Queueing theory is the study of waiting in line. Exciting, right?
Really, though—queueing theory is a management science that’s all about finding the best ways to use limited resources. In every phase of business, there are steps that have to happen in order to produce, ship, stock, and sell an item. As soon as an item moves through one step in that process, it joins a queue of other items waiting to move to the next phase (like a car on an assembly line waiting to be painted).
Similarly, customers seeking to buy your product might have to complete multiple steps in order to purchase your product (like ordering in the drive-through, paying at the first window, then picking up food at the last window).
For both your behind-the-scenes and customer-facing business processes, each step has the potential to become a bottleneck, which makes your company less efficient, drives up costs, and negatively affects customer satisfaction. Application of queueing theory aims to reduce these mishaps by analyzing the following factors:
- Arrival process: How many items or customers arrive in the queue in any given hour? Is the arrival rate steady or stochastic (a.k.a. variable)? What’s the average time interval between arrivals? Does that vary depending on the time?
- Queueing behavior: Is there a risk of spoilage or damage if products are left in the queue too long? Does long queueing time affect costs? If analyzing customers, is there a chance that customers in line will leave if they wait too long?
- Service: What is the service time for this particular step? What are the rules for deciding which items or customers get serviced first (e.g., first come, first served)? Are items or customers served one by one or in batches? How many items or customers can be served at a time?
- Waiting room: Is there a limited amount of space or resources (like funds to cover storage costs) available for items or customers waiting in the queue?
From there, you can use a few types of mathematical models to figure out important information:
- Average wait time per customer (or item): The average time your customers (or items) wait in your queue
- Average items (or customers) in queue: The average number of items in your system at a time (including in your queue and your actual process)
- Utilization time: The percentage of time that your employees or machines are actually being utilized in your system (e.g., the number of minutes that each of your machines is in actual operation out of your total workday time)
- Capacity: The maximum number of items or customers your system can handle at a time
Once you know the limits of your current system or process, you can effectively plan around those limits—or find areas where you can improve.