[math] \newcommand{\NA}{{\rm NA}} \newcommand{\mat}[1]{{\bf#1}} \newcommand{\exref}[1]{\ref{##1}} \newcommand{\secstoprocess}{\all} \newcommand{\NA}{{\rm NA}} \newcommand{\mathds}{\mathbb}[/math]

Write a computer program to simulate the queue in Exercise. Have your program keep track of the proportion of the time that the queue length is [math]j[/math] for [math]j = 0, 1, \ldots,n[/math] and the average queue length. Show that the behavior of the queue length is very different depending upon whether the traffic intensity [math]s[/math] has the property [math]s \lt 1[/math], [math]s =1[/math], or [math]s \gt 1[/math].