In this article, I will give a detailed overview of waiting line models. I will discuss when and how to use waiting line models from a business standpoint. In the second part, I will go in-depth into multiple specific queuing theory models, that can be used for specific waiting lines, as well as other applications of queueing theory.

Introduction to waiting line models

Waiting line models are mathematical models used to study waiting lines. Another name for the domain is queuing theory.

Waiting lines can be set up in many ways. In a theme park ride, you generally have one line. In the supermarket, you have multiple cashiers with each their own waiting line. And at a fast-food restaurant, you may encounter situations with multiple servers and a single waiting line.

The goal of waiting line models is to describe expected result KPIs of a waiting line system, without having to implement them for empirical observation. Result KPIs for waiting lines can be for instance reduction of staffing costs or improvement of guest satisfaction.

When to use waiting line models?

Waiting line models can be used as long as your situation meets the idea of a waiting line. This means that there has to be a specific process for arriving clients (or whatever object you are modeling), and a specific process for the servers (usually with the departure of clients out of the system after having been served).

Waiting line models need arrival, waiting and service

This idea may seem very specific to waiting lines, but there are actually many possible applications of waiting line models. For example, waiting line models are very important for:

• Computer processors and task handling. Many tasks arrive at the same time to your computer’s processor, and it has to handle them one by one without the computer failing.
• Telecommunication models. For example when many messages are being sent in a short time frame and have to be dealt with correctly while limiting the “waiting time” / “delay” of the message.
• Traffic engineering. For example when many cars arrive at the same location at the same time and they have to wait.
• Complicated multi-layer systems like call centers with multiple services are an example of multiple waiting lines connected together.

#operations-research #industrial-engineering #statistics #data-science #mathematics