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Queueing theory

The queuing theory is an important area within the stochastics. Queues occur in many situations in production and logistics and are usually undesirable because of the need of temporary storage of semi-finished components and because storage will employ capital. If customers will have to wait for a longer period of time this can have a negative impact on the company's image or have concrete material losses, if people give up waiting prematurely and thus they are lost as a customer.

Due to stochastic influences in both the inter-arrival times of customers as well as the service times there can be no simple relationship between arrival and service rate on the one side and the waiting time on the other side. Methods for studying the stochastic processes will be needed here.

Interactive pages on queuing theory

Queueing calculator

Enables the calculation of parameters for a G/G/c system based on the Allen-Cunneen approximation formula.

Design of queueing systems

Queuing theory can be used to analyze and evaluate everyday waiting situations.

Queuing calculator for smartphones

This simple web app uses Little's formula to estimate your waiting time in a queue.

Extended Erlang-C Formula

With the help of the Erlang-C model, an initial analysis can be performed for many waiting situations based on just a few parameters.

M/G/1 queue

Further information on the topic of queuing theory

The basic model of queueing theory

Explains the basic terms used to describe simple queueing models

Design of queuing systems

Depending on how queues and service counters are set up, different parameters may result for the same service performance.

Queue systems with control

By cleverly assigning customers to queues, the parameters of a system can be improved while keeping all other parameters identical.

Why do people so often end up in the wrong queue?

Simulation software

Queueing simulator

Open source Java application for modeling and simulating complex queueing networks

Call center simulator

Open source Java application for analyzing and optimizing complex call center networks consisting of several sub-call centers and several caller groups

Mini call center simulator

Open source Java application for simulating simple queueing models

Mini Queueing Simulator

Open source web application for modeling and simulating queueing networks

G/G/c/K+G Simulator

Open source web app for simulating G/G/c/K+G queueing models

Queueing Calculator

Open source web application for calculating the parameters of various queueing models (Erlang-B, Erlang-C, Pollaczek-Chintschin, Allen-Cunneen)

QueueSim (Python)

Open source Python library (including examples in the form of Jupyter notebooks) for creating simulation models in Python

Literature

Simulation with the queue simulator - Mathematical modeling and simulation of production and…

A. Herzog, Springer, 2021

Call center analysis and management: Modeling and optimization with queuing systems

A. Herzog, Springer, 2017