Transient Analysis of M/M/R Machining System with Mixed Standbys, Switching Failures, Balking, Reneging and Additional Removable Repairmen


1 Mathematics, WCTM, Gurgaon

2 Mathematics, I.B.S, AGRA

3 Department Of Mathematics, IIT Roorkee,Roorkee,India


The objective of this paper is to study the M/M/R machine repair queueing system with mixed standbys. The life-time and repair time of units are assumed to be exponentially distributed. Failed units are repaired on FCFS basis. The standbys have switching failure probability q (0≤q≤1). The repair facility of the system consists of R permanent as well as r additional removable repairmen. Due to impatience, the failed units may balk or renege, with a certain probability, on finding all repairmen busy. Transient probabilities of various states are obtained by solving the set of governing equations via Runge-Kutta method. Expressions for various performance measures are established in terms of transient probabilities of system states. By varying different parameters, the system behavior is examined with the help of numerical illustrations.