User-Perceived Reliability of Shared Protection Systems with a Finite Number of Repairers

In this paper we investigate the user-perceived availability and Mean Time to Failure (MTTF) of M-for-N shared protection systems with a finite number of repairers. We assume that there are M backup units, N mutually independent users' (working) units, and C repairers (1 les Cles M + N)We investigate a Markov-chain model (with failure rate lambda per unit, repair rate mu per repairer) that is subject to an FCFS (First Come, First Served) protection switching and FCFS unit re-housing discipline. When a working unit fails, the service for the user of the unit is protected by one of the M protection units if available. If the service is not protected, the user enters a queue waiting for the service restoration. On the other hand, a failed unit immediately enters another queue waiting for repairs. Namely, there are two kinds of queues in the system. An analysis based on state transition diagrams gives a closed-form solution of the user-perceived availability and a recurrence computation method of the use-perceived MTTF. Our numerical examples reveal the effects of the number of repairers.