A survey of stochastic modelling approaches for liberalised electricity markets

Liberalisation of energy markets, climate policy and the promotion of renewable energy have changed the framework conditions of the formerly strictly regulated energy markets. Generating companies are mainly affected by these changing framework conditions as they are exposed to the different risks from liberalised energy markets in combination with huge and largely irreversible investments. Uncertainties facing generating companies include: the development of product prices for electricity as well as for primary energy carriers; technological developments; availability of power plants; the development of regulation and political context, as well as the behaviour of competitors.     

Perturbation analysis of communication networks with feedback control using stochastic hybrid models

Communication networks may be abstracted through Stochastic Fluid Models (SFM) with the node dynamics described by switched flow equations as various events take place, thus giving rise to hybrid automaton models with stochastic transitions. The inclusion of feedback mechanisms complicates these dynamics. In a tandem setting, a typical feedback mechanism is the control of a node processing rate as a threshold-based function of the downstream node’s buffer level. We consider the problem of controlling the threshold parameters so as to optimize performance metrics involving average workload and packet loss and show how Infinitesimal Perturbation Analysis (IPA) can be used to analyze congestion propagation through a network and develop gradient estimators of such metrics.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

The advantage of small machines in a stochastic fluid production process

We consider a stochastic fluid production model, where m machines which are subject to breakdown and repair, produce a fluid at ratep > 0 per machine if it is working. This fluid is fed into an infinite buffer with stochastic output rate. Under the assumption that the machine processes are independent and identically distributed, we prove that the buffer content at timet is less or equal in the increasing convex ordering to the buffer content at time t of a model withm m machines and production ratep =m/m p. This formulation includes a conjecture posed by Mitra [6]. More-over, it is shown how to extend this result to Brownian flow systems, systems obtained by diffusion approximation and simple stochastic flow networks like tandem buffer and assembly systems.     

Equation-Free multiscale computational analysis of individual-based epidemic dynamics on networks

The surveillance, analysis and ultimately the efficient long-term prediction and control of epidemic dynamics appear to be some of the major challenges nowadays. Detailed individual-based mathematical models on complex networks play an important role towards this aim. In this work, it is shown how one can exploit the Equation-Free approach and optimization methods such as Simulated Annealing to bridge detailed individual-based epidemic models with coarse-grained, system-level analysis within a pair-wise representation perspective. The proposed computational methodology provides a systematic approach for analyzing the parametric behavior of complex/multiscale epidemic simulators much more efficiently than simply simulating forward in time. It is shown how steady state and (if required) time-dependent computations, stability computations, as well as continuation and numerical bifurcation analysis can be performed in a straightforward manner. The approach is illustrated through a simple individual-based SIRS epidemic model deploying on a random regular connected graph. Using the individual-based simulator as a black box coarse-grained timestepper and with the aid of Simulated Annealing I compute the coarse-grained equilibrium bifurcation diagram and analyze the stability of the stationary states sidestepping the necessity of obtaining explicit closures at the macroscopic level.     

Mathematical modelling and analysis of temperature effects in MEMS

This article is concerned with the mathematical analysis of models for Micro-Electro-Mechanical Systems (MEMS). These models arise in the form of coupled partial differential equations with a moving boundary. Although MEMS devices are often operated in non-isothermal environments, temperature is often neglected in the mathematical investigations. In light of this finding the focus of our modelling is to incorporate temperature and the related material properties. We derive a full model for this coupling and discuss a simplified version as well. Lastly, we prove local well-posedness in time and also global well-posedness under additional assumptions on the model’s parameters.     

Probabilistic qualification of attack in abstract argumentation

An argument graph is a graph where each node denotes an argument, and each arc denotes an attack by one argument on another. It offers a valuable starting point for theoretical analysis of argumentation following the proposals by Dung. However, the definition of an argument graph does not take into account the belief in the attacks. In particular, when constructing an argument graph from informal arguments, where each argument is described in free text, it is often evident that there is uncertainty about whether some of the attacks hold. This might be because there is some expressed doubt that an attack holds or because there is some imprecision in the language used in the arguments. In this paper, we use the set of spanning subgraphs of an argument graph as a sample space. A spanning subgraph contains all the arguments, and a subset of the attacks, of the argument graph. We assign a probability value to each spanning subgraph such that the sum of the assignments is 1. This means we can reflect the uncertainty over which is the actual subgraph using this probability distribution. Using the probability distribution over subgraphs, we can then determine the probability that a set of arguments is admissible or an extension. We can also obtain the probability of an attack relationship in the original argument graph as a marginal distribution (i.e. it is the sum of the probability assigned to each subgraph containing that attack relationship). We investigate some of the features of this proposal, and we consider the utility of our framework for capturing some practical argumentation scenarios.     

On modeling failure and repair times in stochastic models of manufacturing systems using generalized exponential distributions

Failures of machines have a significant effect on the behavior of manufacturing systems. As a result it is important to model this phenomenon. Many queueing models of manufacturing systems do incorporate the unreliability of the machines. Most models assume that the times to failure and the times to repair of each machine are exponentially distributed (or geometrically distributed in the case of discrete-time models). However, exponential distributions do not always accurately represent actual distributions encountered in real manufacturing systems. In this paper, we propose to model failure and repair time distributions bygeneralized exponential (GE) distributions (orgeneralized geometric distributions in the case of a discretetime model). The GE distribution can be used to approximate distributions with any coefficient of variation greater than one. The main contribution of the paper is to show that queueing models in which failure and repair times are represented by GE distributions can be analyzed with the same complexity as if these distributions were exponential. Indeed, we show that failures and repair times represented by GE distributions can (under certain assumptions) be equivalently represented by exponential distributions.This work was performed while the author was visiting the Laboratory for Manufacturing and Productivity, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.     

A new multicriteria approach for the analysis of efficiency in the Spanish olive oil sector by modelling decision maker preferences

The efficiency in production is often analysed as technical efficiency using the production frontier function. Efficiency scores are usually based on distance computations to the frontier in an m + s-dimensional space, where m inputs produce s outputs. In addition, efficiency improvements consider the total consumption of each input. However, in many cases, the “consumption” of each input can be divided into input-consumption sections (ICSs), and trade-off among the ICSs is possible. This share framework can be used for computing efficiency. This analysis provides information about both the total optimal consumption of each input, as does data envelopment analysis, and the most efficient allocation of the “consumption” among the ICSs. This paper studies technical efficiency using this approach and applies it to the olive oil sector in Andalusia (Spain). A non-parametrical methodology is presented, and an input-oriented Multi-Criteria Linear Programming model (MLP) is proposed. The analysis is developed at global, input and ICSs levels, defining the extent of satisfaction achieved at all these levels for each company, in accordance with their own preferences. The companies’ preferences are modelled with their utility function and their set of weights. MLP offers more detailed information to assist decision makers than other models previously proposed in the literature. In addition to this application, it is concluded that there is room for improvement in the olive oil sector, particularly in the management of the skilled labour. Additionally, the solutions with two opposite scenarios indicate that the model is suitable for the intended decision making process.