Parametric Schedulability Analysis of Fixed Priority Real-Time Distributed Systems

Parametric analysis is a powerful tool for designing modern embedded systems, because it permits to explore the space of design parameters, and to check the robustness of the system with respect to variations of some uncontrollable variable. In this paper, we address the problem of parametric schedulability analysis of distributed real-time systems scheduled by fixed priority. In particular, we propose two different approaches to parametric analysis: the first one is a novel technique based on classical schedulability analysis, whereas the second approach is based on model checking of Parametric Timed Automata (PTA). The proposed analytic method extends existing sensitivity analysis for single processors to the case of a distributed system, supporting preemptive and non-preemptive scheduling, jitters and unconstrained deadlines. Parametric Timed Automata are used to model all possible behaviours of a distributed system, and therefore it is a necessary and sufficient analysis. Both techniques have been implemented in two software tools, and they have been compared with classical holistic analysis on two meaningful test cases. The results show that the analytic method provides results similar to classical holistic analysis in a very efficient way, whereas the PTA approach is slower but covers the entire space of solutions.Comment: Submitted to ECRTS 2013 (http://ecrts.eit.uni-kl.de/ecrts13

Genetic Algorithm Combined with Gradient Information for Flexible Job-shop Scheduling Problem with Different Varieties and Small Batches

To solve the Flexible Job-shop Scheduling Problem (FJSP) with different varieties and small batches, a modified meta-heuristic algorithm based on Genetic Algorithm (GA) is proposed in which gene encoding is divided into process encoding and machine encoding, and according to the encoding mode, the machine gene fragment is connected with the process gene fragment and can be changed with the alteration of process genes. In order to get the global optimal solutions, the crossover and mutation operation of the process gene fragment and machine gene fragment are carried out respectively. In the initialization operation, the machines with shorter manufacturing time are more likely to be chosen to accelerate the convergence speed and then the tournament selection strategy is applied due to the minimum optimization objective. Meanwhile, a judgment condition of the crossover point quantity is introduced to speed up the population evolution and as an important interaction bridge between the current machine and alternative machines in the incidence matrix, a novel mutation operation of machine genes is proposed to achieve the replacement of manufacturing machines. The benchmark test shows the correctness of proposed algorithm and the case simulation proves the proposed algorithm has better performance compared with existing algorithms

Robustness analysis for scheduling problems using the inverse method

Abstract—Given a Parametric Timed Automaton (PTA) A and a reference valuation for timings, the Inverse Method (IM) synthesizes a constraint around the reference valuation where A behaves in the same time-abstract manner. This provides us with a quantitative measure of robustness of the behavior of A around the reference valuation. We show in this paper how IM can be applied in a specific way to treat the robustness of scheduling systems. We also explain how to use the method in order to synthesize large zones of the timing parameter space where the system is guaranteed to be schedulable. We illustrate the method on several examples of the literature as well as a case study originating from an industrial design project. I