Measures of Risk on Variability with Application in Stochastic Activity Networks

We propose a simple measure of variability of some of the more commonly used distribution functions in the class of New-Better-than-Used in Expectation (NBUE). The measure result in a ranking of the distributions, and the methodology used is applicable to other distributions in NBUE class beside the one treated here. An application to stochastic activity networks is given to illustrate the idea and the applicability of the proposed measure. Keywords: Alternative Risk measure, Portfolio, Coefficient of Variation, Skewness, Project management,  Stochastic activity networks

Characterization of gradient estimators for stochastic activity networks

This thesis aims to characterize the statistical properties of Monte Carlo simulation-based gradient estimation techniques for performance measures in stochastic activity networks (SANs) using the estimators' variance as the comparison criterion. When analyzing SANs, both performance measures and their sensitivities (gradient, Hessian) are important. This thesis focuses on analyzing three direct gradient estimation techniques: infinitesimal perturbation analysis, the score function or likelihood ratio method, and weak derivatives. To investigate how statistical properties of the different gradient estimation techniques depend on characteristics of the SAN, we carry out both theoretical analyses and numerical experiments. The objective of these studies is to provide guidelines for selecting which technique to use for particular classes of SANs based on features such as complexity, size, shape and interconnectivity. The results reveal that a specific weak derivatives-based method with common random numbers outperforms the other direct techniques in nearly every network configuration tested

Stochastic Activity Networks Templates: Supporting Variability in Performability Models

Model-based evaluation is extensively used to estimate performance and reliability of dependable systems. Traditionally, those systems were small and self-contained, and the main challenge for model-based evaluation has been the efficiency of the solution process. Recently, the problem of specifying and maintaining complex models has increasingly gained attention, as modern systems are characterized by many components and complex interactions. Components share similarities, but also exhibit variations in their behavior due to different configurations or roles in the system. From the modeling perspective, variations lead to replicating and altering a small set of base models multiple times. Variability is taken into account only informally, by defining a sample model and explaining its possible variations. In this paper we address the problem of including variability in performability models, focusing on Stochastic Activity Networks (SANs). We introduce the formal definition of Stochastic Activity Networks Templates (SAN-T), a formalism based on SANs with the addition of variability aspects. Differently from other approaches, parameters can also affect the structure of the model, like the number of cases of activities. We apply the SAN-T formalism to the modeling of the backbone network of an environmental monitoring infrastructure. In particular, we show how existing SAN models from the literature can be generalized using the newly introduced formalism

An investigation of heuristic decision rules for allocating limited resources in stochastic activity networks

The effort of this thesis has been directed toward the examination of decision rules concerning resource allocation in stochastic activity networks whose resources are constrained. Specifically, the objective was to determine if any one decision rule serves as an effective one for producing consistently low completion times in any network

The optimal resource allocation in stochastic activity networks via the electromagnetism approach

An optimal resource allocation approach to stochastic multimodal projects had been previously developed by applying a Dynamic Programming model, which proved to be very demanding computationally. Approximations to the initial model had been also developed, still within DP framework. Computing times were improved, but demonstrated the need for further developments. In this paper we report on the application of a recently developed technique for global optimization, the Electromagnetism Algorithm (EMA), to this problem and demonstrate its superior performance to previously attempted approximations

On the optimal resource allocation in projects considering the time value of money

The optimal resource allocation in stochastic activity networks had been previously developed by applying three different approaches: Dynamic Programming (DP), an Electromagnetism Algorithm (EMA) and an Evolutionary Algorithm (EVA). This paper presents an extension to the initial problem considering the value of money over time. This extended problem was implemented using the Java programming language, an Object Oriented Language, following the approaches previously used (DP, EMA and EVA).Fundação para a Ciência e a Tecnologia (FCT

Algorithms for Performance, Dependability, and Performability Evaluation using Stochastic Activity Networks

Modeling tools and technologies are important for aerospace development. At the University of Illinois, we have worked on advancing the state of the art in modeling by Markov reward models in two important areas: reducing the memory necessary to numerically solve systems represented as stochastic activity networks and other stochastic Petri net extensions while still obtaining solutions in a reasonable amount of time, and finding numerically stable and memory-efficient methods to solve for the reward accumulated during a finite mission time. A long standing problem when modeling with high level formalisms such as stochastic activity networks is the so-called state space explosion, where the number of states increases exponentially with size of the high level model. Thus, the corresponding Markov model becomes prohibitively large and solution is constrained by the the size of primary memory. To reduce the memory necessary to numerically solve complex systems, we propose new methods that can tolerate such large state spaces that do not require any special structure in the model (as many other techniques do). First, we develop methods that generate row and columns of the state transition-rate-matrix on-the-fly, eliminating the need to explicitly store the matrix at all. Next, we introduce a new iterative solution method, called modified adaptive Gauss-Seidel, that exhibits locality in its use of data from the state transition-rate-matrix, permitting us to cache portions of the matrix and hence reduce the solution time. Finally, we develop a new memory and computationally efficient technique for Gauss-Seidel based solvers that avoids the need for generating rows of A in order to solve Ax = b. This is a significant performance improvement for on-the-fly methods as well as other recent solution techniques based on Kronecker operators. Taken together, these new results show that one can solve very large models without any special structure

Stochastic modelling of the effects of interdependencies between critical infrastructure

An approach to Quantitative Interdependency Analysis, in the context of Large Complex Critical Infrastructures, is presented in this paper. A Discrete state–space, Continuous–time, Stochastic Process models the operation of critical infrastructure, taking interdependencies into account. Of primary interest are the implications of both model detail (that is, level of model abstraction) and model parameterisation for the study of dependencies. Both of these factors are observed to affect the distribution of cascade–sizes within and across infrastructure

Simulating the communication of commands and signals in a distribution grid

The report presents the simulation of communication scenarios involving one area control centre and a set of substations inside a distribution grid of the Electrical Power System. In such scenarios, the communication is affected by threats different from those under exam in [1, 2]; in particular, here, we consider the denial of service attack to the communication network, and the temporary internal failure of a subset of substations. The scenarios have been modeled and simulated in form of Stochastic Activity Networks (SAN); the goal is the evaluation of the impact of the threats, on the communication reliability