Trade-offs between speed and processor in hard-deadline scheduling

This paper revisits the problem of on-line scheduling of sequential jobs with hard deadlines in a preemptive, multiprocessor setting. An on-line scheduling algorithm is said to be optimal if it can schedule any set of jobs to meet their deadlines whenever it is feasible in the off-line sense. It is known that the earliest-deadline-first strategy (EDF) is optimal in a one-processor setting, and there is no optimal on-line algorithm in an m-processor setting where m≥2. Recent work however reveals that if the on-line algorithm is given faster processors, EDF is actually optimal for all m (e.g., when m = 2, it suffices to use processors 1.5 times as fast). This paper initiates the study of the trade-off between increasing the speed and using more processors in deriving optimal on-line scheduling algorithms. Several upper bound and lower bound results are presented. For example, the speed requirement of EDF can be reduced to 2-1+p/m+p when it is given p≥0 extra processors. The main result is a new on-line algorithm which demands less speedy processors so as to attain optimality (e.g., when m = 2, the speed requirement is 1 1/3) and admits a better speed-processor trade-off than EDF (e.g., when m = 2 and p = 1, the speed requirement is 1.2). In general, no optimal algorithm exists when the speed factor is less than 1/(2√2+p/m-2).published_or_final_versio

On-line deadline scheduling under relaxed metrics of optimality

tocabstractpublished_or_final_versionComputer Science and Information SystemsDoctoralDoctor of Philosoph

Performance Guarantee for EDF under Overload

Earliest deadline first (edf) is a widely used algorithm for online deadline scheduling. It has been known for long that edf is optimal for scheduling an underloaded, single-processor system; recent results on the extra-resource analysis of edf further revealed that edf when using moderately faster processors can achieve optimal performance in the underloaded, multi-processor setting. This paper initiates the extra-resource analysis of edf for overloaded systems, showing that edf supplemented with a simple form of admission control can provide a similar performance guarantee in both the single and multi-processor settings

Non-migratory Online Deadline Scheduling on Multiprocessors

In this paper we consider multiprocessor scheduling with hard deadlines and investigate the cost of eliminating migration in the online setting. Let I be any set of jobs that can be completed by some migratory offline schedule on m processors. We show that I can also be completed by a non-migratory online schedule using m speed-5.828 processors (i.e., processors of 5.828 times faster). This result supplements the previous results that I can also be completed by a non-migratory offline schedule using 6m unit-speed processors [8] or a migratory online schedule using m speed-2 processors [13]. Our result is based on a simple conservative scheduling algorithm called PARK which commits a processor to a job only when the processor has zero commitment before its deadline. A careful analysis of PARK further shows that the processor speed can be reduced arbitrarily close to 1 by exploiting more processors (say, using 16m speed-1.8 processors). PARK also finds application in overloaded systems; it gives the first online nonmigratory algorithm that can exploit moderately faster processors to match the performance of any migratory offline algorithm

Performance Guarantee of EDF under Overload

This paper is concerned with online algorithms for scheduling jobs with deadlines. A typical example is the earliest deadline rst (edf) algorithm, which has been widely used in real-time systems (see [15] for a survey). It is well-known that edf is optimal for a single processor system that is underloaded, i.e., whenever there exists an oline schedule meeting the deadlines of all jobs released, edf can always do so [7]. However, when the system is overloaded or involves more than one processor, edf has no performance guarantee in the sense that its performance cannot match or even be competitive against the optimal oline algorithm. Indeed, in most settings, no online algorithm has this sort of performance guarantee [2, 8]. In recent years, a plausible approach to studying performance guarantee for online scheduling without restricting the inputs is to allow the online scheduler to use faster processors [1, 3, 5, 9, 10, 13, 14]. Intuitively, we want to study how eective faster processors can compensate the online scheduler for the lack of future information. Phillips et al. [14] were able to extend the optimality of edf to the underloaded, multiprocessor setting by allowing the online scheduler to use double-speed processor

Competitive Deadline Scheduling via Additional or Faster Processors

We consider the online problem of scheduling jobs with deadlines in a single-processor system that allows preemption. The aim is to maximize the total value of jobs completed by their deadlines. It is known that the competitive ratio for this problem is (k), where k is the ratio of the maximum possible value density to the smallest possible one. Yet, if the online scheduler is given a processor faster (say, two times faster) than the adversary, there exists an algorithm called Slacker that can achieve an O(1) competitive ratio. In this paper, we show that using only additional unit speed processors is a possible but not a cost eective way to achieve constant competitiveness. Specically, we nd that (log k) unit speed processors are required. On the other hand, we give a better analysis of the competitiveness of Slacker; this new analysis enables us to show that Slacker when extended to the multi-processor systems can still guarantee constant competitiveness