Solutions to Queueing Systems
Simple and computationally efficient semi-numerical solutions for the evaluation of the steady-state queue length distribution using conditional probabilities.
This site presents some of our work related to the numerical analysis of queueing systems.
G/M/c-like queue
The solution to this queue with multiple servers is fast, based on a simple recurrence and numerically stable.
- Try it Now! Solution to the steady-state behavior.
- Associated publication:
[1] A Recurrent Solution of Ph/M/c/N-like and Ph/M/c-like Queues. A. Brandwajn, T. Begin – Journal of Applied Probability, Volume 49, Number 1, Pages 84-99.
[2] A tool for solving Ph/M/c and Ph/M/c/N queues. T. Begin, A. Brandwajn, – Proceedings of the 9th ACM International Conference on Quantitative Evaluation of SysTems, QEST12.
- Download the source code (in C).
M/G/1-like queue
The solution to this classical queue is fast, based on a simple recurrence and numerically stable.
- Try it Now! Solution to the steady-state behavior. New!
- Associated publication:
[3] A conditional probability approach to M/G/1-like queues. A. Brandwajn, H. Wang – Performance Evaluation, Volume 65, Issue 5, 2008, Pages 386-405. - Download the source code (in C).
More to come
G/G/1-like queue, G/G/c-like queue,...
Under construction 
Compatible browsers
This site is compatible with the following browsers:
- Google Chrome
- Internet Explorer 9.0
- Safari 5
- Firefox 3.x, 4.x and 7.x
If you use IE 8.0, the steady-state distribution for the number of customers in the system will not be displayed as a plot, but instead as a table since svg format is not supported.
Acknowledgement
Thanks to Dominique Ponsard and Lucas Delobelle.
Authors
Alexandre Brandwajn and Thomas Begin.
Last update: June 2012