Consider a simple system which has two servers and a single FIFO queue. Customers arrive at a rate of $60$ per hour. A customer

will choose the first available server. Both servers work at approximately the same distribution, Uniform $[1,2]$ minutes. Using the

attached handout, perform a hand simulation for the first $10$ minutes. Assume the first arrival is at time $0.$ Draw the plot for the

number of busy servers, B$($t$),$ the plot for the number of customers waiting in the queue, Q$($t$)$ and the plot for the work$-$in$-$process

in the system, WIP$($t$).$ All inter$-$arrival times and service times are provided with the following table for the chart. Also, record final

statistics $($at time $10)$ for the average number of busy servers, the server utilization, the average queue size, and the average time

waiting in the queue. You can use $$Lesson$\_3\_$Simulation by Hand.xlsx$$ sheet for your answer.

Table $1$: Interarrival time and service times of the customers

Customer $12345678910...$

Interarrival times $0\mathrm{.}61\mathrm{.}20\mathrm{.}60\mathrm{.}44\mathrm{.}10\mathrm{.}715\mathrm{.}53\mathrm{.}11\mathrm{.}71\mathrm{.}0...$

Service Time $1\mathrm{.}62\mathrm{.}02\mathrm{.}31\mathrm{.}51\mathrm{.}41\mathrm{.}31\mathrm{.}01\mathrm{.}31\mathrm{.}31\mathrm{.}4...$

a$)$ Average time in Q per part

b$)$ Server Utilization $=$

c$)$ Average # waiting in Q $=$

d$)$ Average Waiting time in queue $=$

e$)$ Avg WIP $=$

f$)$ Avg Total Time $=$