Anne Katharina Ingrid Remke

CSL model checking algorithms for QBDs

We present an in-depth treatment of model checking algorithms for a class of infinite-state continuous-time Markov chains known as quasi-birth death processes. The model class is described in detail, as well as the logic CSL to express properties of interest. Using a new property-independency concept, 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 stopping criterion, the algorithm stops whenever the property to be checked can be certified (or falsified). A comprehensive case study of a connection management system shows the versatility of our new algorithms.

Hybrid Petri Nets with General One-Shot Transitions for Dependability Evaluation of Fluid Critical Infrastructures

A hybrid Petri net formalism that is specifically tailored towards so-called fluid critical infrastructures is introduced, allowing for timed, generally distributed and fluid transitions. Such models are analyzed with Parametric Reachability Analysis, by separating the deterministic and the stochastic evolution of the system. Several performance metrics, such as the distribution of fluid over time, can be derived by deconditioning according to arbitrary continuous probability distributions. This efficient concept allows for the analysis of an arbitrary number of fluid places, as opposed to classical stochastic hybrid Petri net approaches. Moreover, validation of our results against the FSPN tool shows that parametric reachability analysis provides more accurate results. A case study motivates and shows the feasibility of our approach.

Survivability Evaluation of Fluid Critical Infrastructures Using Hybrid Petri Nets

In this paper we propose a formal, model-checking based procedure to evaluate the survivability of fluid critical infrastructures. To do so, we introduce the Stochastic Time Logic (STL), which allows to precisely express intricate state-based and until-based properties for an important class of hybrid Petri nets. We present an efficient model checking procedure which recursively traverses the underlying state-space of the hybrid Petri net model, and identifies those regions (subsets of the discrete-continuous state space) that satisfy STL formulae. A case study studying the survivability of a water refinery and distribution plant shows the feasibility of our approach.

A logic for model-checking mean-field models

Recently the mean-field method has been adopted for analysing systems consisting of a large number of interacting objects in computer science, biology, chemistry, etc. It allows for a quick and accurate analysis of such systems, while avoiding the state-space explosion problem. So far, the method has primarily been used for performance evaluation. In this paper, we use the mean-field method for model-checking. We define and motivate a logic MF-CSL for describing properties of systems composed of many identical interacting objects. The proposed logic allows describing both properties of the overall system and of a random individual object. Algorithms to check the satisfaction relation for all MF-CSL operators are proposed. Furthermore, we explain how the set of all time instances that fulfill a given MF-CSL formula for a certain distribution of objects can be computed.

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.

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.

Evaluating repair strategies for a water-treatment facility using Arcade

The performance and dependability of critical infrastructures, such as water-treatment facilities is essential. In this paper we use various performance and dependability measures to analyze a simplified model of a water treatment facility. Building on the existing architectural framework Arcade a model is derived in XML format and then automatically mapped to the model checker PRISM. Using the stochastic model checking capabilities that PRISM offers, we compare different repair strategies, with respect to their costs, system reliability, availability and survivability. For this case study we conclude that using non-preemtive priority scheduling with additional repair crews is the best choice with respect to performance, dependability and costs.

Energy Resilience Modelling for Smart Houses

The use of renewable energy in houses and neighbourhoods is very much governed by national legislation and has recently led to enormous changes in the energy market and poses a serious threat to the stability of the grid at peak production times. One of the approaches towards a more balanced grid is, e.g., taken by the German government by subsidizing local storage for solar power. While the main interest of the energy operator and the government is to balance the grid, thereby ensuring its stability, the main interest of the client is twofold: the total cost for electricity should be as low as possible and the house should be as resilient as possible in the presence of power outages. Using local battery storage can help to overcome the effects of power outages. However, the resulting resilience highly depends on the battery usage strategy employed by the controller, taking into account the state of charge of the battery. We present a Hybrid Petri net model of a house (that is mainly powered by solar energy) with a local storage unit, and analyse the impact of different battery usage strategies on its resilience for different production and consumption patterns. Our analysis shows that there is a direct relationship between resilience and flexibility, since increased resilience, i.e., reserving battery capacity for backup, decreases the flexibility of the storage unit.

Survivability Evaluation of Gas, Water and Electricity Infrastructures

The infrastructures used in cities to supply power, water and gas are consistently becoming more automated. As society depends critically on these cyber-physical infrastructures, their survivability assessment deserves more attention. In this overview, we first touch upon a taxonomy on survivability of cyber-physical infrastructures, before we focus on three classes of infrastructures (gas, water and electricity) and discuss recent modelling and evaluation approaches and challenges.

Model checking infinite-state markov chains

In this paper algorithms for model checking CSL (continuous stochastic logic) against infinite-state continuous-time Markov chains of so-called quasi birth-death type are developed. In doing so we extend the applicability of CSL model checking beyond the recently proposed case for finite-state continuous-time Markov chains, to an important class of infinite-state Markov chains. We present syntax and semantics for CSL and develop efficient model checking algorithms for the steady-state operator and the time-bounded next and until operator. For the former, we rely on the so-called matrix-geometric solution of the steady-state probabilities of the infinite-state Markov chain. For the time-bounded until operator we develop a new algorithm for the transient analysis of infinite-state Markov chains, thereby exploiting the quasi birth-death structure. A case study shows the feasibility of our approach.