Performance Analysis of Modified SRPT in Multiple-Processor Multitask Scheduling

In this paper we study the multiple-processor multitask scheduling problem in both deterministic and stochastic models. We consider and analyze Modified Shortest Remaining Processing Time (M-SRPT) scheduling algorithm, a simple modification of SRPT, which always schedules jobs according to SRPT whenever possible, while processes tasks in an arbitrary order. The M-SRPT algorithm is proved to achieve a competitive ratio of $\Theta(\log \alpha +\beta)$ for minimizing response time, where $\alpha$ denotes the ratio between maximum job workload and minimum job workload, $\beta$ represents the ratio between maximum non-preemptive task workload and minimum job workload. In addition, the competitive ratio achieved is shown to be optimal (up to a constant factor), when there are constant number of machines. We further consider the problem under Poisson arrival and general workload distribution (\ie, $M/GI/N$ system), and show that M-SRPT achieves asymptotic optimal mean response time when the traffic intensity $\rho$ approaches $1$, if job size distribution has finite support. Beyond finite job workload, the asymptotic optimality of M-SRPT also holds for infinite job size distributions with certain probabilistic assumptions, for example, $M/M/N$ system with finite task workload

Restart-Based Fault-Tolerance: System Design and Schedulability Analysis

Embedded systems in safety-critical environments are continuously required to deliver more performance and functionality, while expected to provide verified safety guarantees. Nonetheless, platform-wide software verification (required for safety) is often expensive. Therefore, design methods that enable utilization of components such as real-time operating systems (RTOS), without requiring their correctness to guarantee safety, is necessary. In this paper, we propose a design approach to deploy safe-by-design embedded systems. To attain this goal, we rely on a small core of verified software to handle faults in applications and RTOS and recover from them while ensuring that timing constraints of safety-critical tasks are always satisfied. Faults are detected by monitoring the application timing and fault-recovery is achieved via full platform restart and software reload, enabled by the short restart time of embedded systems. Schedulability analysis is used to ensure that the timing constraints of critical plant control tasks are always satisfied in spite of faults and consequent restarts. We derive schedulability results for four restart-tolerant task models. We use a simulator to evaluate and compare the performance of the considered scheduling models

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan