A system is composed of CPU, Disk and Network. The execution of a process proceeds

as follows:

$1.$ The process uses the CPU and then with probability $0\mathrm{.}2$ proceeds to step $2,$ with

probability $0\mathrm{.}3$ proceeds to step $3,$ and with probability $0\mathrm{.}5$ proceeds to step $4.$

$2.$ The process performs Disk I$/$O and then with probability $0\mathrm{.}3$ proceeds to step

$1,$ and with probability $0\mathrm{.}7$ proceeds to step $4.$

$3.$ The process performs Network I$/$O and then with probability $0\mathrm{.}4$ proceeds to

Step $1$ and with probability $0\mathrm{.}6$ proceeds to step $4.$

$4.$ The process leaves the system $($perhaps due to an I$/$O error$).$

The following information is known about this system:

$$ Processes $($each process starts from step $1)$ arrive according to a Poisson process

with an average rate of $40$ processes per second.

$$ The service time of the CPU is exponentially distributed with an average of $15$

msec.

$$ The service time of the Disk is exponentially distributed with an average of $50$

msec.

$$ The service time of the Network is exponentially distributed with an average

of $60$ msec.

$$ All buffers are of infinite sizes.

Answer the question below:

$(1)$ Draw a queuing diagram depicting the system above.

a$)$ Which resource is the bottleneck resource?

b$)$ What is the average total turnaround time for a process submitted to the above

system?

c$)$ What is the probability that a process would not experience any waiting time

once it gets submitted to the CPU?

d$)$ What arrival rate would render this system unstable?