Build a simulation model with Simio of the toll booth starting from a brand-new empty file.

Assume there is a single toll booth fed by a single lane.

Cars arrive to the toll booth according to a Poisson process (i.e. exponentially distributed inter-arrival times) at a rate of 24 cars/hour.

The processing time for each car at the toll booth is also exponentially distributed with a mean time of 1.8 minutes.

Include a dynamic plot that shows the total number of cars in the system (i.e. the number in queue plus the number being served).

Make sure all of your objects have nice labels.

Include text annotations and/or other drawing elements to make your model look nice.

Set the model run time to 5000 hours with a warm up time of 500 hours.

Run the model and use the output to answer the following questions. For each question, provide the answer from your model output as well as a screen shot from the Results Grid section you used to find the answer. If you needed to do some additional computation for an answer, show the computation.

Q10. If the average processing time at the toll booth is increased by 10%, by how much does the average wait time in queue increase (both in absolute terms and on a percentage basis)?

Q11. Using the increased processing time from part 10, use your model to estimate the maximum hourly arrival rate of cars that the toll booth can handle while keeping the average time in queue to no more than 10 minutes. Create a graph in Excel showing the relationship between the arrival rate of cars and the mean wait time in queue. What shape do you think this graph will take (put the arrival rate on the X-axis)?

Q12. Set the arrival rate and service time parameters back to their original values. Assume that 5% of cars passing through the toll booth are selected randomly for a more in-depth interview and search at the customs office. There is a single customs officer on duty at all times. The processing time for this extended search is triangularly distributed with a minimum of 20 minutes, a mode of 25 minutes and a maximum of 40 minutes.

Modify this model to include this extended search process. Use this new model to estimate the average number of cars in process (in queue or being searched) at the customs office.