In this paper, the steady-state availability and the mean time to system failure of a repairable system with m operating units, w warm standby units and R repairmen in which units balking and reneging are considered. It is assumed that failed units balk (refuse to join) with a constant probability (1 - b) and renege (leave the queue after joining) according to a negative exponential distribution with parameter r. The failure times of the operating and warm standby units are assumed to be exponentially distributed with parameters λ and α, respectively. The repair time distribution of each server is also exponentially distributed with parameter μ. This paper presents derivations for the steady-state availability, AT(∞) the mean time to system failure, MTTF and numerical examples. Several cases are analyzed to study the effects of various system parameters on the AT(∞) and the MTTF. © 2002 Published by Elsevier Science Inc.
Wang, K. H., & Ke, J. C. (2003). Probabilistic analysis of a repairable system with warm standbys plus balking and reneging. Applied Mathematical Modelling, 27(4), 327–336. https://doi.org/10.1016/S0307-904X(02)00133-6