This paper models the problem of the maintenance of N identical stations looked after by one operative who patrols the stations unidirectionally in the order 1, 2 ,..., N, 1, 2 ,... . The travel time between adjacent stations is a random variable, independently and identically distributed for each i, should it be found in a failed state, is a random variable, identically and independentlydistributed for each adjacent pair. The time taken to repair station i. In addition it is assumed that σ is the probability that a repair attempt is successful. It is further assumed that each station fails at random at an average λ in running time. It is shown that the important characteristics of the system – response time, waiting time, and availability for example – all depend on the quantity α, the probability that a station is found in the failed state. The model for the system shows how α can be found from values of N, λ σ, and the Laplace transforms of the travel-time and repair-time variables.
