Enter the arrival rate and service rate into the calculator to determine the average queue length. The calculator assumes a single-server queue with a first-come, first-served discipline.
Queue Length Formula
The following formula is used to calculate the average queue length.
L = (λ^2) / (μ * (μ - λ))
Variables:
- L is the average queue length (customers)
- λ (lambda) is the arrival rate (customers per hour)
- μ (mu) is the service rate (customers per hour)
To calculate the average queue length, square the arrival rate, then divide by the service rate multiplied by the difference between the service rate and the arrival rate. Note that the service rate must be greater than the arrival rate for the formula to be valid.
What is Queue Length?
Queue length is a measure of the number of customers waiting in line to be served in a queuing system. It is an important metric in operations management and service industries, as it helps determine the efficiency of service delivery and customer satisfaction. A longer queue may indicate a need for more servers or faster service to reduce wait times.
How to Calculate Queue Length?
The following steps outline how to calculate the average Queue Length.
- First, determine the arrival rate (λ) in customers per hour.
- Next, determine the service rate (μ) in customers per hour.
- Next, gather the formula from above = L = (λ^2) / (μ * (μ – λ)).
- Finally, calculate the average Queue Length (L) in customers.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
arrival rate (λ) = 10 customers per hour
service rate (μ) = 15 customers per hour
