Question $1(40\%)$ Hand Simulation

The following data yields the arrival and service times each customer will require for the first $13$ customers

at a single server queue system $(\frac{M}{M}\frac{?}{1}).$ Upon arrival, a customer either enters the service if the server is

idle or joins the waiting line. When the server completes the work on a particular customer, the next one in

line $($i$.$e$.,$ the one who has been waiting for the longest$)$ enters the service. The studied period ends when

the last customer leaves the system$)$

Arrival Times: $1231639599154198221304346415449526$

Service Times: $42355147194851252954407232$

a$)$ Determine the departure times of these $13$ customers

b$)$ Calculate the expected waiting time of customers in the system

c$)$ Calculate the expected number of customers waiting in the queue, and the system

d$)$ Calculate the expected system utilization.