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 youâ€™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:
|Step||Average Wait Time||Average Service Time|
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
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 Â more.