Simple and computationally efficient solutions for the evaluation of the steady-state queue length distribution.

The G/M/c-like queue

The solution to this queue with multiple servers is fast, based on a simple recurrence and numerically stable.

• Solve the G/M/c queue
• For more information: [1]

The M/G/1-like queue

The solution to this classical queue is fast, based on a simple recurrence and numerically stable.

• Solve the M/G/1 queue
• For more information: [3]

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.

• Solve the M/G/c queue
• For more information: [4]

The G/G/c-like queue (Beta version)

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 queues.

• Solve the G/G/c queue
• For more information: [5]

Associated publications

• [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.
• [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.
• [4] Reduced complexity in M/Ph/c/N queues. A. Brandwajn, T. Begin – Performance Evaluation, Volume 78, 2014, Pages 42-54.
• [5] Reducing the complexity of performance analysis of a multi-server facilities. T. Atmaca, T. Begin, A. Brandwajn, H. Castel – Technical Report, 2014.

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

Many thanks to Dominique Ponsard and Lucas Delobelle for their help.

Authors

Thomas Begin and Alexandre Brandwajn.