Rhythmic Tasks: A New Task Model with Continually Varying Periods for Cyber-Physical Systems

Traditional mechanical subsystems in automobiles are being replaced by electronically controlled systems, often with no mechanical backup. This trend towards "drive-by-wire" systems is becoming increasingly popular. In these cyber-physical systems, a critical task not meeting its timing deadline can lead to a safety violation and damage to life and/or property. Classical real-time scheduling techniques such as RMS and EDF can be used to guarantee the schedulability of periodic tasks. However, certain critical tasks like the engine control task are activated by engine events such as pulses generated by sensors at the engine crankshaft. The periods of these engine tasks vary continually and even dramatically depending on the engine speed. The conventional periodic task model is inadequate for handling such tasks in cyber-physical systems due to its pessimism when combined with common schedulability analyses. In this paper, we define a new task model called Rhythmic Tasks for tasks having periods that vary due to external physical events. To the best of our knowledge, this is the first model that considers continually varying periods for fixed-priority scheduling in dynamic operating environments. We formally define the rhythmic task model and study its scheduling properties. In the context of rhythmic engine control tasks, we offer schedulability tests for determining the maximum possible utilization under the steady state, which is related to the physical engine speed. We also investigate the range of possible engine acceleration and deceleration rates. We show that excessive acceleration and deceleration can make the system unschedulable. We provide algorithms to find the appropriate ranges for acceleration and deceleration rates. We use a specific case study of engine control to illustrate our analysis.