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Guest Post: A Teaching Tip for Visualizing Waiting Line Flows and Interarrival Times

April 8, 2013

steve harrodWhile Jay and Barry attend the INFORMS meeting in San Antonio, Dr. Steven Harrod, Assistant Professor of Operations Management at the University of Dayton provides this, his 5th Guest Post for our blog.

I find in teaching Waiting Line Models in Module D of the Heizer/Render text that the definitions and relationship of rates of flow and inter-arrival times are frustratingly difficult for some students to grasp. Here is a classroom exercise that may help:

Introduce the following video ( ), explaining that it shows traffic starting after a red light turns to green. Start the video at 0:17 (prepare the video in advance so you don’t have to watch the commercial during lecture). Draw the students’ attention to the second lane of traffic, headed by the Range Rover.

Explain that this flow of traffic may be described either by how many cars cross the white stop line in a period of time, or by how long each car takes to cross the line. Either way, the traffic flow described is identical. Play the video, and count ten cars across the line (ignore the car that changes lanes). Car number ten is a yellow cab, so stop the video with the eleventh car at the white line. You should find the video counter at 0:42, or 25 elapsed seconds. This is a flow of 10 cars in 25 seconds, or 10/25 cars per second, or 1440 cars per hour.

Restart the video at 0:17. Now, count the seconds between each successive car at the white line. They are, approximately, 5, 3, 2, 1, 3, 2, 2, 3, 2, and 2. The average time between cars is then 2.5 seconds. Now, since in both cases we have witnessed the same traffic flow, make the argument that these two measurements are equivalent. Indeed they are, after you explain that the inter-arrival time of a flow and the rate of flow are inverses of each other. In this case in particular, (1/2.5) = (10/25) and [1/(10/25)] = 2.5.

For some students, this is a difficult concept, and I  repeat this approach multiple times in the course.

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