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

APPLICATION OF TIMED PETRI NETS TO MODELING AND ANALYSIS OF FLEXIBLE MANUFACTURING CELLS

Timed Petri nets are proposed as models of simple and composite schedules for a large class of manufacturing (or robotic) cells. For simple schedules, exactly one part enters and one leaves the cell in each cycle. Net models of simple schedules can easily be derived from the sequences of robot actions. For composite schedules, several parts enter and leave the cell in each cycle. It appears that models of composite schedules can be obtained by composition of simple schedule. A systematic method of deriving all composite schedules is proposed, and decomposition of derived composite schedules into simple ones is presented. It is shown that simple as well as composite schedules can easily be transformed into timed Petri net models. Invariant analysis of timed net models of schedules is used to derive the cycle times of net models. The solutions are obtained in analytical (or symbolic) form, so they are applicable to a wide spectrum of specific cases. Performance characterization (the cycle time or the throughput) obtained in this way can be used for the 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 for a uniform representation and analysis of entire classes of schedules. Simple examples illustrate the proposed approach for a robotic cell with three machines

Composite schedules of manufacturing cells and their timed Petri net models

In composite schedules, several (identical or different) parts enter and leave a manufacturing cell in each cycle. A systematic method of generating all composite schedules is proposed, and it is shown that the generated schedules can easily be transformed into timed Petri net models. Invariant analysis of these timed net models provides performance characteristics of the cell. The characteristics are obtained in analytical (or symbolic) form, so they are applicable to a wide spectrum of specific cases. Simple examples illustrate an application of the proposed approach to a robotic cell with three machines

Hierarchical derivation of Petri net models of composite schedules for manufacturing cells

Composite schedules for manufacturing cells (or robotic cells) are schedules in which several parts enter and leave the cell in each cycle (although the parts which leave the cell are not necessarily the same as the ones that enter the cell). It appears that composite schedules can easily be transformed into timed Petri net models in which the timed transitions represent the actions (including the durations) of the robot and the machines of the cell. Moreover such models can be derived using stepwise refinements of net models. Hierarchical modeling is obtained by systematic application of the refinement steps

A New timed Petri net model for loop scheduling with resource constraints

Projet CHLOEThis report uses timed Petri net to model and analyze the problem of instruction-level loop scheduling with resource constraints, which has been proven to be an NP complete problem. First, we present a new timed Petri net model to integrate loop scheduling, functional unit allocation, register allocation and spilling into a unified theoretical framework. Secondly, we theoretically discuss the schedulability of our model. Thirdly, we develop a state subgraph, called register allocation solution graph, which can effectively describe the major behavior of our new model. The main property of this state subgraph is that the number of all its nodes is polynomial. Finally, we present a timed Petri net based loop scheduling approach with polynomial computation complexity, by which the optimum loop schedules can be found under resource constraints for almost all practical loop programs

Testing real-time systems using TINA

The paper presents a technique for model-based black-box conformance testing of real-time systems using the Time Petri Net Analyzer TINA. Such test suites are derived from a prioritized time Petri net composed of two concurrent sub-nets specifying respectively the expected behaviour of the system under test and its environment.We describe how the toolbox TINA has been extended to support automatic generation of time-optimal test suites. The result is optimal in the sense that the set of test cases in the test suite have the shortest possible accumulated time to be executed. Input/output conformance serves as the notion of implementation correctness, essentially timed trace inclusion taking environment assumptions into account. Test cases selection is based either on using manually formulated test purposes or automatically from various coverage criteria specifying structural criteria of the model to be fulfilled by the test suite. We discuss how test purposes and coverage criterion are specified in the linear temporal logic SE-LTL, derive test sequences, and assign verdicts

Stepwise refinements of net models and their place invariants

Schedules for manufacturing cells can be systematically derived by simple stepwise refinements which, in consecutive steps, increase the complexity of the cell by introducing its components one after another. Timed Petri net models of schedules derived in this way have some convenient structural properties-net models are covered by conflict-free subnets, determined by place invariants of the model. These place invariant implied subnets can be used for evaluation of the basic performance characteristics of the model. The paper shows that place invariants of net models of schedules can be obtained by the same stepwise refinements that are used for model derivation. Simple examples of performance evaluation are included as an illustration of the use of place invariants in the analysis of schedules

Hybrid algorithm for scheduling and risk assessment of projects

IFAC CONFERENCE ON ANALYSIS AND DESIGN OF HYBRID SYSTEMS (.2003.SAINT-MALO BRITTANY, FRANCIA)This work presents a technique for optimal scheduling of projects in terms of time and cost, taking into account risk assessment. Tasks are characterized by p-timed Petri nets, where places have assigned an execution time. The proposed technique minimizes the time execution and the cost of the whole project taking into account the Petri nets describing the tasks and the project risk assessment plan. The risk mitigation is carried on through actions where variables that model them may be discrete or continuousMinisterio de Ciencia y Tecnología DPI200 1-2380-C02-0

A Compositional Approach for Schedulability Analysis of Distributed Avionics Systems

This work presents a compositional approach for schedulability analysis of Distributed Integrated Modular Avionics (DIMA) systems that consist of spatially distributed ARINC-653 modules connected by a unified AFDX network. We model a DIMA system as a set of stopwatch automata in UPPAAL to verify its schedulability by model checking. However, direct model checking is infeasible due to the large state space. Therefore, we introduce the compositional analysis that checks each partition including its communication environment individually. Based on a notion of message interfaces, a number of message sender automata are built to model the environment for a partition. We define a timed selection simulation relation, which supports the construction of composite message interfaces. By using assume-guarantee reasoning, we ensure that each task meets the deadline and that communication constraints are also fulfilled globally. The approach is applied to the analysis of a concrete DIMA system.Comment: In Proceedings MeTRiD 2018, arXiv:1806.09330. arXiv admin note: text overlap with arXiv:1803.1105