The M/Ek/r machine interference model steady state equations and numerical solutions

Abstract This paper studies the machine interference problem in which the running times follow the negative exponential distribution, the repair times the Erlang distribution and the number of operatives is more than one. The steady state equations are derived and it is shown that unlike the case of the M/E k / r ordinary queueing model, the solution cannot be taken in closed form. An efficient numerical procedure is developed instead, based on a decomposition principle. Tabulated results of the average number of machines running and the operative utilization for a range of the problem parameters are given, for the cases M/E 3 /2 and M/E 3 /3. A tentative conclusion for a closeness in performance between the models M/M/ r and M/E k / r is drawn.