Probabilistic analysis of a repairable system with warm standbys plus balking and reneging

摘要

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, A_T(∞), the mean time to system failure, MTTF and numerical examples. Several cases are analyzed to study the effects of various system parameters on the A_T(∞) and the MTTF.