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 about queueing theory

Queueing calculator

Queueing calculator

Allows to calculate the characteristics of a G/G/c system based on the Allen-Cunneen approximation formula.

Design of queueing systems
Verschiedene Modelle in der Warteschlangentheorie

Design of queueing systems

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

Queueing calculator for smartphones
Programmfenster im Wartezeitrechner

Queueing calculator for smartphones

This simple webapp can be used to determine estimates for one's wait time in a queue based on Little's formula.

 

Extended Erlang C formular

Extended Erlang C formular

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

M/G/1 queue

In dieser Webapp wird der zeitliche Verlauf der Anzahl an Kunden im System in einem M/G/1-Modell dargestellt.

More information on queueing theory

The basic model of queueing theory

The basic model of queueing theory

Explains the basic terms used to describe simple queueing models

Design of queueing system
Modelle von Warteschlangensystemen

Design of queueing system

Depending on how queues and operating counters are set up, different characteristic values can result for the same service performance.

Queueing system with control
Diagramme zu Warteschlangensystemen mit Steuerung

Queueing system with control

By cleverly assigning customers to queues, the parameters of a system can be improved with otherwise identical parameters.

 

Why one is chosing the wrong queue so often?
Auswahl der kürzeren Warteschlange

Why one is chosing the wrong queue so often?

Simulation software

TU Clausthal offers a number of simulation programs via the Simulation Science Center. All of these are open source programs that can be used free of charge:

Queueing Simulator

Queueing Simulator

Opensource Java application for modeling and simulation of complex queueing networks

Callcenter Simulator

Callcenter Simulator

Opensource Java application for analysis and optimization of complex call center networks consisting of several sub-call centers and several caller groups

Mini Callcenter Simulator

Mini Callcenter Simulator

Opensource Java application for simulation of simple queueing models

Mini Queueing Simulator

Mini Queueing Simulator

Opensource webapp for modeling and simulation of queueing networks

G/G/c/K+G Simulator

G/G/c/K+G Simulator

Opensource webapp for simulation of G/G/c/K+G queue models

Queueing Calculator

Queueing Calculator

Opensource webapp for calculating the characteristics of different queue models (Erlang-B, Erlang-C, Pollaczek-Chintschin, Allen-Cunneen)

QueueSim (Python)

QueueSim (Python)

Opensource Python library (incl. examples in the form of Jupyter notebooks) for creating simulation models in Python

Literatur