Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

A case study in model-driven synthetic biology

We report on a case study in synthetic biology, demonstrating the modeldriven design of a self-powering electrochemical biosensor. An essential result of the design process is a general template of a biosensor, which can be instantiated to be adapted to specific pollutants. This template represents a gene expression network extended by metabolic activity. We illustrate the model-based analysis of this template using qualitative, stochastic and continuous Petri nets and related analysis techniques, contributing to a reliable and robust design

Reliability models for dataflow computer systems

The demands for concurrent operation within a computer system and the representation of parallelism in programming languages have yielded a new form of program representation known as data flow (DENN 74, DENN 75, TREL 82a). A new model based on data flow principles for parallel computations and parallel computer systems is presented. Necessary conditions for liveness and deadlock freeness in data flow graphs are derived. The data flow graph is used as a model to represent asynchronous concurrent computer architectures including data flow computers

Performance Bounds for Synchronized Queueing Networks

Las redes de Petri estocásticas constituyen un modelo unificado de las diferentes extensiones de redes de colas con sincronizaciones existentes en la literatura, válido para el diseño y análisis de prestaciones de sistemas informáticos distribuidos. En este trabajo se proponen técnicas de cálculo de cotas superiores e inferiores de las prestaciones de redes de Petri estocásticas en estado estacionario. Las cotas obtenidas son calculables en tiempo polinómico en el tamaño del modelo, por medio de la resolución de ciertos problemas de programación lineal definidos a partir de la matriz de incidencia de la red (en este sentido, las técnicas desarrolladas pueden considerarse estructurales). Las cotas calculadas dependen sólamente de los valores medios de las variables aleatorias que describen la temporización del sistema, y son independientes de los momentos de mayor orden. Esta independencia de la forma de las distribuciones de probabilidad asociadas puede considerarse como una útil generalización de otros resultados existentes para distribuciones particulares, puesto que los momentos de orden superior son, habitualmente, desconocidos en la realidad y difíciles de estimar. Finalmente, las técnicas desarrolladas se aplican al análisis de diferentes ejemplos tomados de la literatura sobre sistemas informáticos distribuidos y sistemas de fabricación. ******* Product form queueing networks have long been used for the performance evaluation of computer systems. Their success has been due to their capability of naturally expressing sharing of resources and queueing, that are typical situations of traditional computer systems, as well as to their efficient solution algorithms, of polynomial complexity on the size of the model. Unfortunately, the introduction of synchronization constraints usually destroys the product form solution, so that general concurrent and distributed systems are not easily studied with this class of models. Petri nets have been proved specially adequate to model parallel and distributed systems. Moreover, they have a well-founded theory of analysis that allows to investigate a great number of qualitative properties of the system. In the original definition, Petri nets did not include the notion of time, and tried to model only the logical behaviour of systems by describing the causal relations existing among events. This approach showed its power in the specification and analysis of concurrent systems in a way independent of the concept of time. Nevertheless the introduction of a timing specification is essential if we want to use this class of models for the performance evaluation of distributed systems. One of the main problems in the actual use of timed and stochastic Petri net models for the quantitative evaluation of large systems is the explosion of the computational complexity of the analysis algorithms. In general, exact performance results are obtained from the numerical solution of a continuous time Markov chain, whose dimension is given by the size of the state space of the model. Structural computation of exact performance measures has been possible for some subclasses of nets such as those with state machine topology. These nets, under certain assumptions on the stochastic interpretation are isomorphic to Gordon and Newell's networks, in queueing theory terminology. In the general case, efficient methods for the derivation of performance measures are still needed. Two complementary approaches to the derivation of exact measures for the analysis of distributed systems are the utilization of approximation techniques and the computation of bounds. Approximate values for the performance parameters are in general more efficiently derived than the exact ones. On the other hand, "exactness" only exists in theory! In other words, numerical algorithms must be applied in practice for the computation of exact values, therefore making errors is inevitable. Performance bounds are useful in the preliminary phases of the design of a system, in which many parameters are not known accurately. Several alternatives for those parameters should be quickly evaluated, and rejected those that are clearly bad. Exact (and even approximate) solutions would be computationally very expensive. Bounds become useful in these instances since they usually require much less computation effort. The computation of upper and lower bounds for the steady-state performance of timed and stochastic Petri nets is considered in this work. In particular, we study the throughput of transitions, defined as the average number of firings per time unit. For this measure we try to compute upper and lower bounds in polynomial time on the size of the net model, by means of proper linear programming problems defined from the incidence matrix of the net (in this sense, we develop structural techniques). These bounds depend only on the mean values and not on the higher moments of the probability distribution functions of the random variables that describe the timing of the system. The independence of the probability distributions can be viewed as a useful generalization of the performance results, since higher moments of the delays are usually unknown for real cases, and difficult to estimate and assess. From a different perspective, the obtained results can be applied to the analysis of queueing networks extended with some synchronization schemes. Monoclass queueing networks can be mapped on stochastic Petri nets. On the other hand, stochastic Petri nets can be interpreted as monoclass queueing networks augmented with synchronization primitives. Concerning the presentation of this manuscript, it should be mentioned that chapter 1 has been written with the object of giving the reader an outline of the stochastic Petri net model: its definition, terminology, basic properties, and related concepts, together with its deep relation with other classic stochastic network models. Chapter 2 is devoted to the presentation of the net subclasses considered in the rest of the work. The classification presented here is quite different from the one which is usual in the framework of Petri nets. The reason lies on the fact that our classification criterion, the computability of visit ratios for transitions, is introduced for the first time in the field of stochastic Petri nets in this work. The significance of that criterion is based on the important role that the visit ratios play in the computation of upper and lower bounds for the performance of the models. Nevertheless, classical important net subclasses are identified here in terms of the computability of their visit ratios from different parameters of the model. Chapter 3 is concerned with the computation of reachable upper and lower bounds for the most restrictive subclass of those presented in chapter 2: marked graphs. The explanation of this fact is easy to understand. The more simple is the model the more accessible will be the techniques an ideas for the development of good results. Chapter 4 provides a generalization for live and bounded free choice nets of the results presented in the previous chapter. Quality of obtained bounds is similar to that for strongly connected marked graphs: throughput lower bounds are reachable for bounded nets while upper bounds are reachable for 1-bounded nets. Chapter 5 considers the extension to other net subclasses, like mono-T-semiflow nets, FRT-nets, totally open deterministic systems of sequential processes, and persistent nets. The results are of diverse colours. For mono-T-semiflow nets and, therefore, for general FRT-nets, it is not possible (so far) to obtain reachable throughput bounds. On the other hand, for bounded ordinary persistent nets, tight throughput upper bounds are derived. Moreover, in the case of totally open deterministic systems of sequential processes the exact steady-state performance measures can be computed in polynomial time on the net size. In chapter 6 bounds for other interesting performance measures are derived from throughput bounds and from classical queueing theory laws. After that, we explore the introduction of more information from the probability distribution functions of service times in order to improve the bounds. In particular, for Coxian service delay of transitions it is possible to improve the throughput upper bounds of previous chapters which held for more general forms of distribution functions. This improvement shows to be specially fruitful for live and bounded free choice nets. Chapter 7 is devoted to case studies. Several examples taken from literature in the fields of distributed computing systems and manufacturing systems are modelled by means of stochastic Petri nets and evaluated using the techniques developed in previous chapters. Finally, some concluding remarks and considerations on possible extensions of the work are presented

Structural translation from time petri nets to timed automata

International audienceIn this paper, we consider Time Petri Nets (TPN) where time is associated with transitions. We give a formal semantics for TPNs in terms of Timed Transition Systems. Then, we propose a translation from TPNs to Timed Automata (TA) that preserves the behavioral semantics (timed bisimilarity) of the TPNs. For the theory of TPNs this result is two-fold: i) reachability problems and more generally TCTL model-checking are decidable for bounded TPNs; ii) allowing strict time constraints on transitions for TPNs preserves the results described in i). The practical appli- cations of the translation are: i) one can specify a system using both TPNs and Timed Automata and a precise semantics is given to the composition; ii) one can use existing tools for analyzing timed automata (like Kronos, Uppaal or Cmc) to analyze TPNs. In this paper we describe the new feature of the tool Romeo that implements our translation of TPNs in the Uppaal input format. We also report on experiments carried out on various examples and compare the result of our method to state-of-the-art tool for analyzing TPNs

Integrated Modeling and Verification of Real-Time Systems through Multiple Paradigms

Complex systems typically have many different parts and facets, with different characteristics. In a multi-paradigm approach to modeling, formalisms with different natures are used in combination to describe complementary parts and aspects of the system. This can have a beneficial impact on the modeling activity, as different paradigms an be better suited to describe different aspects of the system. While each paradigm provides a different view on the many facets of the system, it is of paramount importance that a coherent comprehensive model emerges from the combination of the various partial descriptions. In this paper we present a technique to model different aspects of the same system with different formalisms, while keeping the various models tightly integrated with one another. In addition, our approach leverages the flexibility provided by a bounded satisfiability checker to encode the verification problem of the integrated model in the propositional satisfiability (SAT) problem; this allows users to carry out formal verification activities both on the whole model and on parts thereof. The effectiveness of the approach is illustrated through the example of a monitoring system.Comment: 27 page

Mapping RT-LOTOS specifications into Time Petri Nets

RT-LOTOS is a timed process algebra which enables compact and abstract specification of real-time systems. This paper proposes and illustrates a structural translation of RT-LOTOS terms into behaviorally equivalent (timed bisimilar) finite Time Petri nets. It is therefore possible to apply Time Petri nets verification techniques to the profit of RT-LOTOS. Our approach has been implemented in RTL2TPN, a prototype tool which takes as input an RT-LOTOS specification and outputs a TPN. The latter is verified using TINA, a TPN analyzer developed by LAAS-CNRS. The toolkit made of RTL2TPN and TINA has been positively benchmarked against previously developed RT-LOTOS verification tool

Read Operators and their Expressiveness in Process Algebras

We study two different ways to enhance PAFAS, a process algebra for modelling asynchronous timed concurrent systems, with non-blocking reading actions. We first add reading in the form of a read-action prefix operator. This operator is very flexible, but its somewhat complex semantics requires two types of transition relations. We also present a read-set prefix operator with a simpler semantics, but with syntactic restrictions. We discuss the expressiveness of read prefixes; in particular, we compare them to read-arcs in Petri nets and justify the simple semantics of the second variant by showing that its processes can be translated into processes of the first with timed-bisimilar behaviour. It is still an open problem whether the first algebra is more expressive than the second; we give a number of laws that are interesting in their own right, and can help to find a backward translation.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407