Lucia Cloth

Model checking performability properties

Model checking has been introduced as an automated technique to verify whether functional properties, expressed in a formal logic like computational tree logic (CTL), do hold in a formally-specified system. We present a number of computational procedures to perform model checking of continuous stochastic reward logic (CSRL) over finite Markov reward models, thereby stressing their computational complexity (time and space) and applicability from a practical point of view (accuracy, stability). A case study in the area of ad hoc mobile computing under power constraints shows the merits of CSRL and the new computational procedures.

Model Checking Markov Chains with Actions and State Labels

In the past, logics of several kinds have been proposed for reasoning about discrete-time or continuous-time Markov chains. Most of these logics rely on either state labels (atomic propositions) or on transition labels (actions). However, in several applications it is useful to reason about both state properties and action sequences. For this purpose, we introduce the logic as CSL which provides a powerful means to characterize execution paths of Markov chains with actions and state labels. asCSL can be regarded as an extension of the purely state-based logic CSL (continuous stochastic logic). In asCSL, path properties are characterized by regular expressions over actions and state formulas. Thus, the truth value of path formulas depends not only on the available actions in a given time interval, but also on the validity of certain state formulas in intermediate states. We compare the expressive power of CSL and asCSL and show that even the state-based fragment of asCSL is strictly more expressive than CSL if time intervals starting at zero are employed. Using an automaton-based technique, an asCSL formula and a Markov chain with actions and state labels are combined into a product Markov chain. For time intervals starting at zero, we establish a reduction of the model checking problem for asCSL to CSL model checking on this product Markov chain. The usefulness of our approach is illustrated with an elaborate model of a scalable cellular communication system, for which several properties are formalized by means of asCSL formulas and checked using the new procedure

Model checking for survivability

Business and social life have become increasingly dependent on large-scale communication and information systems. A partial or complete breakdown as a consequence of natural disasters or purposeful attacks might have severe impacts. Survivability refers to the ability of a system to recover from such disaster circumstances. Evaluating survivability should therefore be an important part of communication system design. In this paper we take a model checking approach toward assessing survivability. We use the logic CSL to phrase survivability in a precise manner. The system operation is modelled through a labelled CTMC. Model checking algorithms can then decide automatically whether the system is survivable. We illustrate our method by evaluating the survivability of the Google file system using stochastic Petri nets.

MeanField analysis for the evaluation of gossip protocols

Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, that tend to be expensive in computation time and memory consumption. We employ mean-¿eld approximation for an analytical evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic models. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to in¿nity, however, mean-¿eld analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.

Computing Battery Lifetime Distributions

The usage of mobile devices like cell phones, navigation systems, or laptop computers, is limited by the lifetime of the included batteries. This lifetime depends naturally on the rate at which energy is consumed, however, it also depends on the usage pattern of the battery. Continuous drawing of a high current results in an excessive drop of residual capacity. However, during intervals with no or very small currents, batteries do recover to a certain extend. We model this complex behaviour with an inhomogeneous Markov reward model, following the approach of the so-called kinetic battery model (KiBaM). The state-dependent reward rates thereby correspond to the power consumption of the attached device and to the available charge, respectively. We develop a tailored numerical algorithm for the computation of the distribution of the consumed energy and show how different workload patterns influence the overall lifetime of a battery.

Model checking action- and state-labelled Markov chains

In this paper we introduce the logic asCSL, an extension of continuous stochastic logic (CSL), which provides powerful means to characterise execution paths of action- and state-labelled Markov chains. In asCSL, path properties are characterised by regular expressions over actions and state-formulas. Thus, the executability of a path not only depends on the available actions but also on the validity of certain state formulas in intermediate states. Our main result is that the model checking problem for asCSL can be reduced to CSL model checking on a modified Markov chain, which is obtained through a product automaton construction. We provide a case study of a scalable cellular phone system which shows how the logic asCSL and the model checking procedure can be applied in practice.

Model checking Markov reward models with impulse rewards

This paper considers model checking of Markov reward models (MRMs), continuous-time Markov chains with state rewards as well as impulse rewards. The reward extension of the logic CSL (continuous stochastic logic) is interpreted over such MRMs, and two numerical algorithms are provided to check the reachability of a set of goal states under a time and an accumulated reward constraint. This extends existing model-checking techniques for MRMs with just state rewards, and improves the applicability to thousands of states. Our approach is illustrated by using rewards for energy consumption in the setting of dynamic power management.

Mean-Field Analysis for the Evaluation of Gossip Protocols

Gossip protocols are designed to operate in very large, decentralised networks. A node in such a network bases its decision to interact (gossip) with another node on its partial view of the global system. Because of the size of these networks, analysis of gossip protocols is mostly done using simulations, that tend to be expensive in computation time and memory consumption. We employ mean-?eld approximation for an analytical evaluation of gossip protocols. Nodes in the network are represented by small identical stochastic models. Joining all nodes would result in an enormous stochastic process. If the number of nodes goes to in?nity, however, mean-?eld analysis allows us to replace this intractably large stochastic process by a small deterministic process. This process approximates the behaviour of very large gossip networks, and can be evaluated using simple matrix-vector multiplications.

Performability assessment by model checking of Markov reward models

This paper describes efficient procedures for model checking Markov reward models, that allow us to evaluate, among others, the performability of computer-communication systems. We present the logic CSRL (Continuous Stochastic Reward Logic) to specify performability measures. It provides flexibility in measure specification and paves the way for the numerical evaluation of a wide variety of performability measures. The formal measure specification in CSRL also often helps in reducing the size of the Markov reward models that need to be numerically analysed. The paper presents background on Markov-reward models, as well as on the logic CSRL (syntax and semantics), before presenting an important duality result between reward and time. We discuss CSRL model-checking algorithms, and present five numerical algorithms and their computational complexity for verifying time- and reward-bounded until-properties, one of the key operators in CSRL. The versatility of our approach is illustrated through a performability case study.

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.