Timed reachability analysi

Behrmann, G., Larsen, K.G., Pearson, J., et al. (1999) Efficient Timed Reachability Analysis Using Clock Difference Diagrams. Proceedings of CAV 99, Springer, Berlin, pp. 341-353. 

Scheduling Based on Reachability Analysis of Timed Automata... 

TA are used to model and analyze dynamic systems with discrete and timed behavior. One of their strengths is the easy modeling in a decomposed fashion as a set of often small and individually acting automata. Time in TA is modeled in a very natural way by a set of clocks that simply measure the time between events. This is a major difference to MIP techniques, where time and dynamic components are described in a rather artificial way by providing variables and inequalities for every point of time within a discretized time horizon. In addition to the advantages in modeling, TA serve as a computational model which can be analyzed by techniques for reachability analysis. These techniques are widely used in the context of verification, in which the objective is to detect possible undesired (bad or forbidden) behaviors [9-11]. The success of these techniques was pushed by the availability and increasing performance of tools for TA, e.g., Uppaal [9, 10, 12, 13]. 

A recent and very promising application of the reachability analysis of TA is scheduling. This development, however, required the introduction of the notion of cost. In contrast to the verification of whether a behavior fulfills a specification or not, costs introduce a quantitative measure to evaluate the individual behaviors. Successful applications of priced TA [15, 16] by using the standard and a special version of Uppaal are documented in [17-19]. The first application to deterministic job-shop scheduling was published by Abdeddaim [20] and Abdeddaim and Maler [21], In order to further motivate the use of TA, the next section shows how the schedule in Figure 10.2 and the plant on which the operations are scheduled naturally translate into a set of timed automata. 

Keywords Batch plants, scheduling, timed automata, reachability analysis. 

Recently, the approach to solve scheduling problems by reachability analysis for timed automata has gained great attention. The framework of TA has been originally proposed... 

Molecular reinforcement is affected by the consequent translation of fiber reinforcement to the molecular level. At the same time, in composite science and technology, it is well known that the mechanical performance of a composite material depends on two main factors, namely, the aspect ratio of the reinforcing component and the adhesion quality between matrix and reinforcement. Analysis of the mechanical data, as well as the superior reachable aspect ratio of single stiff molecules, identifies single molecule fibers as the limit of materials aimed at fiber reinforcement. Lindenmeyer [1] explained the concept of molec-... 

DFT Analysis. DFTCalc can compute a number of different reliability metrics, namely all metrics that can be expressed as reachability properties in the logic CSL. This includes properties such as (1) Timed-Reliability the probability that the system fails until a given time point T or in a given interval [T, T ] (2) Mean time to failure the expected time to a system failure (3) Reliability the probability that the system fails in the long-run. In case of non-determinism, we calculate the minimum and maximum values for the above metrics. Each of these properties can either be evaluated from the initial state (i.e. the system is fully functional), or by setting evidence (i.e certain components have failed already). 

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