Queueing Theory: Part 3

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This post is part of a series on Queueing Theory. The other articles can be found here:

1. Queueing Theory: Part 1
2. Queueing Theory: Part 2
3. Queueing Theory: Part 3
4. Queueing Theory: Part 4
5. What is Waste?
6. On Time-Traps and Waste
7. Call Centers as Queueing Systems
8. Travel Time & Waste
9. Little’s Law for Product Development

I previously wrote on Queueing Theory and titled those posts as Queueing Theory: Part 1 and Queueing Theory: Part 2. Today, I’ll briefly explain how to set-up a model in Microsoft Excel to simulate a Single-Server Queue.

Queueing Theory shows the interplay between the arrival rate and the service rate, which both reveal the characteristics of the queue and, ultimately the customer experience. The items in parenthesis below are the cell/row numbers in my example image (see below).

1. Arrival Rate: Set-up a field to accept the Customers Per Hour (B5); Followed by a field to accept the Average Minutes Between Arrivals (60/B5).
2. Service Rate: Next, we need to set-up the Service Rate. To do this, create a field that will accept Customers Per Hour (B7). This is followed by a field to accept Average Service Time in Minutes (60/B7).

Now, we can learn about the characteristics of the queue and also how the customer might experience the queue:

3. Average Server Utilization: Create a field to calculate the Average Server Utilization (B5/B7).
4. Average Number of Customers in the Line: Set-up a field to calculate the Average Number of Customers in the Line (B5^2/(B7*(B7-B5))).
5. Average Number of Customers in the System: Now, create a field to calculate the Average Number of Customers in the System (B5/(B7-B5)).
6. Average Waiting Time in the Line: Now, we can determine how long it is, on average, for a customer to Wait in the Line in hours (B5/(B7*(B7-B5)) and in minutes ((B5/(B7*(B7-B5)))*60).
7. Average Time in the System: System here is defined the cumulative time of (Waiting in the Line + Being Served). For Hours, create a field that will calculate the following (1/(B7-B5)) and for Minutes ((1/(B7-B5)*60).

That’s it. With a few simple calculations we can determine the the load of a system the how long it is on average for a customer to wait for service. Queueing Theory is very pragmatic, applicable, and fairly easy to do. There’s a lot of quant-jock mystique around it, but it’s really not difficult to understand and it can really impact how companies conduct business. Where can you apply this?

Any business process where lines are a matter of fact — this means:

• Emergency or Doctor’s offices
• Restaurants
• Server Load in a network environment
• Fulfillment/Distribution Center or Warehousing
• Project Management
• Call Centers
• Software Engineering
• etc…

Queueing Theory isn’t used enough, in my experience. More businesses could stand to benefit from its use and application. At the end of the day, simply learning about how long a customer might wait in line will help a business better design their service to provide more value-add to the customer experience.

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