Enter the arrival rate and service rate of a queue into the calculator to determine the average queue length, average total time, and average waiting time.

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## Queuing Theory Formulas

The following formulas are used in queuing theory for the case of random arrival, deterministic service, and only one service channel.

AQL = (2p-p^2)/2 * (1-p)

ATT = 2-p/2*u*(1-p)

AWT = p/ 2*u*(1-p)

- Where p is the arrival rate divided by the service rate.
- u is the service rate
- AQL is the average queue length
- ATT is the average total time of service
- AWT is the average waiting time

## Queuing Theory Definition

Queuing theory is a set of equations that describe the behavior of queues (lines) of customers to a store or service center. These behaviors include average queue length, average total time, and average waiting time.

## How does queuing theory work?

Queuing theory works by understanding the principles of customer management and wait times. The formulas are theorized for ideal queuing situations.

## Why is queuing theory important?

Queuing theory is important because it can allow a business to understand how lines and queues will form even before customers enter the store. The business can then make adjustments to change the wait and service times.

## Queuing Theory Example

How to calculate average wait time of a que?

**First, determine the arrival rate.**Calculate or measure the rate of arrival. (people per time)

**Next, determine the service rate.**Calculate the average service rate. (people per time)

**Finally, calculate the average wait time.**Using the formula above, calculate the average wait time.

## FAQ

**What is a queue?**

A queue is typically referred to as a line of people waiting for something, usually a service.