Simulation of a M/G/1 queue

The inter-arrival times of the customers are exponentially distributed, the distribution for the service times can be selected to be gamma distribution, exponential distribution and log-normal distribution. In the case of the exponential distribution this results in an M/M/ 1 queue.

At the bottom of the page the parameters of the inter-arrival and service time distributions can be adjusted. The ratio of service and the arrival rate defines the traffic rate.

In the diagram the number of clients in the system at time t is specified. Each jump upwards defines a customer arrival, each jump to the bottom means the end of a service time. The service time are also denoted below.

Number of clients in the system

Service time

Simulation software

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


Warteschlangensimulator allows the simulation of any complex queueing network. The models are defined in Warteschlangensimulator in the form of flowcharts. Optionally, an animation can be displayed during the simulation of the models to illustrate the movement of the customers through the system. For the automated examination of different models, parameter series can be created automatically and an optimizer is also available. Furthermore, external data sources can be connected directly during the simulation of models and (partial) results can also be transferred directly to external programs (e.g. databases).


Warteschlangensimulator requires a Java runtime environment and was published as open source.

Callcenter Simulator

Callcenter Simulator is designed to map real call center systems consisting of several sub-call centers, different caller groups, different agent groups (with different skill levels and different shift plans), complex assignment rules, etc. It can be used directly for staff requirements planning and for the analysis of possible control strategies in large call center networks. In addition to pure simulation, the program also provides functions for automatic optimization of the number of agents.


Callcenter Simulator requires a Java runtime environment and has been published as open source.

Mini Callcenter Simulator

Mini Callcenter Simulator essentially reproduces the same G/G/c/K+G model that the webapp contains. However, it has much more probability distributions that can be used for inter-arrival times, service times, post-processing times, waiting time tolerances and repeat distance distributions. In addition, considerably more characteristics are recorded and various export options are available for the simulation results. Furthermore, the simulation results can be directly compared to corresponding Erlang-C results and explanations can be displayed why deviations occur at which points.


Mini Callcenter Simulator requires a Java runtime environment and has been published as open source.

Mini Simulator (Webapp)

The Mini Simulator is a web app fully implemented in Javascript that can be run in any modern browser (including tablets and smartphones). The app maps a G/G/c/K+M model, i.e. a model consisting of a queue and a operating station. Batch arrivals, batch operations, customer impatience, repeaters and forwarding can be mapped.


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