Question $1$: $(70$ pts$)$ 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 interarrival times of the customers are

known to be:

Interarrival Time $($mins$)$ Probability

$50\mathrm{.}35$

$100\mathrm{.}40$

$150\mathrm{.}25$

The service time for the first server is Uniform$(15,20)$ minutes, and it is Uniform$(14,24)$

minutes for the second server.

$1.(45$ pts$)$ Prepare a formal $$event$-$scheduling$$ simulation table, hand$-$simulate the system

until the $4$th customer departs

$2.(25$ pts$)$ Report the following statistics:

i$)$ average number of customers in the system

ii$)$ average time spent in the queue

iii$)$ the average utilization of each server

IE $341$ Spring $2024$ Assignment # $22/2$

Assume that the first server is busy initially. When an arrival and a departure must be

simultaneously scheduled, use the convention of scheduling the departure first.

Use the following sequence of random numbers: $0\mathrm{.}4970\mathrm{.}3800\mathrm{.}8620\mathrm{.}0200\mathrm{.}3910\mathrm{.}9750\mathrm{.}480$

$0\mathrm{.}9050\mathrm{.}7590\mathrm{.}5600\mathrm{.}5930\mathrm{.}7440\mathrm{.}0690\mathrm{.}3700\mathrm{.}7900\mathrm{.}1760\mathrm{.}0200\mathrm{.}7140\mathrm{.}5390\mathrm{.}9280\mathrm{.}8600\mathrm{.}717$

$0\mathrm{.}8610\mathrm{.}5630\mathrm{.}5430\mathrm{.}8580\mathrm{.}537...$