Wlodzimierz M. Zuberek

Timed Petri nets definitions, properties, and applications

Abstract In timed Petri nets, the transitions fire in “real-time”, i.e., there is a (deterministic or random) firing time associated with each transition, the tokens are removed from input places at the beginning of firing, and are deposited into output places when the firing terminates (they may be considered as remaining “in” the transitions for the firing time). Any “state” description of timed nets must thus take into account the distribution of tokens in places as well as in (firing) transitions, and the state space of timed nets can be quite different from the space of reachable markings. Performance analysis of timed nets is based on stationary probabilities of states. For bounded nets stationary probabilities are determined from a finite set of simultaneous linear equilibrium equations. For unbounded nets the state space is infinite, the set of linear equilibrium equations is also infinite and it must be reduced to a finite set of nonlinear equations for effective solution. Simple examples illustrate capabilities of timed Petri net models.

Timed Petri nets and preliminary performance evaluation

It is shown that the behavior of a certain class of timed Petri nets can be represented by a finite labeled directed graph in which the labels describe times and probabilities of transitions between vertices of the graph. Further analysis of such a graph can be done by techniques known for Markov chains. The method is applied to evaluation of some performance indices for two simple processor architectures. The timed Petri nets modeling the processors are shown and the resulting performance indices are compared. Some other architectures are discussed shortly.

Timed Petri nets in modeling and analysis of cluster tools

Timed Petri nets are used as models of cluster tools representing the flow of wafers through the chambers of the tool as well as sequences of actions performed by the robotic transporter. Since the durations of all activities are also represented in the model, performance characteristics can be derived from the model for steady-state, as well as transient behaviors. The performance of single-blade tools is compared with that of dual-blade tools. The effects of multiple loadlocks, redundant chambers and multiple robots are discussed and, analyzed. Modeling of wafer routings with chamber revisiting and processing of wafers of multiple types is also briefly discussed.

M-timed Petri nets, priorities, preemptions, and performance evaluation of Petri nets

In M-timed Petri nets, firing times are exponentially distributed random variables associated with transitions of a net. Several classes of M-timed Petri nets are discussed in this paper to show increasing “modelling power” of different nets. Conflict-free nets can model M- and E k -type queueing systems. Free-choice nets can also represent H k -type systems. Systems with several classes of users and with service priorities assigned to user classes require nets with inhibitor arcs. Preemption of service can be represented by extended nets with escape (or generalized inhibitor) arcs. Finally, to provide flexible modelling of scheduling and decision strategies, enhanced Petri nets are introduced with two classes of transitions, immediate and timed ones, and with (exponentially distributed) firing times associated with the timed transitions. It is shown that the behavior of bounded M-timed Petri nets can be represented by finite “state” graphs which are finite-state continuous-time homogeneous Markov processes. Stationary probabilities of states can thus be obtained by standard techniques used for analysis of Markov chains, and then operational analysis can be applied for performance evaluation. Simple models of interactive systems are used as an illustration of modelling.

Timed petri nets in modeling and analysis of simple schedules for manufacturing cells

Abstract It is shown that a large class of flexible manufacturing cells can be modeled using timed Petri nets. Net models of simple schedules (i.e., schedules in which exactly one part enters and one leaves the cell during each cycle) are conflict-free nets. Two complementary approaches to analysis of such models are presented: invariant analysis and throughput analysis. Invariant analysis provides analytic (or symbolic) solutions for the cycle time of a cell analyzing (invariant) subnets of the original net. Throughput analysis performs a series of performance-preserving net reductions to simplify the original model. Several directions for further research are indicated.

Temperature dependence of DC currents in HBT

A DC thermal-electrical heterojunction bipolar transistor (HBT) model is presented. Only three parameters were needed to simulate completely an HBT with the self-heating effect. It can be very easily implemented in any CAD software which uses the SPICE bipolar junction transistor model. Parameter extraction has been carried out on measured data and good fits were obtained over a wide temperature range. This model can be used to design high-power heterojunction bipolar transistors and circuits with analysis of their thermal effects.<<ETX>>

Compatibility of Software Components - Modeling and Verification

Component-based software engineering (CBSE) has been emerging as a promising approach to the development of large-scale software architectures in which software components with well-defined interfaces can be quickly assembled into complex software systems. However, assembled components must be compatible in the sense that any sequence of operations requested by one of the interacting components must be provided by the other component(s). Component incompatibility may result in subtle software failures which are difficult to detect and correct. A formal model of component interaction is proposed by representing component behaviors by labeled Petri nets. These net models are designed in such a way that component incompatibility is manifested by deadlocks in the net model of interacting components. Reachability-based as well as structural methods of deadlock detection are discussed. A simple example illustrating the proposed approach is provided

Throughput analysis of manufacturing cells using timed Petri nets

It is shown that a large class of flexible manufacturing cells can be modeled by timed Petri nets. Several net transformations are proposed to simplify the structure of the modeling nets while preserving their performance properties. The throughput of the model can be obtained by applying simple rules of operational analysis to simplified nets. Several extensions of the proposed approach are also indicated.<<ETX>>

Timed Petri Net Models of ATM LANs

The Asynchronous Transfer Mode (ATM) is a fast packet-switching communication method using small fixed-length cells. A model of an ATM LAN is presented which provides a realistic representation of data transmission by modeling both the ATM network and the applications running over it. Colored Petri nets are used to create a compact model that is capable of representing a variety of different protocols at a high level of detail. The model is designed to allow easy reconfiguration or addition of details at different levels of the system. Simulation is used to evaluate the performance of the modeled system, and some results are compared to actual data gathered from the campus network at Memorial University.

Schedules of flexible manufacturing cells and their timed colored Petri net models

It is shown that flexible manufacturing cells can conveniently be represented and evaluated by colored Petri nets in which transitions represent operations performed by the machines of the cell and the transporting robot, tokens represent parts transported by the robot from one machine to another, and the colors are used to indicate different scheduling policies for the same cell.