This site presents some of our work related to the numerical analysis
of queueing systems. We provide the solution for some classical models
The G/M/c-like queue
The solution to this queue with multiple servers is fast, based on
a simple recurrence and numerically stable.
The M/G/1-like queue
The solution to this classical queue is fast, based on a simple
recurrence and numerically stable.
The M/G/c-like queue (New)
The solution to this classical queue is based on a simple yet
accurate approximation using a reduced-state description.
The G/G/c-like queue (Beta
The solution to this classical queue is found using the solutions
of two simpler models, i.e. M/G/c-like and G/M/c-like
We are working
to include more models
 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.
 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,
 A conditional probability approach to M/G/1-like
queues. A. Brandwajn, H. Wang – Performance Evaluation,
Volume 65, Issue 5, 2008, Pages 386-405.
 Reduced complexity in M/Ph/c/N queues. A.
Brandwajn, T. Begin – Performance Evaluation, Volume 78, 2014,
 Reducing the complexity of performance analysis of a
multi-server facilities. T. Atmaca, T. Begin, A. Brandwajn,
H. Castel – Technical Report, 2014.
This site is compatible with the following
- 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
Many thanks to Dominique Ponsard and Lucas
Delobelle for their help.
Last update: January 2015