For the queueing system of Section 3.61 define V(t), the work in the system at time, as the sum of the remaining service times of all customers in the system at Let V = lim V(s) ds/t. 00+ Also, let D, denote the amount of time the ith customer spends waiting in queue and define W = lim (D, + + Dn)/n 11-%

(a) Argue that V and Wo exist and are constant with probability 1.

(b) Prove the identity V=E[Y]WQ+E[Y]/2,

where 1/A is the mean interarrival time and Y has the distribution of a service time.