$16\mathrm{.}2$ More Closed System Performance For the closed interactive network in Figure $16\mathrm{.}12,$ there are N$=4$ users, think time is Z $$Exp$(\backslash$lambda $=2),$ service time is S $$Exp$(\backslash$mu $=4),$ and routing probabilities are as shown. $($a$)$ Use operational laws to approximate throughput, X$.($b$)$ Derive the exact throughput, X$.($c$)$ Derive the exact mean response time, $[$R$],$ not including think time. $($d$)$ What is the mean number of users that are thinking? $16\mathrm{.}8$ EXEIRCISES Figure $16\mathrm{.}12.$ Closed queueing network from Exercise $16\mathrm{.}2.$