Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks

Cataloged from PDF version of article.Stochastic automata networks (SANs) have been developed and used in the last 15 years as a modeling formalism for large systems that can be decomposed into loosely connected components. In this work, we concentrate on the not so much emphasized discrete-time SANs. First, we remodel and extend an SAN that arises in wireless communications. Second, for an SAN with functional transitions, we derive conditions for a special case of ordinary lumpability in which aggregation is done automaton by automaton. Finally, for this class of lumpable discrete-time SANs we devise an efficient aggregation–iterative disaggregation algorithm and demonstrate its performance on the SAN model of interest. © 2002 Elsevier Science B.V. All rights reserved

Lumpable continuous-time stochastic automata networks

Cataloged from PDF version of article.The generator matrix of a continuous-time stochastic automata network (SAN) is a sum of tensor products of smaller matrices, which may have entries that are functions of the global state space. This paper specifies easy to check conditions for a class of ordinarily lumpable partitionings of the generator of a continuous-time SAN in which aggregation is performed automaton by automaton. When there exists a lumpable partitioning induced by the tensor representation of the generator, it is shown that an efficient aggregation-iterative disaggregation algorithm may be employed to compute the steady-state distribution. The results of experiments with two SAN models show that the proposed algorithm performs better than the highly competitive block Gauss-Seidel in terms of both the number of iterations and the time to converge to the solution. © 2002 Elsevier Science B.V. All rights reserved

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions

Multiphysics modeling for bone remodeling simulation: A methodological framework

In the present study an object oriented integrative modeling methodology is proposed for the construction of synthetic, computational models of bone-bone environment system that allow its simulation under in vivo conditions. The analytical mathematical approach to model and study ordinary materials will be outlined, indicating its limitations when dealing with biomaterials in physiological environments. The proposed object oriented integrative modeling will be explained emphasizing its advantages and possibilities. Finally, the architecture of the "in vivo" modeling and simulation software framework is shown, described and explained indicating further work based on this framework

An Aggregation Technique for Large-Scale PEPA Models with Non-Uniform Populations

Performance analysis based on modelling consists of two major steps: model construction and model analysis. Formal modelling techniques significantly aid model construction but can exacerbate model analysis. In particular, here we consider the analysis of large-scale systems which consist of one or more entities replicated many times to form large populations. The replication of entities in such models can cause their state spaces to grow exponentially to the extent that their exact stochastic analysis becomes computationally expensive or even infeasible. In this paper, we propose a new approximate aggregation algorithm for a class of large-scale PEPA models. For a given model, the method quickly checks if it satisfies a syntactic condition, indicating that the model may be solved approximately with high accuracy. If so, an aggregated CTMC is generated directly from the model description. This CTMC can be used for efficient derivation of an approximate marginal probability distribution over some of the model's populations. In the context of a large-scale client-server system, we demonstrate the usefulness of our method

Decompositional analysis of Kronecker structured Markov chains

This contribution proposes a decompositional iterative method with low memory requirements for the steadystate analysis ofKronecker structured Markov chains. The Markovian system is formed by a composition of subsystems using the Kronecker sum operator for local transitions and the Kronecker product operator for synchronized transitions. Even though the interactions among subsystems, which are captured by synchronized transitions, need not be weak, numerical experiments indicate that the solver benefits considerably from weak interactions among subsystems, and is to be recommended specifically in this case. © 2008, Kent State University

Symptoms of complexity in a tourism system

Tourism destinations behave as dynamic evolving complex systems, encompassing numerous factors and activities which are interdependent and whose relationships might be highly nonlinear. Traditional research in this field has looked after a linear approach: variables and relationships are monitored in order to forecast future outcomes with simplified models and to derive implications for management organisations. The limitations of this approach have become apparent in many cases, and several authors claim for a new and different attitude. While complex systems ideas are amongst the most promising interdisciplinary research themes emerged in the last few decades, very little has been done so far in the field of tourism. This paper presents a brief overview of the complexity framework as a means to understand structures, characteristics, relationships, and explores the implications and contributions of the complexity literature on tourism systems. The objective is to allow the reader to gain a deeper appreciation of this point of view.Comment: 32 pages, 3 figures, 1 table; accepted in Tourism Analysi

Compositional Performance Modelling with the TIPPtool

Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations