Open soft real-time systems, such as mobile robots, must respond adaptively to varying operating conditions, while balancing the need to perform multiple mission specific tasks against the requirement that those tasks complete in a timely manner. Setting and enforcing a utilization target for shared resources is a key mechanism for achieving this behavior. However, because of the uncertainty and non-preempt ability of some tasks, key assumptions of classical scheduling approaches do not hold. In previous work we presented foundational methods for generating task scheduling policies to enforce proportional resource utilization for open soft real-time systems with these properties. However, these methods scale exponentially in the number of tasks, limiting their practical applicability.In this paper, we present a novel parameterized scheduling policy that scales our technique to a much wider range of systems. These policies can represent geometric features of the scheduling policies produced by our earlier methods, but only require a number of parameters that is quadratic in the number of tasks. We provide empirical evidence that the best of these policies are competitive with exact solution methods in small problems, and significantly outperform heuristic methods in larger ones.

Abstract—Classical scheduling abstractions such as deadlines and priorities do not readily capture the complex timing semantics found in many real-time cyber-physical systems. Time utility functions provide a necessarily richer description of timing semantics, but designing utility-aware scheduling policies using them is an open research problem. In particular, scheduling design that optimizes expected utility accrual is needed for realtime cyber-physical domains. In this paper we design scheduling policies that optimize expected utility accrual for cyber-physical systems with periodic, non-preemptable tasks that run with stochastic duration. These policies are derived by solving a Markov Decision Process formulation of the scheduling problem. We use this formulation to demonstrate that our technique improves on existing heuristic utility accrual scheduling policies. I.

Open soft real-time systems, such as mobile robots, experience unpredictable interactions with their environments and yet must respond both adaptively and with reasonable temporal predictability. New scheduling approaches are needed to address the demands of such systems, in which many of the assumptions made by traditional real-time scheduling theory do not hold. In previous work we established foundations for a scheduling policy design and verification approach for open soft real-time systems, that can use different decision models, e.g., a Markov decision process (MDP), to capture the nuances of their scheduling semantics.However, several important refinements to the preliminary techniques developed in that work are needed to make the approach applicable in practice. This paper makes three main contributions to the state of the art in scheduling open soft real-time systems: (1) it defines a novel representation of the scheduling state space that is both more compact and more expressive than the model defined in our previous work; (2) it exploits regular structure of that representation to allow efficient verification of properties involving both discrete and continuous system state variables under specific scheduling policies; and (3) it removes the unnecessary use of a time horizon in our previous approach, thus allowing the more precise specification and enforcement of a wider range of scheduling policies for open soft real-time systems.