Calculate queue waiting time from people ahead and service time, or from arrival and service rates (M/M/1, M/M/c), plus the servers needed to hit a target wait.

Doctor office
Restaurant
Pharmacy
Coffee shop
DMV

Simple line method: wait equals people ahead divided by total service rate.

Related Calculators

Waiting Time Formula

The following formula is used to calculate the average waiting time in the system (W).

W = 1 / (ฮผ - ฮป) ร— 60

Variables:

  • W is the average waiting time in the system (minutes)
  • ฮผ is the service rate (customers per hour)
  • ฮป is the arrival rate (customers per hour)

To calculate the average waiting time, divide 1 by the difference between the service rate and the arrival rate, then multiply by 60 to convert from hours to minutes.

What is Waiting Time?

Waiting time is the average time a customer spends waiting in the system before being serviced. It is a key performance indicator in service industries and is used to assess the efficiency of service delivery. A lower waiting time generally indicates a more efficient system with sufficient capacity to handle the incoming customer flow.

How to Calculate Waiting Time?

The following steps outline how to calculate the average waiting time.

  1. First, determine the service rate (ฮผ) in customers per hour.
  2. Next, determine the arrival rate (ฮป) in customers per hour.
  3. Next, gather the formula from above = W = 1 / (ฮผ - ฮป) * 60.
  4. Finally, calculate the average waiting time (W) in minutes.
  5. 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.

Service rate (ฮผ) = 15 customers per hour

Arrival rate (ฮป) = 10 customers per hour