A production plant has three machines and the two products move about among these three machines. Upon completion of the process at machine i, it moves to the next available machine out of the two remaining machines. Therefore, there are always two busy machines. If the service times of these machines follow an exponential distribution with a rate of 1=2/min, 2=1 /min, 3=4 /min, respectively, what proportion of time machine 1 will be idle?