In the Passenger Screening Simulation, you used discrete event simulation to estimate the average waiting times for different scenarios. But, although simulation is a very powerful tool because it can be adapted to replicate almost any system, it can only provide statistical estimates of performance metrics. The accuracy of these estimates depends on the run length of the simulation and on the stability of the system. In the Passenger Screening scenario, when utilization gets high $($e$.$g$.$ above $90\%),$ the queue experiences infrequent but long busy periods. In order to get an accurate estimate of the average waiting time, we must run the simulation long enough to process millions of students to average out these busy periods. It$$s a safe bet that you did not run your simulation long enough for this.

Unlike simulation, the VUT equation provides a closed$-$form formula for computing the waiting time in a single$-$station queueing system. When arrivals are Poisson $($i$.$e$.$ CVa $=1),$ the VUT equation is exact. When CVa is not equal to $1,$ it is a reasonable approximation. Hence, we can use it as a check of the accuracy of our simulation results.

In this exercise, your job is to use the VUT equation spreadsheet to compute the average waiting time $($in seconds to one decimal place of accuracy$)$ for each scenario in the following table. Recall that the average service rate is $10$ passengers per minute in all scenarios. The average arrival rate, CVa, and CVp are given in the table.