions between pairs of locations are also non-identical.