$13\mathrm{.}3$ M$/$M$/1$ Simulation

This problem is a slight twist on Exercise $4\mathrm{.}3.$ Your job is to simulate an M$/$M$/1$ queue. You can write your simulator in any programming language. See Chapter $4$ for techniques for generating the needed random variables. The mean job size is $10.$ The mean arrival rate is $\backslash$lambda $.$ Adjust $\backslash$lambda as needed to create the following three loads $\backslash$rho $=0\mathrm{.}5,\backslash$rho $=0\mathrm{.}7,$ and $\backslash$rho $=0\mathrm{.}9$ and run your simulator under each load to measure mean response time. Compare your results with the steady$-$state mean response time derived in this chapter.