We present the last version of XBorne a software tool for the probabilistic modeling with Markov chains. The tool which has been developed initially as a test- bed for the algorithmic stochastic comparisons of stochastic matrices and Markov chains, is now a general purpose framework which can be used for the Markovian modelling in education and research, further details in [1].
Xborne is organized as a set of programs which exchange files to analyse a model. Files contain data (the matrices, the description of states) and programs in C (definition of state-dependant probabilities, definition of transitions, definition of rewards). Some programms must be compiled with this new functions to analyse a new model.
--> User's guide : view details of utilisation in file xbornV1-3.pdf
--> Directories :
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SrongStochasticBoundTotal : Various implementation of Vincent algoritms available. IMSUB is only available with a band structure for internal representation of the matrix (thus it can use a lot of memory and be slow). Also the FQ algorithm with a banded form for the matrix.
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CensorBounds : DPY and Truffet methods are available. New methods will be available soon.
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BlocksGeneration : not available anymore (a new release to be consistent with the other tools)
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NablaAlgorithms: some of the algorithms are here (INABLAU, INABLAL, SLUB).
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Format : a set of file descriptions and format to make the programs run.
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MarkovGeneration : generMarkov.c (replace newgen.c, some bugs fixed, some improvements)
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Reward : You can easily use "rewardIndice.c" which computes typical rewards while "reawrdComponents.c" needs that you provide a description of your own rewards by a C file called funReward.c. In that case, your model must also have a "model.cd" file for state description. An example is provided but the comments are in French.
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Solve: GTH (also sparse GTH), Power, GaussSeidel, and SOR. Not the best methods but you can transform your model into a MM form and use state of the art solver available on the web.
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BirthDeath: Solves any classical Birth-Death process numerically. However, one should inform the main parameters as arrival rates and service rates in each state (adapt Taux() function to your model). Examples of M/M/1/B and M/M/C/B are given.
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MatrixOPerations: some programs to transform the matrices: transpose for instance. Also possible to export.
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MitraniDemo and MitraniDemo2 : Exemple of building, solving and calcuting Rewards of Mitran's model. matrix to Latex, Scilab, Matrix Market format. Uniformisation and the T-transform are also available.
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Lumpabillity: Tarjan's algorithm to find best partition for lumpable and quasi-lumpable matrix will be available soon. Ana's version of Limsub (with LMSUB, LIMSUB and LL as possible options) is in this directory.
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AutomataGeneration: to build an automata instead of the Markov chain. The output is a tgf file which can be used by yed to find a nice drawing. See also Lam2Tgf which transform the .Rii and .cd files into a tgf files for drawing.
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Simulation: create a simulator of the DTMC from the fun.c file instead of generating the matrix. Use the same fun.c file but it neeeds extra information in const.h. 2 versions here: with or without information on the coverage of the state space.
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LR : some programs to calculate the steady-state distribution and transient distribution for Low Rank and Class G Markov chains.
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Util : Construction of the two tables of Walker's algorithm. To use in alais method for a simulation. as input : a probabilistic distribution. output : two vectors in the same file the size is in the .sz file.
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Muntz : Lower and Upper algorithm for the steady state distribution.
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Properties : verifications algorithms of some proprieties of Markov chain graphs.
- Youssef AIT EL MAHJOUB
- Jean-Michel Fourneau
- Franck Quessette
- Dimitris Vekris
- This code is open source. However, one can cite the original document [1] published in ISCIS 2016.
[1] "XBorne 2016: A Brief Introduction", Youssef AIT EL MAHJOUB, Jean-Michel FOURNEAU, Franck QUESSETTE, Dimitris VEKRIS". in ISCIS - International Symposium on Computer and Information Sciences, 2016.