*32. For an interarrivai distribution F having mean , we define the equilibrium distribution of F, denoted...

*32. For an interarrivai distribution F having mean ì, we define the equilibrium distribution of F, denoted Fe, by travel from / to j is a random variable with mean m^. Suppose that tx = 1, t2 = 2, t3 = 4, Pl2 = 1, P 2 3 = 1, P 3 1 = f = 1 - P3 2 , m1 2 = 10, m2 3 = 20, m3l = 15, m3 2 = 25. Define an appropriate semi-Markov process and determine

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

(b) the proportion of time the taxi is on the road from / to y, /, j= 1,2,3.