| Abstract: | This paper models the problem of the maintenance of N identicalstations looked after by one operative who patrols the stationsunidirectionally in the order 1, 2, ..., N, 1, 2,... The traveltime between adjacent stations is a random variable, identicallyand independently distributed for each adjacent pair. The timetaken to repair station i, should it be found in a failed state,is a random variable, independently and identically distributedfor each i. In addition it is assumed that  is the probabilitythat a repair attempt is successful. It is further assumed thateach station fails at random at an average  in running time. It is shown that the important characteristics of the system—responsetime, waiting time, and availability for example—all dependon the quantity  , the probability that a station is found inthe failed state. The model for the system shows how can befound from the values of N,i,, and the Laplace transforms ofthe travel-time and repair-time variables. |
