Question $2$: $(75pts)$ Consider a queuing system with two parallel servers and a single

waiting line: customers join a single line if both servers are busy. They are eventually

serviced by the first free server. If a customer arrives while both servers are idle, $($s$)$he then

prefers server $1($who happens to work faster$).$

The inter$-$arrival time of customers are known to be distributed Uniform $(5,15)$ minutes.

The service time for the first server is Uniform $(15,20)$ minutes, and for the second server

it is given as:

$(50$ pts$)$ Prepare a simulation table and hand$-$simulate the system for one hour exactly.

Assume that both servers are busy but the queue is empty initially.

$(25$ pts$)$ Use the sequence of random numbers given below and estimate:

i$)$ Average number of customers in the system

ii$)$ Average time spent in the queue

iii$)$ The average utilization of each server

iv$)$ Probability of no waiting in the queue

$0\mathrm{.}8700\mathrm{.}132.$

$($Use continuous time. When an arrival and a departure must be simultaneously scheduled,

use the convention of scheduling the arrival first$).$