Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

A study of the evolution of the representational capabilities of process modeling grammars

A plethora of process modeling techniques has been proposed over the years. One way of evaluating and comparing the scope and completeness of techniques is by way of representational analysis. The purpose of this paper is to examine how process modeling techniques have developed over the last four decades. The basis of the comparison is the Bunge-Wand-Weber representation model, a benchmark used for the analysis of grammars that purport to model the real world and the interactions within it. This paper presents a comparison of representational analyses of several popular process modeling techniques and has two main outcomes. First, it provides insights, within the boundaries of a representational analysis, into the extent to which process modeling techniques have developed over time. Second, the findings also indicate areas in which the underlying theory seems to be over-engineered or lacking in specialization.

A framework of issues in large process modeling projects

As process management projects have increased in size due to globalised and company-wide initiatives, a corresponding growth in the size of process modeling projects can be observed. Despite advances in languages, tools and methodologies, several aspects of these projects have been largely ignored by the academic community. This paper makes a first contribution to a potential research agenda in this field by defining the characteristics of large-scale process modeling projects and proposing a framework of related issues. These issues are derived from a semi -structured interview and six focus groups conducted in Australia, Germany and the USA with enterprise and modeling software vendors and customers. The focus groups confirm the existence of unresolved problems in business process modeling projects. The outcomes provide a research agenda which directs researchers into further studies in global process management, process model decomposition and the overall governance of process modeling projects. It is expected that this research agenda will provide guidance to researchers and practitioners by focusing on areas of high theoretical and practical relevance.

Specification and validation of process constraints for flexible workflows

Workflow systems have traditionally focused on the so-called production processes which are characterized by pre-definition, high volume, and repetitiveness. Recently, the deployment of workflow systems in non-traditional domains such as collaborative applications, e-learning and cross-organizational process integration, have put forth new requirements for flexible and dynamic specification. However, this flexibility cannot be offered at the expense of control, a critical requirement of business processes. In this paper, we will present a foundation set of constraints for flexible workflow specification. These constraints are intended to provide an appropriate balance between flexibility and control. The constraint specification framework is based on the concept of pockets of flexibility which allows ad hoc changes and/or building of workflows for highly flexible processes. Basically, our approach is to provide the ability to execute on the basis of a partially specified model, where the full specification of the model is made at runtime, and may be unique to each instance. The verification of dynamically built models is essential. Where as ensuring that the model conforms to specified constraints does not pose great difficulty, ensuring that the constraint set itself does not carry conflicts and redundancy is an interesting and challenging problem. In this paper, we will provide a discussion on both the static and dynamic verification aspects. We will also briefly present Chameleon, a prototype workflow engine that implements these concepts. (c) 2004 Elsevier Ltd. All rights reserved.

Do process modelling techniques get better? A comparative ontological analysis of BPMN

Current initiatives in the field of Business Process Management (BPM) strive for the development of a BPM standard notation by pushing the Business Process Modeling Notation (BPMN). However, such a proposed standard notation needs to be carefully examined. Ontological analysis is an established theoretical approach to evaluating modelling techniques. This paper reports on the outcomes of an ontological analysis of BPMN and explores identified issues by reporting on interviews conducted with BPMN users in Australia. Complementing this analysis we consolidate our findings with previous ontological analyses of process modelling notations to deliver a comprehensive assessment of BPMN.

A new chemorheological analysis of highly filled thermosets used in integrated circuit packaging

Chemorheology (and thus process modeling) of highly filled thermosets used in integrated circuit (IC) packaging has been complicated by their highly filled nature, fast kinetics of curing, and viscoelastic nature. This article summarizes a more thorough chemorheological analysis of a typical IC packaging thermoset material, including novel isothermal and nonisothermal multiwave parallel-plate chemorheology. This new chemorheological analysis may be used to optimize existing and design new IC packaging processes. (C) 1997 John Wiley & Sons, Inc.

Ontological evaluation of enterprise systems interoperability using ebXML

Enterprise systems interoperability (ESI) is an important topic for business currently. This situation is evidenced, at least in part, by the number and extent of potential candidate protocols for such process interoperation, viz., ebXML, BPML, BPEL, and WSCI. Wide-ranging support for each of these candidate standards already exists. However, despite broad acceptance, a sound theoretical evaluation of these approaches has not yet been provided. We use the Bunge-Wand-Weber (BWW) models, in particular, the representation model, to provide the basis for such a theoretical evaluation. We, and other researchers, have shown the usefulness of the representation model for analyzing, evaluating, and engineering techniques in the areas of traditional and structured systems analysis, object-oriented modeling, and process modeling. In this work, we address the question, what are the potential semantic weaknesses of using ebXML alone for process interoperation between enterprise systems? We find that users will lack important implementation information because of representational deficiencies; due to ontological redundancy, the complexity of the specification is unnecessarily increased; and, users of the specification will have to bring in extra-model knowledge to understand constructs in the specification due to instances of ontological excess.

A diffusion approach to approximating preservation probabilities for gene duplicates

Consider a haploid population and, within its genome, a gene whose presence is vital for the survival of any individual. Each copy of this gene is subject to mutations which destroy its function. Suppose one member of the population somehow acquires a duplicate copy of the gene, where the duplicate is fully linked to the original gene's locus. Preservation is said to occur if eventually the entire population consists of individuals descended from this one which initially carried the duplicate. The system is modelled by a finite state-space Markov process which in turn is approximated by a diffusion process, whence an explicit expression for the probability of preservation is derived. The event of preservation can be compared to the fixation of a selectively neutral gene variant initially present in a single individual, the probability of which is the reciprocal of the population size. For very weak mutation, this and the probability of preservation are equal, while as mutation becomes stronger, the preservation probability tends to double this reciprocal. This is in excellent agreement with simulation studies.

Accelerated leap methods for simulating discrete stochastic chemical kinetics

Biologists are increasingly conscious of the critical role that noise plays in cellular functions such as genetic regulation, often in connection with fluctuations in small numbers of key regulatory molecules. This has inspired the development of models that capture this fundamentally discrete and stochastic nature of cellular biology - most notably the Gillespie stochastic simulation algorithm (SSA). The SSA simulates a temporally homogeneous, discrete-state, continuous-time Markov process, and of course the corresponding probabilities and numbers of each molecular species must all remain positive. While accurately serving this purpose, the SSA can be computationally inefficient due to very small time stepping so faster approximations such as the Poisson and Binomial τ-leap methods have been suggested. This work places these leap methods in the context of numerical methods for the solution of stochastic differential equations (SDEs) driven by Poisson noise. This allows analogues of Euler-Maruyuma, Milstein and even higher order methods to be developed through the Itô-Taylor expansions as well as similar derivative-free Runge-Kutta approaches. Numerical results demonstrate that these novel methods compare favourably with existing techniques for simulating biochemical reactions by more accurately capturing crucial properties such as the mean and variance than existing methods.

Model driven distribution of collaborative business processes

In this paper, we present a top down approach for integrated process modelling and distributed process execution. The integrated process model can be utilized for global monitoring and visualization and distributed process models for local execution. Our main focus in this paper is the presentation of the approach to support automatic generation and linking of distributed process models from an integrated process definition.

Modeling control objectives for business process compliance

Business process design is primarily driven by process improvement objectives. However, the role of control objectives stemming from regulations and standards is becoming increasingly important for businesses in light of recent events that led to some of the largest scandals in corporate history. As organizations strive to meet compliance agendas, there is an evident need to provide systematic approaches that assist in the understanding of the interplay between (often conflicting) business and control objectives during business process design. In this paper, our objective is twofold. We will firstly present a research agenda in the space of business process compliance, identifying major technical and organizational challenges. We then tackle a part of the overall problem space, which deals with the effective modeling of control objectives and subsequently their propagation onto business process models. Control objective modeling is proposed through a specialized modal logic based on normative systems theory, and the visualization of control objectives on business process models is achieved procedurally. The proposed approach is demonstrated in the context of a purchase-to-pay scenario.