MAMSolver: A Matrix-Analytic Solver for M/G/1, GI/M/1 and QBD processes

MAMSolver is a tool that provides implementation for the matrix-analytic algorithms. The tool provides solutions for both continuous and discrete time Markov chains of QBD, GI/M/1 and M/G/1-types. The solution of these type of processes using the matrix-analytic methodology is characterized by matrix-based operations. The two most important matrices computed are R for QBD and GI/M/1-type processes and G for QBD and M/G/1-type processes.

These two important matrices in MAMSolver are computed using both classic and the most recent efficient algorithms. For example the matrix G and R for QBD processes are computed using the logarithmic reduction algorithm, while the matrix G for M/G/1-type processes is computed using the cyclic-reduction algorithm.

The input for MAMSolver is a text file which consist of the matrices of the infinitesimal generator (or the transition probability matrix) for the process under study (check the examples on the left for more details).

The output from MAMSolver consist of:

1 - system load measured using the drift condition and caudal charateristic (file "drift -conditions")

2 - matrix G (file "G-matrix")

3 - matrix R (file "R-matrix")

4 - stationary probability distribution (file "probability")

5 - queue length distribution (file "QL-dist")

6 - average queue length (file "QL-length")

More information on the structure of MAMSolver can be found in the paper presented at the TOOLS 2002 conference (ps, or pdf).

This work has been supported by National Science Foundation under grands EIA-9974992, CCR-0098278, and ACI-0090221.