6.4.3 A factory has five machines and a single repairman. The operating time until failure of a machine is an exponentially distributed random variable with parameter

(rate) 0.20 per hour. The repair time of a failed machine is an exponentially distributed random variable with parameter (rate) 0.50 per hour. Up to five machines may be operating at any given time, their failures being independent of one another, but at most one machine may be in repair at any time. In the long run, what fraction of time is the repairman idle?