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

Analysis of Petri Nets and Transition Systems

This paper describes a stand-alone, no-frills tool supporting the analysis of (labelled) place/transition Petri nets and the synthesis of labelled transition systems into Petri nets. It is implemented as a collection of independent, dedicated algorithms which have been designed to operate modularly, portably, extensibly, and efficiently.Comment: In Proceedings ICE 2015, arXiv:1508.0459

Recent advances in petri nets and concurrency

CEUR Workshop Proceeding

Decidability Issues for Petri Nets

This is a survey of some decidability results for Petri nets, covering the last three decades. The presentation is structured around decidability of specific properties, various behavioural equivalences and finally the model checking problem for temporal logics

Verification of soundness and other properties of business processes

In this thesis we focus on improving current modeling and verification techniques for complex business processes. The objective of the thesis is to consider several aspects of real-life business processes and give specific solutions to cope with their complexity. In particular, we address verification of a proper termination property for workflows, called generalized soundness. We give a new decision procedure for generalized soundness that improves the original decision procedure. The new decision procedure reports on the decidability status of generalized soundness and returns a counterexample in case the workflow net is not generalized sound. We report on experimental results obtained with the prototype implementation we made and describe how to verify large workflows compositionally, using reduction rules. Next, we concentrate on modeling and verification of adaptive workflows — workflows that are able to change their structure at runtime, for instance when some exceptional events occur. In order to model the exception handling properly and allow structural changes of the system in a modular way, we introduce a new class of nets, called adaptive workflow nets. Adaptive workflow nets are a special type of Nets in Nets and they allow for creation, deletion and transformation of net tokens at runtime and for two types of synchronizations: synchronization on proper termination and synchronization on exception. We define some behavioral properties of adaptive workflow nets: soundness and circumspectness and employ an abstraction to reduce the verification of these properties to the verification of behavioral properties of a finite state abstraction. Further, we study how formal methods can help in understanding and designing business processes. We investigate this for the extended event-driven process chains (eEPCs), a popular industrial business process language used in the ARIS Toolset. Several semantics have been proposed for EPCs. However, most of them concentrated solely on the control flow. We argue that other aspects of business processes must also be taken into account in order to analyze eEPCs and propose a semantics that takes data and time information from eEPCs into account. Moreover, we provide a translation of eEPCs to Timed Colored Petri nets in order to facilitate verification of eEPCs. Finally, we discuss modeling issues for business processes whose behavior may depend on the previous behavior of the process, history which is recorded by workflow management systems as a log. To increase the precision of models with respect to modeling choices depending on the process history, we introduce history-dependent guards. The obtained business processes are called historydependent processes.We introduce a logic, called LogLogics for the specification of guards based on a log of a current running process and give an evaluation algorithm for such guards. Moreover, we show how these guards can be used in practice and define LogLogics patterns for properties that occur most commonly in practice

Approximation methods for stochastic petri nets

Stochastic Marked Graphs are a concurrent decision free formalism provided with a powerful synchronization mechanism generalizing conventional Fork Join Queueing Networks. In some particular cases the analysis of the throughput can be done analytically. Otherwise the analysis suffers from the classical state explosion problem. Embedded in the divide and conquer paradigm, approximation techniques are introduced for the analysis of stochastic marked graphs and Macroplace/Macrotransition-nets (MPMT-nets), a new subclass introduced herein. MPMT-nets are a subclass of Petri nets that allow limited choice, concurrency and sharing of resources. The modeling power of MPMT is much larger than that of marked graphs, e.g., MPMT-nets can model manufacturing flow lines with unreliable machines and dataflow graphs where choice and synchronization occur. The basic idea leads to the notion of a cut to split the original net system into two subnets. The cuts lead to two aggregated net systems where one of the subnets is reduced to a single transition. A further reduction leads to a basic skeleton. The generalization of the idea leads to multiple cuts, where single cuts can be applied recursively leading to a hierarchical decomposition. Based on the decomposition, a response time approximation technique for the performance analysis is introduced. Also, delay equivalence, which has previously been introduced in the context of marked graphs by Woodside et al., Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's method and flow equivalent aggregation are applied to the aggregated net systems. The experimental results show that response time approximation converges quickly and shows reasonable accuracy in most cases. The convergence of Marie's is slower, but the accuracy is generally better. Delay equivalence often fails to converge, while flow equivalent aggregation can lead to potentially bad results if a strong dependence of the mean completion time on the interarrival process exists

Verification and synthesis of asynchronous control circuits using petri net unfoldings

PhD ThesisDesign of asynchronous control circuits has traditionally been associated with application of formal methods. Event-based models, such as Petri nets, provide a compact and easy to understand way of specifying asynchronous behaviour. However, analysis of their behavioural properties is often hindered by the problem of exponential growth of reachable state space. This work proposes a new method for analysis of asynchronous circuit models based on Petri nets. The new approach is called PN-unfolding segment. It extends and improves existing Petri nets unfolding approaches. In addition, this thesis proposes a new analysis technique for Signal Transition Graphs along with an efficient verification technique which is also based on the Petri net unfolding. The former is called Full State Graph, the latter - STG-unfolding segment. The boolean logic synthesis is an integral part of the asynchronous circuit design process. In many cases, even if the verification of an asynchronous circuit specification has been performed successfully, it is impossible to obtain its implementation using existing methods because they are based on the reachability analysis. A new approach is proposed here for automated synthesis of speed-independent circuits based on the STG-unfolding segment constructed during the verification of the circuit's specification. Finally, this work presents experimental results showing the need for the new Petri net unfolding techniques and confirming the advantages of application of partial order approach to analysis, verification and synthesis of asynchronous circuits.The Research Committee, Newcastle University: Overseas Research Studentship Award

Service substitution : a behavioral approach based on Petri Nets

Service-Oriented Computing is an emerging computing paradigm that supports the modular design of (software) systems. Complex systems are designed by composing less complex systems, called services. Such a (complex) system is a distributed application often involving several cooperating enterprises. As a system usually changes over time, individual services will be substituted by other services. Substituting one service by another one should not affect the correctness of the overall system. Assuring correctness becomes particularly challenging, as the services rely on each other, and each of the involved enterprises only oversees a part of the overall system. In addition, services communicate asynchronously which makes the analysis even more difficult. For this reason, formal methods to support service substitution are indispensable. In this thesis, we study service substitution at the level of service models. Thereby we restrict ourselves to service behavior. As a formalism to model service behavior, we use Petri nets. The first contribution of this thesis is the definition of several substitutability criteria that are suitable in the context of Service-Oriented Computing. Substituting a service S by a service S0 should preserve some behavioral properties of the overall system. For each set of behavioral properties and a given service S, there exists a set of behaviorally compatible services for S. A substitutability criterion defines which of these behaviorally compatible services of S have to be preserved by S0. We relate our substitutability criteria to preorders and equivalences known from process theory. The second contribution of this thesis is to present, for each substitutability criterion, a procedure to decide whether a service S0 can substitute a service S. The decision requires the comparison of the in general infinite sets of behaviorally compatible services for the services S and S0. Hence, we extend existing work on an abstract representation of all behaviorally compatible services for a given service. For each notion of behavioral compatibility, we present an algorithmic solution to represent all behaviorally compatible services. Based on these representations, we can decide substitutability of a service S by a service S0. The third contribution of this thesis is a method to support the design of a service S0 that can substitute a service S according to a substitutability criterion. Our approach is to derive a service S0 from the service S by stepwise transformation. To this end, we present several transformation rules. Finally, we formalize and we extend the equivalence notion for services specified in the language WS-BPEL. That way, we demonstrate the applicability of our work