Article: jMarkov: An Integrated Framework for Markov Chain Modelling by Juan F. Pérez, Daniel F. Silva, Julio C. Góez, Andrés Sarmiento, Andrés Sarmiento-Romero, Raha Akhavan-Tabatabaei, Germán Riaño.

Abstract:

Markov chains (MC) are a powerful tool for modelling complex stochastic systems. Whereas a number of tools exist for solving different types of MC models, the first step in MC modelling is to define the model parameters. This step is, however, error prone and far from trivial when modelling complex systems. In this article, we introduce jMarkov, a framework for MC modelling that provides the user with the ability to define MC models from the basic rules underlying the system dynamics. From these rules, jMarkov automatically obtains the MC parameters and solves the model to determine steady-state and transient performance measures. The jMarkov framework is composed of four modules: (i) the main module supports MC models with a finite state space; (ii) the jQBD module enables the modelling of Quasi-Birth-and-Death processes, a class of MCs with infinite state space; (iii) the jMDP module offers the capabilities to determine optimal decision rules based on Markov Decision Processes; and (iv) the jPhase module supports the manipulation and inclusion of phase-type variables to represent more general behaviors than that of the standard exponential distribution. In addition, jMarkov is highly extensible, allowing the users to introduce new modelling abstractions and solvers.

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