## Erlang Distribution :

The Erlang distribution is a continuous probability distribution that is often used to model the time it takes for events to occur in a system, such as the time between arrivals of customers at a store or the time it takes to complete a task in a manufacturing process. This distribution is characterized by two parameters: the rate at which events occur, and the number of events that must happen before the system is considered to be “complete.”

One example of the Erlang distribution is the time it takes for a customer to be served at a fast food restaurant. The rate at which customers arrive at the restaurant is a constant, and the number of events (i.e., the number of customers) that must be served before the restaurant is considered to be “empty” is also constant. The time it takes for each customer to be served follows an Erlang distribution, with the rate parameter equal to the average number of customers served per minute, and the number of events parameter equal to the number of customers that must be served before the restaurant is considered empty.

Another example of the Erlang distribution is the time it takes for a manufacturing process to be completed. The rate at which tasks are completed in the manufacturing process is a constant, and the number of tasks that must be completed before the process is considered to be “done” is also constant. The time it takes for each task to be completed follows an Erlang distribution, with the rate parameter equal to the average number of tasks completed per minute, and the number of events parameter equal to the number of tasks that must be completed before the process is considered done.

The Erlang distribution is often used in queuing theory, which is the study of how long it takes for customers or tasks to be served in a system. This distribution is particularly useful in situations where the rate at which events occur is constant and the number of events that must be completed before the system is considered to be “done” is also constant. The Erlang distribution is often used to model the time it takes for events to occur in a system, such as the time between arrivals of customers at a store or the time it takes to complete a task in a manufacturing process. This distribution is characterized by two parameters: the rate at which events occur, and the number of events that must happen before the system is considered to be “complete.”