A Period Assignment Algorithm for EmbeddedDigital

Assigning periods to tasks in an embedded digital controller is a nonlinear integer programming problem which is NP-hard. This paper presents a polynomial time approximation algorithm to this problem with performance ratio bounded by 2. Introduction: Digital controllers found in many embedded real-time systems consist of a number of interacting tasks. These tasks execute periodically at xed rates sampling data from sensors, computing control laws, and updating actuators. Such an end-to-end computation from sensors to actuators forms a chain of tasks called a control loop. In order to sustain the required control quality, a control loop possesses the maximum activation period as a timing constraint. An essential step in developing a digital controller is to assign each task a constant period such that the maximum activation requirements are met while the system utilization is minimized 1]. Where intermediate tasks are shared by control loops with diierent rate constraints, the problem falls into a class of nonlinear integer programming problems which are NP-hard. To the best of our knowledge, no polynomial time approximation algorithm with a known performance bound has been proposed to address the period assignment problem. This paper proposes a polynomial time algorithm which produces a solution whose utilization does not exceed twice the optimal utilization.