Calculate waiting time in a line from the people ahead of you and service time per person, or average queue wait from arrival and service rates.

Simple estimate; ignores time left on the person being served now.

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Waiting Time Formula

For a stable M/M/1 queue with arrivals and service rates per hour, the formula below gives mean time in the system W, including service. Queue-only mean wait is Wq = 60 ร— ฮป / [ฮผ(ฮผ โˆ’ ฮป)]. The line estimate, M/D/1, M/M/c and staffing modes use their own stated assumptions.

W = 1 / (ฮผ - ฮป) ร— 60

Variables:

  • W is the mean time in the system, including service (minutes)
  • ฮผ is the service rate of one server (customers per hour), strictly greater than ฮป for this M/M/1 formula
  • ฮป is the arrival rate (customers per hour)

For M/M/1 time including service, divide 1 by ฮผ โˆ’ ฮป and multiply by 60. For queue-only time, subtract 60/ฮผ minutes. These are steady-state model means, not individual wait guarantees.

What is Waiting Time?

Queue waiting time excludes service. Time in the system includes both waiting and service. 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 mean system time W in minutes; subtract 60/ฮผ to find mean queue wait Wq.
  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. With one M/M/1 server, W = 60/(15 โˆ’ 10) = 12 minutes including service; Wq = 12 โˆ’ 60/15 = 8 minutes before service.