XBorne 2016: A Brief Introduction

Abstract

Abstract. We present the new version of XBorne a software tool for the probabilistic modeling with Markov chains. The tool which has been developed initially as a testbed 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.

Product Form Solution for the Steady-State Distribution of a Markov Chain Associated with a General Matching Model with Self-loops

“…This Markov chain has 11 states: E, 1, 2, 3, 4, (1|4), (4|1), (1|3), (3|1), (2|4), (4|2). The graph of the Markov chain obtained by the XBorne [15] tool is depicted in Fig. 2.…”

marmoteCore

“…One is the standard power method. Two provide an interface to the linear-algebraic methods GTH and SOR (see Stewart [12]): these are borrowed from the XBorne package [4], see Section 5.3. The last one is an interface to the functionality offered by the R package markovchain already mentioned [11].…”

“…XBorne is a set of independent programs, written in C, for building and transforming stochastic matrices, and computing bounds or exact results for their steady-state and transient distributions [4]. For marmoteCore, this is an example of direct reuse of C code.…”

“…Courtesy of the package's maintainers, applications from XBorne have been slightly modified so as to provide their functionality through function calls. 4 Communication of the Markov model is done through files, although in principle the translation of data structures could be performed. The methods SOR and GTH for computing stationary distributions [12] are included this way in marmo-teCore.…”

Processor Sharing G-Queues With Inert Customers and Catastrophes: A Model for Server Aging and Rejuvenation

“…We depict in Fig. 1 a typical sample-path for a queue with both usual and inert customers obtained by the simulation tool in XBorne [6]. We will see that the queue is less and less efficient with aging until it is refreshed by the signal.…”