On Budgeting and Quality, with an Application to Safety-Critical Real-time Systems

Abstract

Mandated by modern real-time applications that operate for long durations under (random) bandwidth limitations, we develop a suitable notion of quality of service (QoS) that makes explicit the inherent tradeoffs between the required execution demand and the available budget. We derive bounds on central timing parameters relating the execution demands of tasks to the available budgets which, if satisfied by the tasks, allows us to establish probably approximately correct (PAC) bounds that quantify the long-term evolution of quality of execution. Such large-deviation bounds furnish proof that tasks achieve their desired QoS levels at an exponentially-decaying rate, and, once attained, these levels are sustained and guaranteed for the entire (possibly indefinite) operation horizon, in spite of random fluctuations in budget availability. We study the case when task execution requirements and/or available budgets are dependent, and we derive sufficient conditions under which non-trivial system-wide PAC-type quality guarantees exist under limited dependence. We do so through a novel application of the Lovász Local Lemma. We also present a use-case involving an application of our bounds to safety-critical systems, where the goal is to synthesize runtime monitors and their timing characteristics under a rather general isochronous execution model on multiple processors. We show how to compute monitor worst-case execution times so that tasks attain given QoS levels and also meet their hard deadlines. We treat the related scheduling and feasibility questions, and we show how to derive feasible isochronous Dp-Fair schedules, if they exist, in polynomial-time.