52. A taxi alternates between three different locations. Whenever it reaches location i, it stops and spends a random time having mean Image before obtaining another passenger, . A passenger entering the cab at location i will want to go to location j with probability . The time to travel from i to j is a random variable with meanI mage. Suppose thatI mage,I mage,I mage. Define an appropriate semi-Markov process and determine

(a) the proportion of time the taxi is waiting at location i, and

(b) the proportion of time the taxi is on the road from i to j, Image.