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.

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?

  1. First, determine the arrival rate.

    Calculate or measure the rate of arrival. (people per time)

  2. Next, determine the service rate.

    Calculate the average service rate. (people per time)

  3. Finally, calculate the average wait time.

    Using the formula above, calculate the average wait time.


What is a queue?

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