Queue waiting time calculator

This calculator helps determine the average waiting time in a queue based on arrival rate, service rate, and queue discipline.

Input Parameters

Calculation Results

Calculation Formula

Lq = λ²/μ(μ-λ)

Where:
Lq = Average queue length
λ = Arrival rate
μ = Service rate

Average Queue Length (Lq)

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Average Waiting Time (Wq)

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Probability of Zero Queue (P0)

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Queue waiting time calculator Calculator Usage Guide

Learn how to use the Queue waiting time calculator and understand its working principles

How to use the calculator

  1. Enter the arrival rate (average number of customers per hour)
  2. Enter the service rate (average number of customers that can be served per hour)
  3. Select the queue discipline (most common is FIFO)
  4. Optionally, specify the maximum queue length
  5. Click the "Calculate" button to see the results

Understanding the results

  • Average Queue Length (Lq): The average number of customers in the queue
  • Average Waiting Time (Wq): The average time a customer waits in the queue (in minutes)
  • Probability of Zero Queue (P0): The probability that there are no customers in the system

Working Principle

This calculator uses queuing theory formulas to calculate queue metrics. The M/M/1 model is assumed by default, where arrivals follow a Poisson process and service times are exponentially distributed.

Practical Applications

This calculator can be used in various scenarios including:

  • Call center operations
  • Banking systems
  • Customer service queues
  • Manufacturing processes
  • Website load balancing