Queueing Theory Business Applications

Queueing Theory, if used appropriately, can describe the a system and its dynamics accurately in order to pave the way for eventually improving the system. Let me illustrate.

PS: Go here if you’re interested in other articles on Queueing Theory.

Let’s assume the following scenario.

Widgets are made to order in an assembly line that consists of three steps, each performed by a single worker. So, there are a total of 3 workers on the assembly line. Here are a few facts and data for this process:

Wait-time between process steps is caused by buildup of work-in-process inventory.
Wait-time in front of Step 1 represents the wait-time from an arrival of an order to the start of production.
After step 3, the product is delivered immediately to the customer.
On average, orders for widgets arrive every 15 minutes.
We define Capacity is its maximum sustainable throughput:

The # of resources simultaneously performing the activity / The time duration of the activity

Below is the data:

Widget Factory
Step	Average Wait Time	Average Service Time
1	28	9
2	20	8
3	30	10

So, given the scenario above,

What is the average number of jobs in the system, including orders waiting to be processing PLUS work-in-process?

To answer the above question, we need the following:

Cycle Time: 28+9+20+8+30+10 = 105 Minutes
Average Throughput Rate = 1/15

So, the average number of jobs in the system including orders waiting and current work-in-process is:

1/15*(105) = 7 Widgets

Application

This simple example shows the power of Queueing Theory. I purposely chose the generic term “widgets” because you can substitute anything you want. For example, the process above can be done to answer the following questions:

On average, how many patients are in the system, including those in the waiting room that haven’t been seen yet and those currently being seen by a doctor?
On average, how many bags are in the airport carousel, including those that are enroute from the landed airplane as well as those currently on the carousel?
On average, how many projects are there, including those that whose business case is still being developed and those projects currently in process?
On average, how many custom bikes are being built including the bike orders that haven’t been started and those currently in process?

As you can see, my example above answers a variety of business questions, that can shed greater light on resource constraints, strategic planning, where constraints are in the system, and many more.