(a) Derive a formula for the stationary probability distribution of the number of customers in the system for an $\mathrm{M} / \mathrm{M} / 2 / 3$ queueing system. Express $p_n$ as a function of $\lambda$ and $\mu$.
(b) Suppose the Free K. Doubt company has modeled a computer subsystem as an $\mathrm{M} / \mathrm{M} / 2 / 3$ queueing system with $\lambda=15$ customers per second and $\mu=5$ customers per second. Calculate $p_n$ (for $n=0,1,2,3$ ), $\lambda_a, \rho, L_q, L, W_q$, and $W$ for this model. (The original form of this exercise was contributed by Dr. Raymond Bryant.)