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Stochastic Modeling

SOFTWARE-STOCHASTIC MODELING

jMarkov (by G. Riaño and others)
A java package to model and solve Markov processes, Markov Decision Processes and QBDs.
Central Limit Theorem (XL-CLT) (by G. Riaño)
This program shows the Central Limit at work.
MarkovExcel (by G. Riaño)
This program is used for steady state and transient analysis of discrete and continuous Markov Chains.
XL-Inventory (by G. Riaño)
This programm is used for analysis of various stochastic inventory models.
Markovi (by G. Riaño)Didactic applications that simulates the behavior of discrete time Markov Chains (in Spanish).

29 Jan 10 | Software, Stochastic Modeling

The jMarkov Project

JMarkov is an Object-Oriented tool used for modeling and solving large-scale Markov Chains.

Modules

jMarkov has the following modules

Core Module: Permits modeling large-scale Markov Chains.
jQBD: Modeling of QBDs
jPhase: Modeling of Phase type distributions
jMDP: Modeling of MarkovDecision Processes.

Downloads

This download inludes all modules, documentation and examples.

jMarkov Release 2.0a

Documentation

Manuals

Reference Manual Documentation

Publications related to the Project

Conference proceedings

Germán Riaño and Julio Góez. jMarkov: An Object Oriented Framework for Modeling and Analyzing Markov Chains and QBDs, in Proceedings of the SMCtools’06, October 2006. Pisa, Italy.
Juan F. Pérez and Germán Riaño . jPhase: an object- oriented tool for modeling Phase-Type distributions, in Proceedings of the SMCtools’06, October 2006. Pisa, Italy.
Diego Bello and Germán Riaño. Linear Programming Solvers for Markov Decision Processes, in Proceedings of the 2006 IEEE Systems and Information Engineering Design Symposium, 2006.
Julio Góez and Germán Riaño JMarkov, librería para la solución de cadenas de Markov de gran escala , in Proceedings of the XII Latin-Ibero-American Congress on Operations Research, 2006. Ciudad de La Habana, Cuba.

Conference Talks

Julio Góez and Germán Riaño Módulo de JMarkov para la solución de procesos de cuasi nacimiento y muerte. XI Latin American Summer Workshop on Operations Research, 2005. Villa de Leyva, Colombia.
Andres Sarmiento and Germán Riaño. JMDP: An Object Oriented Framework for Modeling MDPs. Informa Annual Meeting, San Francisco,2005

Contact Information

Email: copa@uniandes.edu.co

29 Jan 09 | Stochastic Modeling

jPhase

General Information

What is jPhase?
jPhaseFit
jPhaseGenerator

Tutorials
jPhase Manual
Javadoc

Downloads
jMarkov Release 2.0a

Related Projects
The jMarkov Project

Contact Information

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What is jPhase?

jPhase is an object-oriented tool for modeling Phase-Type (PH) distributions in a computational framework. It is built on Java, which allows the encapsulation and easy extension of the developed structure. It allows the computation of relevant quantities related to PH distributions,such as the probability density or mass function, the cumulative distribution function as well as its moments, among others.

Another important issue is the implementation of closure properties, which are the result of operations on the set of PH variables. These include the minimum, maximum and convex mixture between PH variables, the distribution of the waiting time in the M/PH/1 queue, among others. For the matrix and vector represention, it makes extensive use of MTJ, which supports dense and sparse representations as well as solvers for linear systems.

The tool is divided in threem main packages: jPhase, the core package for representation and computation of several quantities around PH variables; jPhaseFit, that contains several algorithms for fitting the paramaters of a PH distribution from a data trace; jPhaseGenerator, that allows the generation of random variates according to a continuous or discrete PH distribution.

jPhaseFit

One of the complementary packages of the tool (jPhaseFit) has a set of classes to fit the parameters of a Phase-Type distribution from a data set, through the implementation of some recently developed algorithms. These classes are included in a computational structure that allows the characterization of the desired input and output of any fitting algorithm, in terms of computational objects.

jPhaseGenerator

This tool includes another complementary package (jPhaseGenerator), which defines the structure for any Phase-Type random variates generator, and implements the algorithms developed by Neuts and Pagano for the discrete and the continuous cases.

Contact Information

Email: copa@uniandes.edu.co

29 Jan 09 | Stochastic Modeling

Markovi

Cadenas de Markov

Descripción

Este progrma permite al estudiante experimentar con cadenas de Markov. Es una herramienta didáctica, no apta para análisis serios.

Usted podra ver el comportamiento de cadenas de máximo ocho estados. Con sólo darle las entradas correspondientes a la matriz P, el programa dibujará el grafo y ejecutará una simulación. Alternativamente, podrá ver el comportamiento de la matriz Pⁿ a medida que n crece. El programa incluye 20 ejemplos.

Antes de ejecutar la simulacion trate de anticiparse a las siguientes preguntas:

¿Existe el límite de Pⁿ ?
¿Son iguales todos los renglones de la matriz límite?
¿Depende dicho límite de las condiciones iniciales?
¿Puede usted predecir por adelantado si hay una columna de 0´s en la matriz límite?

Los vasitos de leche marcados con T y R son respectivamente la probabilidad teórica de encontrarse en el estado y la fracción real de tiempo que ha visitado cada estado (para esa simulación particular). En el modo matriz los vectores Vn y Vr representan lo mismo.

Instalación

Hay dos posiblidades de instalación

Clique aquí para bajar el archivo auto-ejecutable. Guárdelo en la carpeta que quiera y dele doble-clic para descomprimir los archivos internos. Para ejecutar el programa dele doble clic a Markov.exe.
Clique aquí para la versión zip. Descomprima TODOS los archivos en la carpeta de su elección. Para ejecutar el programa dele doble clic a Markov.exe.

Este programa fue desarrollado por Germán Riaño en la Universidad de los Andes, Bogotá Colombia.

23 Jan 09 | Stochastic Modeling

JMarkov