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Guest Post: Teaching Inter-Arrival Times in Queuing Models

January 30, 2013

steve harrodDr. Steven Harrod is Assistant Professor of Operations Management at the University of Dayton and can be reached at steven.harrod@udayton.edu. Here is a link to his syllabus.

The single greatest challenge in teaching queuing in Module D of the Heizer/Render text is getting students to comprehend the difference between inter arrival and rate of flow. There is something deeply psychological and subconscious about this. Students frequently skim over the text and do not distinguish between the two expressions. Here is an in class exercise to practice this concept:
For each scenario in the table below, ask students to calculate the inter-arrival time and the flow rate (with answers shown in the right columns). Clearly state the unit of time measure for each answer. Each description refers to a random flow.

Inter-Arrival=time/(arrival count)       Flow, λ=(arrival count)/time=1/inter-arrivalSrteve Harrod mod. D graphic

Description

Inter-Arrival

λ

The ticket taker at the roller coaster   collected 45 tickets in 3 hours.

4 m

15/h

Cars arrive at the car wash once every 3   minutes.

3 m

20/h

Customers arrive at McDonald’s at the rate of   100 per hour.

0.6 m

100/h

Customers were recorded entering the store at   12:05, 12:07, 12:15, 12:22; 12:30: 12:31, 12:33, 12:40, and 12:50.

5 m

12/h

Fifteen passengers arrived for the 1 pm bus,   then twenty-five passengers arrived for the 2 pm bus, and then ten passengers   arrived for the 3 pm bus.

3.6 m

16.66    /h

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