Pinwheel Scheduling for Fault-tolerant Broadcast Disks in Real-time Database Systems

The design of programs for broadcast disks which incorporate real-time and fault-tolerance requirements is considered. A generalized model for real-time fault-tolerant broadcast disks is defined. It is shown that designing programs for broadcast disks specified in this model is closely related to the scheduling of pinwheel task systems. Some new results in pinwheel scheduling theory are derived, which facilitate the efficient generation of real-time fault-tolerant broadcast disk programs.National Science Foundation (CCR-9308344, CCR-9596282

Migrating Mixed Criticality Tasks within a Cyclic Executive Framework

In a cyclic executive, a series of frames are executed in sequence; once the series is complete the sequence is repeated. Within each frame, units of computation are executed, again in sequence. In implementing cyclic executives upon multi-core platforms, there is advantage in coordinating the execution of the cores so that frames are released at the same time across all cores. For mixed criticality systems, the requirement for separation would additionally require that, at any time, code of the same criticality should be executing on all cores. In this paper we derive algorithms for constructing such multiprocessor cyclic executives for systems of periodic tasks, when inter-processor migration is permitted

Intractability Issues in Mixed-Criticality Scheduling

In seeking to develop mixed-criticality scheduling algorithms, one encounters challenges arising from two sources. First, mixed-criticality scheduling is an inherently an on-line problem in that scheduling decisions must be made without access to all the information that is needed to make such decisions optimally - such information is only revealed over time. Second, many fundamental mixed-criticality schedulability analysis problems are computationally intractable - NP-hard in the strong sense - but we desire to solve these problems using algorithms with polynomial or pseudo-polynomial running time. While these two aspects of intractability are traditionally studied separately in the theoretical computer science literature, they have been considered in an integrated fashion in mixed-criticality scheduling theory. In this work we seek to separate out the effects of being inherently on-line, and being computationally intractable, on the overall intractability of mixed-criticality scheduling problems. Speedup factor is widely used as quantitative metric of the effectiveness of mixed-criticality scheduling algorithms; there has recently been a bit of a debate regarding the appropriateness of doing so. We provide here some additional perspective on this matter: we seek to better understand its appropriateness as well as its limitations in this regard by examining separately how the on-line nature of some mixed-criticality problems, and their computational complexity, contribute to the speedup factors of two widely-studied mixed-criticality scheduling algorithms

Graceful Degradation in Semi-Clairvoyant Scheduling

In the Vestal model of mixed-criticality systems, jobs are characterized by multiple different estimates of their actual, but unknown, worst-case execution time (WCET) parameters. Some recent research has focused upon a semi-clairvoyant model for mixed-criticality systems in which it is assumed that each job reveals upon arrival which of its WCET parameters it will respect. We study the problem of scheduling such semi-clairvoyant systems to ensure graceful degradation of service to less critical jobs in the event that the systems exhibit high-criticality behavior. We propose multiple different interpretations of graceful degradation in such systems, and derive efficient scheduling algorithms that are capable of ensuring graceful degradation under these different interpretations

Towards Efficient Explainability of Schedulability Properties in Real-Time Systems

The notion of efficient explainability was recently introduced in the context of hard-real-time scheduling: a claim that a real-time system is schedulable (i.e., that it will always meet all deadlines during run-time) is defined to be efficiently explainable if there is a proof of such schedulability that can be verified by a polynomial-time algorithm. We further explore this notion by (i) classifying a variety of common schedulability analysis problems according to whether they are efficiently explainable or not; and (ii) developing strategies for dealing with those determined to not be efficiently schedulable, primarily by identifying practically meaningful sub-problems that are efficiently explainable

A Measurement-Based Model for Parallel Real-Time Tasks

Under the federated paradigm of multiprocessor scheduling, a set of processors is reserved for the exclusive use of each real-time task. If tasks are characterized very conservatively (as is typical in safety-critical systems), it is likely that most invocations of the task will have computational demand far below the worst-case characterization, and could have been scheduled correctly upon far fewer processors than were assigned to it assuming the worst-case characterization of its run-time behavior. Provided we could safely determine during run-time when all the processors are going to be needed, for the rest of the time the unneeded processors could be idled in low-energy "sleep" mode, or used for executing non-real time work in the background. In this paper we propose a model for representing parallelizable real-time tasks in a manner that permits us to do so. Our model does not require us to have fine-grained knowledge of the internal structure of the code represented by the task; rather, it characterizes each task by a few parameters that are obtained by repeatedly executing the code under different conditions and measuring the run-times

Mixed-Criticality Job Models: A Comparison

The Vestal model in widely used in the real-time scheduling community for representing mixed-criticality real-time workloads. This model requires that multiple WCET estimates -- one for each criticality level in a system -- be obtained for each task. Burns suggests that being required to obtain too many WCET estimates may place an undue burden on system developers, and proposes a simplification to the Vestal model that makes do with just two WCET estimates per task. Burns makes a convincing case in favor of adopting this simplified model; here, we report on our attempts at comparing the two models -- Vestal’s original model, and Burns’ simplification – with regards to expressiveness, as well as schedulability and the tractability of determining schedulability

Feasibility Analysis of Conditional DAG Tasks

Feasibility analysis for Conditional DAG tasks (C-DAGs) upon multiprocessor platforms is shown to be complete for the complexity class pspace. It is shown that as a consequence integer linear programming solvers (ILP solvers) are likely to prove inadequate for such analysis. A demarcation is identified between the feasibility-analysis problems on C-DAGs that are efficiently solvable using ILP solvers and those that are not, by characterizing a restricted class of C-DAGs for which feasibility analysis is shown to be efficiently solvable using ILP solvers

ILP-based approaches to partitioning recurrent workloads upon heterogeneous multiprocessors

The problem of partitioning systems of independent constrained-deadline sporadic tasks upon heterogeneous multiprocessor platforms is considered. Several different integer linear program (ILP) formulations of this problem, offering different tradeoffs between effectiveness (as quantified by speedup bound) and running time efficiency, are presented

Preemptive uniprocessor scheduling of dual-criticality implicit-deadline sporadic tasks

Many reactive systems must be designed and analyzed prior to deployment in the presence of considerable epistemic uncertainty: the precise nature of the external environment the system will encounter, as well as the run-time behavior of the platform upon which it is implemented, cannot be predicted with complete certainty prior to deployment. The widely-studied Vestal model for mixed-criticality workloads addresses uncertainties in estimating the worst-case execution time (WCET) of real-time code. Different estimations, at different levels of assurance, are made about these WCET values; it is required that all functionalities execute correctly if the less conservative assumptions hold, while only the more critical functionalities are required to execute correctly in the (presumably less likely) event that the less conservative assumptions fail to hold but the more conservative assumptions do. A generalization of the Vestal model is considered here, in which a degraded (but non-zero) level of service is required for the less critical functionalities even in the event of only the more conservative assumptions holding. An algorithm is derived for scheduling dual-criticality implicit-deadline sporadic task systems specified in this more general model upon preemptive uniprocessor platforms, and proved to be speedup-optimal