Region-Based Analysis of Hybrid Petri Nets with a Single General One-Shot Transition

Recently, hybrid Petri nets with a single general one-shot transition (HPnGs) have been introduced together with an algorithm to analyze their underlying state space using a conditioning/deconditioning approach. In this paper we propose a considerably more efficient algorithm for analysing HPnGs. The proposed algorithm maps the underlying state-space onto a plane for all possible firing times of the general transition s and for all possible systems times t. The key idea of the proposed method is that instead of dealing with infinitely many points in the t-s-plane, we can partition the state space into several regions, such that all points inside one region are associated with the same system state. To compute the probability to be in a specific system state at time τ, it suffices to find all regions intersecting the line t = τ and decondition the firing time over the intersections. This partitioning results in a considerable speed-up and provides more accurate results. A scalable case study illustrates the efficiency gain with respect to the previous algorithm

Fitting a code-red virus spread model: An account of putting theory into practice

This paper is about fitting a model for the spreading of a computer virus to measured data, contributing not only the fitted model, but equally important, an account of the process of getting there. Over the last years, there has been an increased interest in epidemic models to study the speed of virus spread. But parameterising such models is hard, because due to the unexpected nature of real outbreaks, there is not much solid measurement data available, and the data may often have imperfections. We propose a mean-field model for computer virus spread, and use parameter fitting techniques to set the model's parameter values based on measured data. We discuss a number of steps that had to be taken to make the fitting work, including preprocessing and interpreting the measurement data, and restructuring the model based on the available data. We show that the resulting parameterised model closely mimics real system behaviour, with a relative squared error of 0.7%

Model Checking Structured Infinite Markov Chains

In the past probabilistic model checking hast mostly been restricted to finite state models. This thesis explores the possibilities of model checking with continuous stochastic logic (CSL) on infinite-state Markov chains. We present an in-depth treatment of model checking algorithms for two special classes of infinite-state CTMCs: (i) Quasi-birth-death processes (QBDs) are a special class of infinite-state CTMCs that combines a large degree of modeling expressiveness with efficient solution methods. (ii) Jackson queuing networks (JQNs) are a very general class of queueing networks that find their application in a variety of settings. The state space of the CTMC that underlies a JQN, is highly structured, however, of infinite size in as many dimensions as there are queues, whereas the underlying state-space of a QBD can be seen as infinite in one dimension. Using a new property-driven independency concept that is adapted to QBDs and JQNs, accordingly, we provide model checking algorithms for all the CSL operators. Special emphasis is given to the time-bounded until operator for which we present a new and efficient computational procedure named uniformization with representatives. By the use of an application-driven dynamic termination criterion, the algorithms stop whenever the property to be checked can be certified (or falsified). Next to the above methodological contributions of this thesis, we also use the new techniques for an extended case study on bottlenecks in wireless two-hop ad hoc networks. The results of our analysis are compared with extensive simulations and show excellent agreement for throughput, mean number of active sources and mean buffer occupancy at the bottleneck station

Exploratory GIS modelling for assessing potential conflict in Australia's central desert region

This paper presents a simple methodology (preliminary and exploratory) to model potential hotspots of land-users' conflict at regional level in preparation of a dispute system design. Australia's central desert region is chosen and modelled in terms of four independent variables - Aboriginal communities, National Parks land, Pastoral lease and Tourism site, and one dependent variable - Strength of Interest. Preparation of the data is detailed in nine steps. Analysis takes place in two forms: overlays and statistical summary. Overlaying two coverages reveals potential conflict by demonstrating which interests have overlapping zones of interest. These zones are divided into areas of Strong, Medium, Weak and No Interest. Three insights from this method of analysis are discussed. Simple statistical summarization describes the conflict potential from the perspective of each respective group of interests and two insights are discussed. An unexpected insight was gained through this process showing potential conflict within groups of interest as well. Through this modelling exercise it is determined that a simple GIS application can produce significant insights in preparing a dispute systems design

Survivability analysis of a sewage treatment facility using hybrid Petri nets

Waste water treatment facilities clean sewage water from households and industry in several cleaning steps. Such facilities are dimensioned to accommodate a maximum intake. However, in the case of very bad weather conditions or failures of system components, the system might not be able to accommodate all waste water. This paper models a real waste water treatment facility, situated in the city of Enschede, the Netherlands, with Hybrid Petri nets with general transitions, to analyse under which circumstances the existing infrastructure will overflow. Comparing to previous models an structural extension is proposed, and one limitation is tackled. First, we extended the hybrid Petri net formalism with guard arcs and dynamic continuous transitions, to be able to model dependencies on continuous places and the rates of continuous transitions. Secondly, we tackle the restriction of having only a single general transition, by proposing a new discretization method. We introduce to different discretization methods, and compare their efficiency in a complex case study. Using recently developed algorithms for model checking STL properties on hybrid Petri nets, the paper computes survivability measures that can be expressed using the path-based until operator. After computing measures for a wide range of parameters, we provide recommendations as to where the system can be improved to reduce the probability of overflow

An analytical model for beaconing in VANETs

IEEE 802.11 CSMA/CA is generally considered to be well-understood, and many detailed models are available. However, most models focus on Unicast in small-scale W-LAN scenarios. When modelling beaconing in VANETs, the Broadcast nature and the (potentially) large number of nodes cause phenomena specific to large-scale broadcast scenarios not captured in present models of the 802.11 DCF. In a VANET scenario, transmissions from coordinated nodes are performed in so-called Streaks, without intermediate backoff counter decrement. We adapt the model by Engelstad and Østerbø and provide several improvements specific to VANET beaconing. The resulting analytical model is shown to have good fit with simulation results