This question is adapted from question $15\mathrm{.}1$ from the text.$)$

$($a$)$ Consider an M$/$M$/$k system, where the processing rate at each server is $\backslash$mu $=1.$ Fix

the system utilization at $\backslash$rho $=0\mathrm{.}95.$ For k $=1,2,4,8,16,32$ and adjusting the arrival

rate $\backslash$lambda to keep the utilization fixed at $0\mathrm{.}95,$ compute the probability that an arriving

job has to wait and the mean response time. Provide an intuitive explanation for

the trends in your results.