Optimal Control of Multilayer Discrete Event Systems With Real-Time Constraint Guarantees

We consider discrete event systems (DESs) involving tasks with dependability requirements in the form of real-time constraints. We seek to control their processing times so as to satisfy these constraints while also minimizing a given cost function. When tasks are processed by a single resource, it has been shown that there are structural properties of the optimal state trajectory for this problem that lead to the critical task decomposition algorithm (CTDA) with a time complexity of O(N²). For a DES with multiple resources, we consider a multilayer network where each layer contains multiple nodes, each node may have multiple inputs and multiple outputs, and tasks are processed so that the real-time constraints apply on an end-to-end basis. Extending earlier results (where each layer contained a single node), we derive structural properties of the optimal solution that lead to the idea of introducing “virtual” deadlines at each node (except for the last layer) and decouple nodes so that the CTDA for single-node problems can be used. We prove that an appropriately constructed sequence of solutions of these simpler problems converges to the global optimum of the original problem and hence obtain an efficient scalable multilayer virtual deadline algorithm (MLVDA). We illustrate the efficiency of the MLVDA through numerical examples.