Performance evaluation of marked graphs by linear programming

Petri nets have traditionally been motivated by their ability to express concurrency. Subclasses of Petri nets with concurrency but without choices or conflicts have been studied extensively. One of the best known - and comparatively restricted - such class are the marked graphs [4]. However, perhaps the largest class of (intuitively) choice-free nets are the persistent nets [7], a class of nets that is significantly larger than marked graphs. Some early results about persistent nets are Keller's theorem [6], which will be recalled in a later part of this paper, and the famous semilinearity result of Landweber and Robertson [7], which states that the set of reachable markings of a persistent net is semilinear. In this paper, we show that in bounded persistent nets, the smallest cycles of its reachability graph enjoy a uniqueness property.

This chapter introduces six subclasses of Petri nets that are of beautiful structures: state machines, marked graphs, free-choice nets, asymmetric-choice nets, weakly persistent nets and normal nets. On the basis of their structural characteristics, some perfect conditions can be provided to decide some important properties such as their liveness and reachability.

The traditional models of distributed computing systems employ the mathematical formalisms of discrete event dynamical systems along with Petri Nets. However, such models are complex to analyze and computationally expensive. Interestingly, the evolving distributed computing systems closely resemble the discrete dynamical systems. This paper constructs and analyzes the model of distributed computing systems by applying mathematical formalisms of the discrete dynamical systems. The proposed model embeds the partial ordering of states under happened-before relation in the set of globally observable states. The stability of the proposed model is analyzed using the first order linear approximation.

With the rapid development of computer science, there are more and more kinds of discrete dynamic systems. Computer integrated system CIMS, network communication database administrator system, and human behavior analysis system are all discrete dynamic systems. At present, many researchers have studied by adding human behavior data to discrete dynamic systems. This paper aims to study the behavior data of English learners by using the discrete dynamic modeling technology of complex systems and the discrete dynamic system modeling method of Petri nets. By adding the behavior data of learners to the discrete dynamic system of fuzzy Petri nets, the system is diagnosed and optimized. The experimental results show that the complex discrete dynamic system in this paper has achieved good experimental results according to the performance indicators selected in theory. Based on the combination of the above technologies and systems, the fuzzy Petri net discrete dynamic system studied in this paper improves the processing speed of English learners' behavior data.

Consider a discrete dynamical system given by a square matrix $M \in \mathbb{Q}^{d \times d}$ and a starting point $s \in \mathbb{Q}^d$. The orbit of such a system is the infinite trajectory $\langle s, Ms, M^2s, \ldots\rangle$. Given a collection $T_1, T_2, \ldots, T_m \subseteq \mathbb{R}^d$ of semialgebraic sets, we can associate with each $T_i$ an atomic proposition $P_i$ which evaluates to true at time $n$ if, and only if, $M^ns \in T_i$. This gives rise to the LTL Model-Checking Problem for discrete linear dynamical systems: given such a system $(M,s)$ and an LTL formula over such atomic propositions, determine whether the orbit satisfies the formula. The main contribution of the present paper is to show that the LTL Model-Checking Problem for discrete linear dynamical systems is decidable in dimension 3 or less.

For many of us, modern-day linear programming (LP) started with the work of George Dantzig in 1947. However, it must be said that many other scientists have also made seminal contributions to the subject, and some would argue that the origins of LP predate Dantzig’s contribution. It is matter open to debate [36]. However, what is not open to debate is Dantzig’s key contribution to LP computation. In contrast to the economists of his time, Dantzig viewed LP not just as a qualitative tool in the analysis of economic phenomena, but as a method that could be used to compute actual answers to specific real-world problems. Consistent with that view, he proposed an algorithm for solving LPs, the simplex algorithm [12]. To this day the simplex algorithm remains a primary computational tool in linear and mixed-integer programming (MIP). In [11] it is reported that the first application of Dantzig’s simplex algorithm to the solution of a non-trivial LP was Laderman’s solution of a 21 constraint, 77 variable instance of the classical Stigler Diet Problem [41]. It is reported that the total computation time was 120 man-days! The first computer implementation of an at-least modestly general version of the simplex algorithm is reported to have been on the SEAC computer at the then National Bureau of Standards [25]. (There were apparently some slightly earlier implementations for dealing with models that were “triangular”, that is, where all the linear systems could be solved by simple addition and subtraction.) Orchard-Hays [35] reports that several small instances having as many as 10 constraints and 20 variables were solved with this implementation. The first systematic development of computer codes for the simplex algorithm began very shortly thereafter at the RAND Corporation in Santa Monica, California. Dantzig’s initial LP work occurred at the Air Force following

This textbook provides a broad introduction to continuous and discrete dynamical systems. With its hands-on approach, the text leads the reader from basic theory to recently published research material in nonlinear ordinary differential equations, nonlinear optics, multifractals, neural networks, and binary oscillator computing. Dynamical Systems with Applications Using Python takes advantage of Python’s extensive visualization, simulation, and algorithmic tools to study those topics in nonlinear dynamical systems through numerical algorithms and generated diagrams. After a tutorial introduction to Python, the first part of the book deals with continuous systems using differential equations, including both ordinary and delay differential equations. The second part of the book deals with discrete dynamical systems and progresses to the study of both continuous and discrete systems in contexts like chaos control and synchronization, neural networks, and binary oscillator computing. These later sections are useful reference material for undergraduate student projects. The book is rounded off with example coursework to challenge students’ programming abilities and Python-based exam questions. This book will appeal to advanced undergraduate and graduate students, applied mathematicians, engineers, and researchers in a range of disciplines, such as biology, chemistry, computing, economics, and physics. Since it provides a survey of dynamical systems, a familiarity with linear algebra, real and complex analysis, calculus, and ordinary differential equations is necessary, and knowledge of a programming language like C or Java is beneficial but not essential.

We describe the destabilizing (in the sense of a decrease in the reserve of mean-square asymptotic stability) effect of random parametric perturbations of the white-noise type in quasilinear continuous and discrete dynamical systems (Lur’e-Postnikov systems of automatic control with nonlinear feedback). We use stochastic Lyapunov functions in the form of linear combinations of the types “a quadratic form of phase coordinates plus the integral of a nonlinearity” (continuous systems) and “a quadratic form of phase coordinates plus the integral sum for a nonlinearity” (discrete systems) and the matrix algebraic Sylvester equations associated with stochastic Lyapunov functions of this form.

Starts with a brief review of the history and the application areas considered in the literature. The author then proceeds with introductory modeling examples, behavioral and structural properties, three methods of analysis, subclasses of Petri nets and their analysis. In particular, one section is devoted to marked graphs, the concurrent system model most amenable to analysis. Introductory discussions on stochastic nets with their application to performance modeling, and on high-level nets with their application to logic programming, are provided. Also included are recent results on reachability criteria. Suggestions are provided for further reading on many subject areas of Petri nets.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A class of synchronized queueing networks with deterministic routing is identified to be equivalent to a subclass of timed Petri nets called marked graphs. Some structural and behavioral properties of marked graphs are used to show interesting properties of this class of performance models. In particular, ergodicity is derived from the boundedness and liveness of the underlying Petri net representation. In the case of unbounded (i.e., nonstrongly connected) marked graphs, ergodicity is computed as a function of the average transition firing delays. For steady-state performance, linear programming problems defined on the incidence matrix of the underlying Petri nets are used to compute tight (i.e., attainable) bounds for the throughput of transitions for marked graphs with deterministic or stochastic time associated with transitions. These bounds depend on the initial marking and the mean values of the delays but not on the probability distortion functions. The benefits of interleaving qualitative and quantitative analysis of marked graph models are shown. >

To fully understand a system is to fully understand its performance in its intended environment. The system can be a logic gate, an algorithm, a computer, an operating system, or a computer network. The scale covered by these systems is huge, extending from switches at nano (molecular) scale to communication systems at astronomical scales. The problems posed in performance evaluation are often extremely difficult, a fact that has strong implications for those who create systems: If a system's performance is hard to evaluate, then the system will be hard to understand; this fact has had less influence on system designers than one might hope for. We risk only slight exaggeration by likening the behavior of 100,000 lines of code to that of an emotional primate, common emotions being obstinacy and crankiness. (Will performance analysis merge with psychoanalysis?So our field of performance measurement, modeling, and evaluation is at the heart of all engineering and applied science. It is strong and vibrant, as it must be, and its practitioners are driven, enthusiastic researchers, educators, and managers; the papers in the proceedings to follow are among their latest contributions to the field's collective wisdom, particularly in the computer and network engineering sciences.The authors of the papers herein are to be congratulated for having met the increasingly stiff standards of the program committees (PCs) of SIGMETRICS and the IFIP Working Group 7.3. On the other side of the coin, the PC members, especially the Program Co-Chairs Zhen Liu and Arif Merchant, deserve our gratitude for their tireless efforts in putting together an outstanding program of presentations; special thanks in the present context go to Yefim Shuf for seeing to the production of these proceedings. The chair takes this opportunity to thank the other members of the organizing committee for their selfless and skillful work on all aspects of conference organization: Vishal Misra (local arrangements - and much more), Li Zhang (tutorials, student support), Sambit Sahu (finance), Jason Nieh (publicity), Philippe Nain (student support), a late addition, and finally our web guys Hanhua Feng and Angelos Stavrou. The chair owes particular thanks to all, as dealing with him (another cranky primate), has not always been easy.

For soil elements surrounding the foundations of offshore wind turbines or oil platforms, very many loading cycles of varying amplitudes and frequencies are quite common. The influence of such cyclic loadings on the soil stiffness is a critical concern in the evaluation of the long-term performance of the foundation-structure system during its service life. Current understanding of this influence is however inadequate due to the scarcity of experimental data. This study investigates the variation of small-strain shear modulus (G0) of saturated Toyoura sand subjected to cyclic torsional shear stress cycles with a small amplitude by using a RC/TS apparatus. Sand specimens of different densities have been tested. It is found that the G0 value tends to decrease with loading cycles and the decrease is mainly associated with the initial loading cycles. When the number of cycles is beyond around 3500, the G0 value tends to become stable. The degree of reduction of G0 is not sensitive to the density of sand specimen and is generally within 10% for the range of densities investigated.KeywordsDynamic propertiesElastic stiffnessSaturated sandLong-term cyclic loadings

This paper considers cycle slipping of discrete phase-controlled system with periodic nonlinearity. The number of slipped cycles is an important characteristic of such nonlinear system. Based on Yakubovich-Kalman Lemma which establishes the equivalence between frequency domain inequalities (FDIs) and linear matrix inequalities (LMIs), the conditions of estimating the number of slipped cycles are derived. Then dynamic output feedback controller is designed to guarantee the nonexistence of cycle slipping. As a result, the transient performance of discrete phase-controlled system is improved. A concrete application to impulse phase-locked loop (PLL) shows the applicability and validity of the proposed approach.

When designing a system-on-chip (SOC), a network-on-chip (NOC) paradigm is the backbone of used interconnection, but in recent years, with a great improvement in silicon technology and the ability to implement billions of transistors on a wafer, it sounds that wire-based communication is not efficient any longer, therefore designers intend to replace wireless transferring data methodology instead. In the following, we show how the performance of the wireless network is improved with subnet extension. This paper focuses on the evaluation of delay and throughput which are two important factors in network proficiency. In fact, to enhance the performance of the system, we need to reduce the number of delay cycles and improve the throughput, therefore to keep balance between these two parameters, designer has to adjust the packet injection rate (PIR) in a safe margin such that it does not exceed a certain point in each state, otherwise delay is uncontrollable, thus it is required to clearly identify the take-off points. About the designer also has to be informed purpose for which the system is going to be designed. It strictly depends on whether high throughput or low delay cycle is desirable. Subnet extension is a way to achieve this target. Here, totally three networks with the number of cores 64, 512 and 1024 have been selected, respectively. The effect of subnet extension is evaluated on each one. The behavior of each network with different number of subnets and IPs is studied. Obtained results from the simulator for different ranges of PIR and subnets are significant. To emphasize, we highlight the take-off points for the delay cycles and the points which does not cross the PIR level. Performance evaluation is conducted based on flit-accurate and open source system C simulator BookSim.

A practical method for the overall performance evaluation of a GPC system (columns) is described. System performance is defined as the ability of the system to give experimental M̄n and M̄w values (uncorrected for instrumental spreading and other distorting factors) which agree with the theoretical values, and it is expressed as the per cent deviation between the theoretical and experimental values. The method consists of running blends of monodispersed polystyrene standards of known compositions through the GPC system to be evaluated. From the resulting chromatograms, their M̄n and M̄w values are calculated (experimental). The theoretical M̄n and M̄w values of the same standards are also calculated from the formulas on the basis of their composition. By plotting the per cent difference of the experimental values from the theoretical values versus the theoretical values on a semilog scale, the overall performance of the GPC system under investigation is pictorially depicted. Results indicate that performance under experimental conditions can vary significantly from system to system. Results also indicate that performance of a system can be improved and optimized by proper column selection and system modifications.