Arvind Easwaran

Global EDF Schedulability Analysis for Synchronous Parallel Tasks on Multicore Platforms

The trend towards multi-core/many-core architectures is well underway. It is therefore becoming very important to develop software in ways that take advantage of such parallel architectures. This particularly entails a shift in programming paradigms towards fine-grained, thread-parallel computing. Many parallel programming models have been introduced targeting such intra-task thread-level parallelism. However, most successful results on traditional multi-core real-time scheduling are focused on sequential programming models. For example, thread-level parallelism is not properly captured into the concept of interference, which is key to many schedulability analysis techniques. Thereby, most interference-based analysis techniques are not directly applicable to parallel programming models. Motivated by this, we extend the notion of interference to capture thread-level parallelism more accurately. We then leverage the proposed notion of parallelism-aware interference to derive efficient EDF schedulability tests that are directly applicable to synchronous parallel task models on multi-core platforms. Our evaluation results indicate that the proposed analysis significantly advances the state-of-the-art in EDF schedulability analysis for synchronous parallel tasks.

Demand-Based Scheduling of Mixed-Criticality Sporadic Tasks on One Processor

Strategies that artificially tighten high-criticality task deadlines in low-criticality behaviors have been successfully employed for scheduling mixed-criticality systems. Although efficient scheduling algorithms have been developed for implicit deadline task systems, the same is not true for more general sporadic tasks. In this paper we develop a new demand-based schedulability test for such general mixed-criticality task systems, in which we collectively bound the low- and high-criticality demand of tasks. We show that the new test strictly dominates the only other known demand-based test for such systems. We also propose a new deadline tightening strategy based on this test, and show through simulations that the strategy significantly outperforms all known scheduling algorithms for a variety of sporadic task systems.

MC-Fluid: Fluid Model-Based Mixed-Criticality Scheduling on Multiprocessors

A mixed-criticality system consists of multiple components with different criticalities. While mixed-criticality scheduling has been extensively studied for the uniprocessor case, the problem of efficient scheduling for the multiprocessor case has largely remained open. We design a fluid model-based multiprocessor mixed-criticality scheduling algorithm, called MC-Fluid, in which each task is executed in proportion to its criticality-dependent rate. We propose an exact schedulability condition for MC-Fluid and an optimal assignment algorithm for criticality-dependent execution rates with polynomial complexity. Since MC-Fluid cannot construct a schedule on real hardware platforms due to the fluid assumption, we propose MC-DP-Fair algorithm, which can generate a non-fluid schedule while preserving the same schedulability properties as MC-Fluid. We show that MC-Fluid has a speedup factor of (1 + v 5)/2 ( 1.618), which is best known in multiprocessor MC scheduling, and simulation results show that MC-DP-Fair outperforms all existing algorithms.

Resource Efficient Isolation Mechanisms in Mixed-Criticality Scheduling

Mixed-criticality real-time scheduling has been developed to improve resource utilization while guaranteeing safe execution of critical applications. These studies use optimistic resource reservation for all the applications to improve utilization, but prioritize critical applications when the reservations become insufficient at runtime. Many of them however share an impractical assumption that all the critical applications will simultaneously demand additional resources. As a consequence, they under-utilize resources by penalizing all the low-criticality applications. In this paper we overcome this shortcoming using a novel mechanism that comprises a parameter to model the expected number of critical applications simultaneously demanding more resources, and an execution strategy based on the parameter to improve resource utilization. Since most mixed criticality systems in practice are component-based, we design our mechanism such that the component boundaries provide the isolation necessary to support the execution of low-criticality applications, and at the same time protect the critical ones. We also develop schedulability tests for the proposed mechanism under both a flat as well as a hierarchical scheduling framework. Finally, through simulations, we compare the performance of the proposed approach with existing studies in terms of schedulability and the capability to support low-criticality applications.

Extending Task-level to Job-level Fixed Priority Assignment and Schedulability Analysis Using Pseudo-deadlines

In global real-time multiprocessor scheduling, a recent analysis technique for Task-level Fixed-Priority (TFP) scheduling has been shown to outperform many of the analyses for Job-level Fixed-Priority (JFP) scheduling on average. Since JFP is a generalization of TFP scheduling, and the TFP analysis technique itself has been adapted from an earlier JFP analysis, this result is counter-intuitive and in our opinion highlights the lack of good JFP scheduling techniques. Towards generalizing the superior TFP analysis to JFP scheduling, we propose the Smallest Pseudo-Deadline First (SPDF) JFP scheduling algorithm. SPDF uses a simple task-level parameter called pseudo-deadline to prioritize jobs, and hence can behave as a TFP or JFP scheduler depending on the values of the pseudodeadlines. This natural transition from TFP to JFP scheduling has enabled us to incorporate the superior TFP analysis technique in an SPDF schedulability test. We also present a pseudo-deadline assignment algorithm for SPDF scheduling that extends the well-known Optimal Priority Assignment (OPA) algorithm for TFP scheduling. We show that our algorithm is optimal for the derived schedulability test, and also present a heuristic to overcome the computational complexity issue of the optimal algorithm. Our simulation results show that the SPDF algorithm with the new analysis significantly outperforms state-of-the-art TFP and JFP analysis.

Composition of Schedulability Analyses for Real-Time Multiprocessor Systems

With increasing popularity and deployment of multi-core chips in embedded systems, a number of real-time multiprocessor scheduling algorithms have been proposed along with their schedulability analyses (or tests), which verify temporal correctness under a specific algorithm. Each of these algorithms often comes with several different schedulability tests, especially when it is difficult to find exact schedulability tests for the algorithm. Such tests usually find different task sets deemed schedulable even under the same scheduling algorithm. While these different tests have been compared with each other in terms of schedulability performance, little has been done on how to combine such different tests to improve the overall schedulability of a given scheduling algorithm beyond a simple union of their individual schedulability. Motivated by this, we propose a composition theory for schedulability tests with two new methods. The first method composes task-level timing guarantees derived from different schedulability tests, and the second one derives system-level schedulability results from a single schedulability test. The unified composition theory with these two methods then utilizes existing schedulability tests effectively so as to cover additional schedulable task sets. The proposed composition theory is shown to be applicable to most existing preemptive/non-preemptive scheduling algorithms. We also present three case-studies, demonstrating how and by how much the theory can improve schedulability by composing existing schedulability tests. Our evaluation results also show that the composition theory makes it possible to cover up to 181.7 percent additional schedulable task sets for preemptive fpEDF, preemptive EDF and non-preemptive EDF scheduling algorithms beyond their existing tests.

Mapping Time-Critical Safety-Critical Cyber Physical Systems to Hybrid FPGAs

Cyber Physical Systems (CPSs), such as those found in modern vehicles, include a number of important time and safety-critical functions. Traditionally, applications are mapped to several dedicated electronic control units (ECUs), and hence, as new functions are added, compute weight and cost increase considerably.%ECU consolidation, where multiple functions are combined on fewer ECUs is an important area, but traditional software ECUs fail to offer the required performance, parallelism, and isolation to support this. With increasing computational and communication demands, traditional software ECUs fail to offer the required performance to provide determinism and predictability, while multi-core approaches fail to provide sufficient isolation between tasks. Hybrid FPGAs, combining a processor and reconfigurable fabric on a single die, allow for parallel hardware implementation of complex sensor processing tightly coupled with the flexibility of software on a processor. We demonstrate the advantages of such architectures in consolidating distributed processing with predictability, determinism and isolation, enabling ECU consolidation and bandwidth reduction.

Under-Approximating Backward Reachable Sets by Polytopes

Under-approximations are useful for falsification of safety properties for nonlinear (hybrid) systems by finding counter-examples. Polytopic under-approximations enable analysis of these properties using reasoning in the theory of linear arithmetic. Given a nonlinear system, a target region of the simply connected compact type and a time duration, we in this paper propose a method using boundary analysis to compute an under-approximation of the backward reachable set. The under-approximation is represented as a polytope. The polytope can be computed by solving linear program problems. We test our method on several examples and compare them with existing methods. The results show that our method is highly promising in under-approximating reachable sets. Furthermore, we explore some directions to improve the scalability of our method.

Contention-free executions for real-time multiprocessor scheduling

A time slot is defined as contention-free if the number of jobs with remaining executions in the slot is no larger than the number of processors, or contending, otherwise. Then an important property holds that in any contention-free slot, all jobs with remaining executions are guaranteed to be scheduled as long as the scheduler is work-conserving. This article aims at improving schedulability by utilizing the contention-free slots. To achieve this, this article presents a policy (called CF policy) that moves some job executions from contending slots to contention-free ones. This policy can be employed by any work-conserving, preemptive scheduling algorithm, and we show that any algorithm extended with this policy dominates the original algorithm in terms of schedulability. We also present improved schedulability tests for algorithms that employ this policy, based on the observation that interference from jobs is reduced when their executions are postponed to contention-free slots. Simulation results demonstrate that the CF policy, incorporated into existing algorithms, significantly improves schedulability of those existing algorithms.

Reach-Avoid Verification for Nonlinear Systems Based on Boundary Analysis

In this technical note, we propose a set-boundary based method to verify reach-avoid properties of non-linear dynamical systems with parametric uncertainty, which works under the assumption that the initial set is a compact set. In comparison to the conventional approach employing safely overapproximating state extrapolation on the full volume of the initial set, our boundary-based method applies such state extrapolation only to the initial sets boundary, and thus to a set of significantly smaller volume. This can help enhance precision and reduce computational burden when solving reach-avoid verification problems, especially for cases with large initial sets and/or large time horizons. Furthermore, our boundary-based method lifts existing reachability-analysis techniques with their often confined geometric representations of reachable sets (like interval boxes, zonotopes, polyhedra, ellipsoids) to considerably more complex geometric shapes, where the boundary of the set is representable as a finite union of such shapes. The resulting benefits brought by our boundary-based method in reach-avoid verification are illustrated through several examples.