Problem Two

Consider a computing system that is composed of $3$ queueing subsystems: two CPUs $($CPU$1$ and CPU$2)$ and one I$/$O server.

The system services two different types of processes: CPU$-$bound processes and I$/$Obound processes.

Both types of processes arrive to CPU$1$ first. The average rate of arrivals of CPU$-$bound processes is $20$ processes per second. The average rate of arrivals of $\frac{\text{I}}{0}-$bound processes is $10$ processes per second.

Once done with CPU$1,$ all CPU$-$bound processes are done and leave the system. I$/$Obound processes proceed to the I$/$O server.

Once done with the I$/$O Server, all$/$T$/$O$-$bound processes go to CPU$2$ for service. Once done with CPU$2,$ they leave the system with probabiliti $25\%$ q g go back for more I$/$O with the remaining probability.

The average service times of CPU$1,$ CPU$2$ and I$/$O server are $10$msec,$10$msec, and $20$ msec, respectively. Assume that all arrivals are Poisson and Service Times are Exponential. Answer the following questions:

$1-$ Draw a queuing diagram depicting, the system above. $[2$ points$]$

$2-$ Which resource is the bottleneck resource? $[2$ points$]$