Scheduling tasks with Markov-chain based constraints

Markov-chain (MC) based constraints have been shown to be an effective QoS measure for a class of real-time systems, particularly those arising from control applications. Scheduling tasks with MC constraints introduces new challenges because these constraints require not only specific task finishing patterns but also certain task completion probability. Multiple tasks with different MC constraints competing for the same resource further complicates the problem. In this paper, we study the problem of scheduling multiple tasks with different MC constraints. We present two scheduling approaches which (i) lead to improvements in "overall" system performance, and (ii) allow the system to achieve graceful degradation as system load increases. The two scheduling approaches differ in their complexities and performances. We have implemented our scheduling algorithms in the QNX real-time operating system environment and used the setup for several realistic control tasks. Data collected from the experiments as well as simulation all show that our new scheduling algorithms outperform algorithms designed for window-based constraints as well as previous algorithms designed for handling MC constraints.