On Tue, Jul 9, 2013 at 6:15 PM, David N. Jansen
Dear Osank,
Op 9 jul. 2013, om 12:42 heeft Osank Jain het volgende geschreven:
> Thanks ,I saw the code for ctmc module .
> I want to ask if there are other tools that analyse transient properties of ctmc by differential equations,I really want to learn that
I think your question is on a different level. A transient analysis problem can be posed as a differential equation, and its closed-form solution is the exponential of a matrix. This is where every analysis method of CTMCs agrees. So in some sense, every CTMC analyser uses differential equations.
But then come the differences: MRMC has chosen to calculate this matrix exponential using uniformisation, while others choose to calculate it in a different way. There is an article entitled ``Nineteen dubious ways to calculate the exponential of a matrix'' by Moler, SIAM Review 2003. Uniformisation is one method suitable for not-too-stiff CTMCs. Perhaps you are looking for other ways to exponentiate the matrix, so that article might help you.
> I was just getting into mmrc.I want to know how the transient analysis of CTMC is done by uniformization or diiferential equations
> I'd be great if someone give some details and point me towards it's code in the package as I not getting it.
> Thanks in advance
The relevant source file is src/modelchecking/transient_ctmc.c. It uses src/algorithms/foxglynn.c. Unfortunately, there are some bugs in the latter file, because there are some typos in the article by Fox and Glynn; see my technical report https://pms.cs.ru.nl/iris-diglib/src/getContent.php?id=2011-Jansen-UnderstandingFoxGlynn for details. I have corrected these bugs in a separate branch of the MRMC svn repository, namely ^branches/nijmegen-small-improvements/src/algorithms/foxglynn.c.
Kind regards,
David N. Jansen.