On-line optimal control of two-stage Discrete Event Systems with real-time constraints

We consider a two-stage Discrete Event System (DES) involving tasks with real-time constraints and seek to control processing times so as to minimize a cost function subject to each task meeting its own constraint. It has been shown that the off-line version of this problem can be efficiently solved by the Virtual Deadline Algorithm (VDA) [8]. In this report, an algorithm is developed to handle an online version with unknown task characteristics in advance. By utilizing the concept of “best solution in probability” introduced in [7] and extend the algorithm to a two-stage system, the algorithm makes uses of probability distributions and results in a less conservative solution compared with worst-case analysis. Numerical examples are included to illustrate our results.