THE MAINTENANCE OF UNIDIRECTIONALLY PATROLLED STATIONS

This 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 R(i) 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 B(i) is needed to carry out this work. The B(i)'s are independent and identically distributed random variables for each i. In addition only a certain proportion of repairs are successfully executed; sigma is the probability that a repair attempt is successful. It is assumed that each station fails randomly at average rate lambda 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 a and the Laplace transforms of R(i) and B(i).