Artur Rataj

A Translator of Java Programs to TADDs

The model checking tools Uppaal and VerICS accept a description of a network of Timed Automata with Discrete Data (TADDs) as input. Thus, to verify a concurrent programwritten in Java by means of these tools, first a TADD model of the program must be build. Therefore, we have developed the J2TADD tool that translates a Java program to a network of TADDs; the paper presents this tool. The J2TADD tool works in two stages. The first one consists in translation of a Java code to an internal assembly language (IAL). Then, the resulting assembly code is translated to a network of TADDs. We exemplify the use of the translator by means of the following well-known concurrency examples written in Java: race condition problem, dining philosophers problem, single sleeping barber problem and readers and writers problem.

A Study of IP Router Queues with the Use of Markov Models

We investigate the use of Markov chains in modeling the queues inside IP routers. The model takes into account the measured size of packets, i.e. collected histogram is represented by a linear combination of exponentially distributed phases. We discuss also the impact of the distribution of IP packets size on the loss probability resulting from the limited size of a router memory buffer. The model considers a self similar traffic generated by on-off sources. A special interest is paid to the duration of a queue transient state following the changes of traffic intensity as a function of traffic Hurst parameter and of the utilization of the link. Our goal is to see how far, taking into account the known constraints of Markov models (state explosion) we are able to refine the queueing model.

A Queueing Model of the Edge Node in IP over All-Optical Networks

The high demand for more bandwidth and high speed networks stimulates research in the design, optimization and performance evaluation of IP over all-optical networks. In this paper we study optical packet filling algorithm applied at ingress nodes of an all-optical network. Arriving electronic packets of variable sizes are stored at a buffer the volume of which is equal to the fixed size of optical packet. When the available space in the buffer is less than the size of an arriving packet, the stored already content of the buffer is sent inside the optical packet and the electronic packet is rescheduled for the next filling cycle. To avoid excessive delays, the optical packet is dispatched also after a specified deadline whatever is the (non-null) content of the buffer. The performance metrics we consider comprises the filling of optical packets (that means the ratio of blocks in the packet to the actual constant size of the packet) and the distribution of optical packets interdeparture times. The paper demonstrates that the variability of the size of arriving packets and the self-similarity of the input traffic have a visible impact on the both parameters.

Delays in IP Routers, a Markov Model

Delays in routers are an important component of end-to-end delay and therefore have a significant impact on quality of service. While the other component, the propagation time, is easy to predict as the distance divided by the speed of light inside the link, the queueing delays of packets inside routers depend on the current, usually dynamically changing congestion and on the stochastic features of the flows. We use a Markov model taking into account the distribution of the size of packets and self-similarity of incoming flows to investigate their impact on the queueing delays and their dynamics.

Indefinite waitings in MIRELA systems.

MIRELA is a high-level language and a rapid prototyping framework dedicated to systems where virtual and digital objects coexist in the same environment and interact in real time. Its semantics is given in the form of networks of timed automata, which can be checked using symbolic methods. This paper shows how to detect various kinds of indefinite waitings in the components of such systems. The method is experimented using the PRISM model checker.

Solving Large Markov Models Described with Standard Programming Language

Continuous time Markov chains (CTMC) are one of the formalisms for building models. This paper discusses OLYMP2 - a system for solving big CTMC models (exceeding \(10^9\) states), described with a standard programming language - Java. OLYMP2 is primarily aimed at modelling of computer networks, so its formalism comes from networking concepts, like queueing systems. Using Java as a model description allows for greater flexibility in comparison to model-checker specific languages that often do not employ complete features of an object-oriented programming. Using Java also makes the parsing of models relatively fast, due to optimised Java run-time environment. Introducing dedicated compression of transition matrices allows for keeping memory usage at reasonable level even for large models.

Extrapolation of an Optimal Policy using Statistical Probabilistic Model Checking

We show how to extrapolate an optimal policy controlling a model, which is itself too large to find the policy directly using probabilistic model checking (PMC). In particular, we look for a global optimal resolution of non–determinism in several small Markov Decision Processes (MDP) using PMC. We then use the resolution to find a respective set of decision boundaries representing the optimal policies found. Then, a hypothesis is formed on an extrapolation of these boundaries to an equivalent boundary in a large MDP. The resulting hypothetical extrapolated decision boundary is statistically approximately verified, whether it indeed represents an optimal policy for the large MDP. The verification either weakens or strengthens the hypothesis. The criterion of the optimality of the policy can be expressed in any modal logic that includes the probabilistic operator P∼p[·], and for which a PMC method exists.

A Queueing Model of an Insurance Database Interactive System, Comparison of Modelling Methods

The article presents a queueing model of a computer network which is installed at a branch of the largest Polish insurance company. The network is used to store and use documents related to company clients. Our model concentrates on the database server and applications used to retrieve and modify the documents. The model is based on measurements gathered in this system. Our goal is twofold: (i) elaborate a tool that is able to predict the performance of the system in case of modifications (more terminals, more servers) (ii) compare the usefulness of several analytical methods implemented in this case-study.

Modelling and Analysing Mixed Reality Applications

Mixed reality systems overlay real data with virtual information in order to assist users in their current task. They generally combine several hardware components operating at different time scales, and software that has to cope with these timing constraints. MIRELA, for MIxed REality LAnguage, is a framework aimed at modelling, analysing and implementing systems composed of sensors, processing units, shared memories and rendering loops, communicating in a well-defined manner and submitted to timing constraints. The framework is composed of (i) a language allowing a high level, and partially abstract, specification of a concurrent real–time system, (ii) the corresponding semantics, which defines the translation of the system to concrete networks of timed automata, (iii) a methodology for analysing various real-time properties, and (iv) an implementation strategy. We present here a summary of several of our papers about this framework, as well as some recent extensions concerning probability and non–deterministic choices.