# POM 4410 USD Statistics Simple Toll Booth Model Questions

POM 4410/5410 – MIS 5410: Operations AnalyticsAssignment #3: Simple Toll Booth Model

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

• Name your file TollBooth_Base_yourlastname.spfx. So, my file would be

TollBooth_Base_aydas.spfx.

• 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.

Grading: Q1 – Q6: 5 points; Q7 – Q11: 8 points; Q12 – Q14: 10 points.

Q1. How many cars made it through the system in the 5000-hour run?

Q2. How many cars would you have expected to have gone through the system in 5000 hours?

Q3. If your answers to the first two questions don’t match, why not?

Q4. What was the average time that cars spent waiting in queue for the toll booth?

Q5. What was the utilization of the toll booth?

Q6. What was the average processing time at the toll booth?

Q7. What were the longest and shortest processing times at the toll booth?

Q8. What was the largest that the toll booth queue got during the run?

Q9. What was the average length of the toll booth queue?

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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. Create a copy of your current

model and name it TollBooth_Extended_yourlastname.spfx.

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.

Q13. The new summer intern working for the traffic authority suggests that instead of

randomly selecting 5% of the cars for the extended search, they should just select every 20th

car for the extended search. She thinks this will lead to less waiting time at the extended search

part of the process. Create a copy of your extended search model and name it

TollBooth_Extended_Every20_yourlastname.spfx. Modify this model to test out the intern’s

idea.

HINT: Create a useful Model State variable and then use it and reuse it. Also, it would be nice if

you did this in a way that made it easy to change the 20 to a different number as a way of

experimenting with the best inter-search interval. How does this new process compare to the

current extended search process in terms of customer waiting and resource utilization?

Q14. The results of the intern’s idea might suggest we could actually send even more cars to

extended search. Rerun the two different model and send every 10th car in the extended

model to customs and send 10% to custom’s in the original model. What do you find in terms of

wait times and server utilization?

To be submitted:

1. Your three simulation models

2. A Word document providing the answers and supporting evidence (i.e. screen shots or

output copy and paste) to all of the questions in this document.

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