An M/M/m/n Queue for the Shortest Distance Priority Machine Interference Problem

A mathematical model is developed for the machine interference problem with the priority of servicing the nearest machine in need of repair. The walking distance to a repair can be very significant in such large scale problems as law enforcement and guerrilla warfare where a first-in-first-out priority would, most likely, yield meaningless results. Compared with other models depicting the problem as a Markov process, the shortest distance priority yields the largest number of operating machines under steady-state conditions.