Erlang Distribution
- Models waiting times until a fixed number of events have occurred when events happen at a constant rate.
- Defined by two parameters: a rate (events per unit time) and the required number of events.
- Commonly used in queuing contexts such as customer service or task completion in manufacturing.
Definition
Section titled “Definition”The Erlang distribution is a continuous probability distribution used to model the time it takes for events to occur in a system. It is characterized by two parameters: the rate at which events occur, and the number of events that must happen before the system is considered “complete.”
Explanation
Section titled “Explanation”The distribution applies when events occur at a constant rate and the quantity of events required before completion is fixed. It models quantities such as the time between arrivals of customers at a store or the time to complete a sequence of tasks in a manufacturing process. In applied examples, the rate parameter corresponds to the average number of events per unit time (for example, customers served per minute), and the number-of-events parameter corresponds to how many such events must occur before the system is considered finished.
Examples
Section titled “Examples”Fast food restaurant service
Section titled “Fast food restaurant service”The time it takes for customers to be served can follow an Erlang distribution when customer arrivals and service completions occur at a constant rate and the number of customers that must be served before the restaurant is considered “empty” is fixed. In this example, the rate parameter equals the average number of customers served per minute, and the number-of-events parameter equals the number of customers that must be served before the restaurant is considered empty.
Manufacturing process completion
Section titled “Manufacturing process completion”The time to complete a manufacturing process can follow an Erlang distribution when tasks complete at a constant rate and a fixed number of tasks must be finished before the process is considered “done.” Here, the rate parameter equals the average number of tasks completed per minute, and the number-of-events parameter equals the number of tasks required for completion.
Use cases
Section titled “Use cases”- Queuing theory: modeling how long it takes for customers or tasks to be served in a system where event rate and required event count are constant.
Related terms
Section titled “Related terms”- Continuous probability distribution
- Queuing theory