### Commercial

MARCA is a software package designed to facilitate the generation of large Markov chain models, to determine mathematical properties of the chain, to compute its stationary probability, and to compute transient distributions and mean time to absorption from arbitrary starting states. It is written in Fortran.

- Four possible approaches are available for constructing transition matrices, including an interactive facility and a sophisicated and very general modelling facility. Matrices may also be read directly from a file.
- The transition matrix is stored in compact form which permits very large ( >100K and up) state spaces to be analyzed.
- MARCA provides a mechanism whereby a Markov chain may be examined to separate essential states from transient states. Access is made available so that essential subsets of states may be analyzed individually.
- Near-complete-decomposability (NCD) characteristics of the Markov chain can be determined for a sequence of decomposability indices. The transition matrix may be permuted into normal NCD form when appropriate numerical solution techniques are applied.
- The “embedded” Markov chain may be analyzed to determine its periodicity, When this is greater than 1, an option is available to permute the transition matrix into normal cyclic form.
- A wide selection of numerical solution methods is available for computing the stationary behavior. They include:
- stable direct solvers based on Gaussian elimination (LU decomposition)
- single vector iterations (power, Gauss-Seidel, SOR, preconditioned power)
- projection methods (Arnoldi, GMRES) with a choice of preconditioners.
- iterative aggregation and disaggregation for NCD systems

- Solution techniques for computing the transient behavior include
- Randomization,
- Runge-Kutta
- Adams-Bashforth/Moulton
- Matrix powering for small systems (< 120 states).

- A mechanism is provided for computing the mean-time-to-absorption from any initial distribution.
- Access to all state variables, searching routines and probability vectors permits convenient analysis of measures of effectiveness.

- Powerful and user friendly markovian modeling and analysis software
- Powerful graphical Markov model editor
- Constructs Markov diagrams
- Models states and transitions
- Phased-mission models
- Steady state analysis
- Discrete and continuous time transition models
- Flexible definition of states and groups of states
- Quantify fault tree, RBD, and event tree events
- Time-based reliability and availability analysis

**RAM Commander’s Markov** is a powerful tool with the following features:

- Up-to-date, intuitive and powerful Markov Chain diagram interface with possibilities of full control over the diagram: elements location, colors, styles, zooms etc.
- Convenient ways of diagram printing and simple Copy & Paste transfer to other applications
- Calculation of Steady-State Mode
- Calculation of Time-Dependency Mode
- Calculation of Availability, Unavailability, Failure and Repair rate and frequency, MTBF, MTTF, MTTR, Reliability/Unreliability and other system parameters
- Results output:
- System parameters for selected times as table or graph
- State probabilities for selected times as table or graph
- Steady-State results report
- Transition Matrix report
- States and Transitions data report
- Results export to Excel, Word, HTML formats.

### Free

Muninn is a software package for estimating generalized ensemble weights in Markov chain Monte Carlo (MCMC) simulations. The method is full automated and makes use of the generalized multihistogram (GMH) equations for estimation the density of states [1]. The package is implemented in C++ and has a convenient interface.

QHQsv++ is a Markov Chain Monte Carlo based statistic library for estimating stochastic volatility models.