M/M/R machine interference model with balking, reneging, spares and two modes of failure

This paper is concerned with M/M/R machine interference model consisting of M operating and S spare units. The units are assumed to fail in two modes. The life times and repair times of units are assumed to follow a negative exponential distribution. Both failure modes have equal probability of repair. Both types of failed units are served by a pool of R repairmen according to first-in-first-out discipline. We obtain queue size distribution at equilibrium in explicit form. The expressions for various performance measures such as the average number of failed units, the average number of idle repairmen etc. have been obtained. The expected total cost per unit time has also been derived. Numerical results are given for various performance measures to validate the analytical results. Optimal allocation of repairmen and spares based on heuristic approach is done in order to minimize the expected total cost under the constraint of availability.