Variables
Description
What is this formula?
The Single-Server Queue Waiting Time formula calculates the average time customers spend waiting in line before service begins in an M/M/1 queueing system.
It is one of the most important performance measures in queueing theory.
When to use it
Use this formula when:
- Analyzing customer waiting times.
- Designing service facilities.
- Evaluating call centers.
- Studying manufacturing bottlenecks.
- Optimizing staffing levels.
Example
A service desk receives:
λ = 18 customers/hour
The service rate is:
μ = 24 customers/hour
Formula:
Wq = λ/[μ(μ−λ)]
Substitution:
Wq = 18/[24(24−18)]
Wq = 18/144
Wq = 0.125 h
Result:
The average waiting time in queue is 0.125 hours or 7.5 minutes.
Applications
- Queueing theory
- Call centers
- Manufacturing systems
- Retail operations
- Healthcare services
- Transportation systems
Note
This formula applies specifically to M/M/1 queues with Poisson arrivals, exponential service times, and a single server. More complex queueing systems require different models and equations.