Consider the system shown in figure below. Let N be the number of customers in the closed queueing system.
Exponentially distributed service times
(a) Determine the values of the routing p1, p2, and p3, such that the throughput rate (i.e., λ(N)) will be maximized for the case N —> + ∞
(b) Let µ1= 4, µ2 = 2, and µ3 = 1. Using the routing probabilities obtained in part (a) above, determine λ(N) for
i. N = 1
ii. N = 3
iii. N —> +∞