Andrea Marin

Petri nets for modelling metabolic pathways: a survey

In the last 15 years, several research efforts have been directed towards the representation and the analysis of metabolic pathways by using Petri nets. The goal of this paper is twofold. First, we discuss how the knowledge about metabolic pathways can be represented with Petri nets. We point out the main problems that arise in the construction of a Petri net model of a metabolic pathway and we outline some solutions proposed in the literature. Second, we present a comprehensive review of recent research on this topic, in order to assess the maturity of the field and the availability of a methodology for modelling a metabolic pathway by a corresponding Petri net.

Exploiting product forms solution techniques in multiformalism modeling

Multiformalism modeling has shown to be a valuable technique to cope with the complexity of the constraints that apply to specifications of computer-based systems state of the art. Multiformalism techniques help modelers and designers by providing a more (natural and) convenient approach in the specification process and in analysis of performance. Although their application does not necessarily provide an advantage in the solutions of the models, this paper shows how a compositional multiformalism modeling approach can leverage the power of product-form solutions to offer both efficient solution and specification of models for complex systems.

A general result for deriving product-form solutions in markovian models

In this paper we provide a general method to derive product-form solutions for stochastic models. We take inspiration from the Reversed Compound Agent Theorem and we provide a different formulation using labeled automata, a generalization which encompasses a bigger class of product-form solutions, and a new proof based on the solution of the system of global balance equations. We show that our result may have practical applications in the performance evaluation of complex software and hardware architectures and can be the base for the development of new analysis tools or the extension of existing ones.

Interconnected Wireless Sensors with Energy Harvesting

This paper studies interconnected wireless sensors with the paradigm of Energy Packet Networks (EPN) which were previously introduced. In the EPN model, both data transmissions and the flow of energy are discretized, so that an energy packet (EP) is the minimum amount of energy (say in microjules) that is needed to process and transmit a data packet (DP) or to process a job. Previous work has modeled such systems to determine the relation between energy flow and DP transmission, or to study the balance between energy and the processing of jobs in Cloud Servers. The lack of energy, in addition to processing times, is the main source of latency in networks of sensor nodes. Thus this paper models this phenomenon, and shows that under some reasonable conditions, assuming feedforward flow of data packets and local consumption and leakage of energy, such networks have product form solutions.

On the Relations between Lumpability and Reversibility

In the literature devoted to the efficient solution of Continuous Time Markov Chains (CTMCs) the notions of lump ability and reversibility have a central role. In the context of lump able Markov chains several definitions have been introduced: strong, exact and strict, just to mention a few of them. On the side of the analysis of reversible CTMCs the research community has shown great interest in the application of this notion with the aim of efficiently computing the stationary distribution of large models (e.g., obtained by composition of several processes). In this paper we show for the first time the relations between the above mentioned notions of lump ability and the concept of reversibility. The major outcome of our research is proving a strong connection between the notion of strict lump ability and that of reversibility.

A probabilistic energy-aware model for mobile ad-hoc networks

We propose a probabilistic, energy-aware, broadcast calculus for the analysis of mobile ad-hoc networks. The semantics of our model is expressed in terms of Segalas probabilistic automata driven by schedulers to resolve the nondeterministic choice among the probability distributions over target states. We develop a probabilistic observational congruence and a energy-aware preorder semantics. The observational congruence allows us to verify whether two networks exhibit the same observable probabilistic behaviour (connectivity), while the preorder is used to compare the energy consumption of different, but behaviourally equivalent, networks. As an application, we analyse and compare the energy consumption of two well-known automatic repeat request (ARQ)- based error control protocols: stop-and-wait (SW) and go-back-N (GBN).

Performance engineering with product-form models: efficient solutions and applications

Performance engineering plays a pivotal role in the successful design of software system and the software development process. Stochastic modelling has been widely applied to predict and evaluate or estimate system performance. We consider the specification of models in terms of compositions of simpler components and their efficient solution. Various formalisms or classes of stochastic models have been applied for system performance engineering and evaluation. These formalisms includes queueing networks, Stochastic Petri Nets, and Stochastic Process Algebras. Their dynamic behaviour can be usually represented by an underlying stochastic (Markov) process. For each formalism some classes of product-form models have been identified, starting from the first remarkable results for BCMP queueing networks. For some product-form models various efficient algorithms have been defined. We discuss the problem of identifying and characterize classes of product-form models. We compare the properties of the various modeling formalisms, their solution and the combination of product-form (sub)models into a heterogeneous model. We illustrate the application of product-form stochastic models for system performance engineering with some examples of tools for the solution of heterogeneous models formed by synchronized sub-models, and some practical applications.

Separable solutions for Markov processes in random environments

In this paper we address the problem of efficiently deriving the steady-state distribution for a continuous time Markov chain (CTMC) S evolving in a random environment E. The process underlying E is also a CTMC. S is called Markov modulated process. Markov modulated processes have been widely studied in literature since they are applicable when an environment influences the behaviour of a system. For instance, this is the case of a wireless link, whose quality may depend on the state of some random factors such as the intensity of the noise in the environment. In this paper we study the class of Markov modulated processes which exhibits separable, product-form stationary distribution. We show that several models that have been proposed in literature can be studied applying the Extended Reversed Compound Agent Theorem (ERCAT), and also new product-forms are derived. We also address the problem of the necessity of ERCAT for product-forms and show a meaningful example of product-form not derivable via ERCAT.

Behavioural equivalences and interference metrics for mobile ad-hoc networks

Connectivity and communication interference are two key aspects in mobile ad-hoc networks (MANETs). This paper proposes a process algebraic model targeted at the analysis of both such aspects. The framework includes a probabilistic process calculus and a suite of analytical techniques based on a probabilistic observational congruence and an interference-sensitive preorder. The former enables the verification of behavioural equivalences; the latter makes it possible to evaluate the interference level of behaviourally equivalent networks. The result is a comprehensive and effective framework for the behavioural analysis and a quantitative assessment of interference for wireless networks in the presence of node mobility. We show our techniques at work on two realistic case studies.

Interference-Sensitive Preorders for MANETs

Connectivity and communication interference are two key aspects in mobile ad-hoc networks (MANETs). We propose a process algebraic model targeted at the analysis of both such aspects of MANETs. The framework includes a probabilistic process calculus and a suite of analytical techniques based on a probabilistic observational congruence and an interference-sensitive preorder. The observational congruence allows us to verify whether two networks exhibit the same behaviour. The preorder makes it possible to evaluate the interference level of different, behaviourally equivalent, networks. We show our framework at work on the analysis of the well-known Alternating Bit Protocol, contrasting the behavior of the standard implementation of the protocol against an alternative implementation that exploits an ideal interference cancellation scheme for CDMA transmissions.