Queuing Problem. Suppose a new full-body-scan security gate system is proposed for the airport, and airport administrators are trying to figure out how long people could expect to wait in line.

Build a very simple model of the set-up.Assume that passengers arrive on average at a rate of 120 per hour and that the security check (assume only one) can screen on average 140 passengers per hour.

Assume that both the arrival process and the service process are Poisson.You will have to use the exponential distribution to simulate the interarrival and service times.

a)Using simulation, answer the following questions.Be sure to show confidence intervals for the values.

i.What is the average amount of time that a person will wait in line?

ii.What percentage of the people will have to wait?

iii.How many feet should the airport administrators plan for the queue length?

iv.Given a queue of 30, what is the time in system of the next traveler?

b)Using the textbook or the queuing handout, calculate the analytic solutions for questions (a.i), (a.ii).