Problem $1)$ Monte Carlo Simulation

Vehicles arrive at a toll booth at an average of $200ve\frac{h}{h}r.$ Assume that the arrival pattern is random. The vehicles are served by a toll attendant with an average service time of $15$ seconds, distributed normally with a standard deviation of $2$ seconds. Prepare a simulation of the system using the Monte Carlo technique and apply to the first $15$ vehicles.

a$).$ On the CDFs you develop, plot the first random Number and corresponding value you look up$.$

b$).$ For each vehicle, detail $($in a table$)$ its headway, arrival time, queuing time, service time, and departure time.

c$).$ How much idle time does the attendant experience.

d$).$ What is the maximum queue length observed during the simulation period?

e$).$ What is the average wait time for vehicles?

Use the following random numbers in your simulation $($in the same order as presented below$)$:

Vehicle arrival random numbers

$\backslash$table$[[20,01],[80,42],[95,31],[22,77],[37,03],[05,84],[94,62],[11,21],[72,99],[55,79],[86,30],[98,29],[28,95],[27,93],[12,04]]$