Performance analysis using timed Petri Nets

Petri Nets have been successfully used to model and evaluate the performance of distributed systems. Several researchers have extended the basic Petri Net model to include time, and have demonstrated that restricted classes of Petri Nets can be analyzed efficiently. Unfortunately, the restrictions prohibit the techniques from being applied to many interesting systems, e.g. communication protocols. This paper proposes a version of timed Petri Nets which accurately models communication protocols, and which can be analyzed using Timed Reachability Graphs. Procedures for constructing and analyzing these graphs are presented. The analysis is shown to be applicable to a larger class of Timed Petri Nets than previously thought. The model and the analysis technique are demonstrated using a simple communication protocol

Timed Petri net models of queueing systems

It is shown that for timed Petri nets with exponentially distributed firing times (M-timed Petri nets), the state space can be generated directly from net specifications, and then the stationary probabilities of states can be obtained by standard methods, developed for analysis of (continuous-time) Markov chains. Numerous performance measures can be derived from stationary probabilities of states. For unbounded nets (models of open network systems are usually unbounded), the state space is infinite. A transformation is thus needed that folds this infinite space into a finite representation, used for effective evaluation of probabilities. The author presents a short theoretical background for performance evaluation using timed Petri nets, followed by several examples of closed and open network models of simple computer systems

Application of timed Petri nets to modeling the schedules of manufacturing cells

Timed Petri nets are proposed as models of simple and composite schedules for a large class of manufacturing cells. Net models of simple schedules can easily be derived from the possible sequences of robot actions. Models of composite schedules can be obtained by different compositions of simple schedules. Timed net models can be evaluated using one of typical methods developed for analysis of timed Petri nets, for example, invariant analysis. Performance characterization (the cycle time or the throughput) obtained in this way can be used for maximization of the cell's performance. Because the number of different schedules grows very quickly with the number of machines as well as the length of the (composite) schedule, colored Petri nets are proposed as a uniform representation of entire classes of schedules. Simple examples illustrate the proposed approach

Performance Analysis of Dataflow Architectures Using Timed Coloured Petri Nets

We present an approach to model dataflow architectures at a high level of abstraction using timed coloured Petri nets. We specifically examine the value of Petri nets for evaluating the performance of such architectures. For this purpose we assess the value of Petri nets both as a modelling technique for dataflow architectures and as an analysis tool that yields valuable performance data for such architectures through the execution of Petri net models. Because our aim is to use the models for performance analysis, we focus on representing the timing and communication behaviour of the architecture rather than the functionality. A modular approach is used to model architectures. We identify five basic hardware building blocks from which Petri net models of dataflow architectures can be constructed. In defining the building blocks we will identify strengths and weaknesses of Petri nets for modelling dataflow architectures. A technique called folding is applied to build generic models of dataflow architectures. A timed coloured Petri net model of the Prophid dataflow architecture, which is being developed at Philips Research Laboratories, is presented. This model has been designed in the tool ExSpect. The performance of the Prophid architecture has been analysed by simulation with this model

Performance Analysis of Stochastic Timed Petri Nets using Linear

Stochastic timed Petri nets are a useful tool in performance analysis of concurrent systems such as parallel computers, communication networks and flexible manufacturing systems. In general, performance measures of stochastic timed Petri nets are difficult to obtain for problems of practical sizes. In this paper, we provide a method to compute efficiently upper and lower bounds for the throughputs and mean token numbers in general Markovian timed Petri nets. Our approach is based on uniformization technique and linear programmin

A Petri Net Tool for Software Performance Estimation Based on Upper Throughput Bounds

Functional and non-functional properties analysis (i.e., dependability, security, or performance) ensures that requirements are fulfilled during the design phase of software systems. However, the Unified Modelling Language (UML), standard de facto in industry for software systems modelling, is unsuitable for any kind of analysis but can be tailored for specific analysis purposes through profiling. For instance, the MARTE profile enables to annotate performance data within UML models that can be later transformed to formal models (e.g., Petri nets or Timed Automatas) for performance evaluation. A performance (or throughput) estimation in such models normally relies on a whole exploration of the state space, which becomes unfeasible for large systems. To overcome this issue upper throughput bounds are computed, which provide an approximation to the real system throughput with a good complexity-accuracy trade-off. This paper introduces a tool, named PeabraiN, that estimates the performance of software systems via their UML models. To do so, UML models are transformed to Petri nets where performance is estimated based on upper throughput bounds computation. PeabraiN also allows to compute other features on Petri nets, such as the computation of upper and lower marking place bounds, and to simulate using an approximate (continuous) method. We show the applicability of PeabraiN by evaluating the performance of a building closed circuit TV system

Performance Analysis of Shared-Memory Bus-Based Multiprocessors Using Timed Petri Nets

In shared-memory bus-based multiprocessors, the number of processors is often limited by the (shared) bus; when the utilization of the bus approaches 100%, processors spend an increasing amount of time waiting to get access to the bus (and shared memory) and this degrades their performance. The limitations imposed by the bus depend upon many parameters, and different parameters affect the performance in different ways. This chapter uses timed Petri nets to model shared-memory bus-based multiprocessors at the instruction execution level and shows how the performance of processors and the system are affected by different modeling parameters. Discrete-event simulation of the developed net models is used to get performance results

Petri Net Simulation of Computer Communications Systems

This thesis presents the design of a simulation method for computer networking systems using timed Petri Nets along with the development of a simulation program based on this method. The use of this simulation program to evaluate the performance of a number of communications systems is described and its suitability as a general-purpose performance evaluation tool for networking systems is discussed. The development of the simulation method arose from the installation within Glasgow Royal Infirmary of a communications network for the transmission of digitised electrocardiograms. This was part of an ongoing project to develop a program for the automatic analysis of electrocardiograms by computer. The networking methodology currently in use on this network was developed using the simulation program. The aim in designing the simulator was to develop a tool which would be of use in simulating as wide a range of systems as possible and to this end a class of Petri net was developed which had a wide range of simulation capabilities, it was further intended that any extensions to the "Classical" Place/Transition net model should be made in such a way that the simplicity of the original model was preserved in as large a measure as possible. During the course of this work, various extensions to the basic Place/Transition net model were indeed made in order to increase the power of the simulation program. Some of these extensions are believed to be unique to the present program, in particular the use of a timed-place scheme. Most current work on timed Petri nets concentrates on timed-transition models as these are easier to implement and analyse; this thesis seeks to show that a timed-place model is viable as a simulation tool and is in many ways preferable to the timed-transition model. To test the range of the simulator, two extra simulation experiments were undertaken in addition to the simulation of the Royal Infirmary network, the first being the evaluation of a simple queueing system and the second the simulation of an Ethernet network. The simulation of the Ethernet network also tested the capability of the timed-place model to handle stochastic Petri net simulations, a type of simulation which is being used increasingly to model computer and networking systems and which is currently dominated by timed-transition models. Descriptions of all three simulation projects are presented along with an analysis of the results of each

The derivation of performance expressions for communication protocols from timed Petri net models

Petri Net models have been extended in a variety of ways and have been used to prove the correctness and evaluate the performance of communication protocols. Several extensions have been proposed to model time. This work uses a form of Timed Petri Nets and presents a technique for symbolically deriving expressions which describe system performance. Unlike past work on performance evaluation of Petri Nets which assumes a priori knowledge of specific time delays, the technique presented here applies to a wide range of time delays so long as the delays satisfy a set of timing constraints. The technique is demonstrated using a simple communication protocol