The maintenance of unidirectionally patrolled stations

AbstractThis paper deals with the problem of the maintenance of N identical stations that are looked after by one operative who patrols the stations in the order 1, 2,..., N, 1, 2,..., (Figure 1). The time to travel from one station to the next, i → i + 1 for i = 1, 2,..., N − 1, or N → 1,is a random variable Ri that is identically and independently distributed for each i. If a station is found to be in need of repair when the operative visits it an additional time Bi is needed to carry out this work. The Bi's are independent and identically distributed random variables for each i. In addition only a certain proportion of repairs are successfully executed; σ is the probability that a repair attempt is successful. It is assumed that each station fails randomly at average rate λ in running time.This paper shows how the important characteristics of the system can be computed from the solution of a set of equations involving σ and the Laplace transforms of Ri and Bi