Scheduling policies for real-time systems exhibit threshold behavior that is related to the utilization of the task set they schedule, and in some cases this threshold is sharp. For the rate monotonic scheduling policy, we show that periodic workload with utilization less than a threshold @math can be scheduled almost surely and that all workload with utilization greater than @math is almost surely not schedulable. We study such sharp threshold behavior in the context of processor scheduling using static task priorities, not only for periodic real-time tasks but for aperiodic real-time tasks as well. The notion of a utilization threshold provides a simple schedulability test for most real-time applications. These results improve our understanding of scheduling policies and provide an interesting characterization of the typical behavior of policies. The threshold is sharp (small deviations around the threshold cause schedulability, as a property, to appear or disappear) for most policies; this is a happy consequence that can be used to address the limitations of existing utilization-based tests for schedulability. We demonstrate the use of such an approach for balancing power consumption with the need to meet deadlines in web servers.
In the realm of aperiodic task sets, great progress has been made recently, by , with the identification of aperiodic schedulability bounds for static priority scheduling @cite_8 . The initial result obtained by Abdelzaher and Lu @cite_7 was a constant time utilization-based test for a set of aperiodic tasks. The original analysis has been extended to deal with end-to-end schedulability for multi-stage resource pipelines @cite_0 . It has also been shown that such analysis can be used to obtain non-utilization bounds for schedulability with static priority policies @cite_23 . In this article, we have studied single-node thresholds for the aperiodic task model. In the future, we will further the ideas described in this article to include resource pipelines and non-utilization metrics.
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This paper generalizes the notion of utilization bounds for schedulability of aperiodic tasks to the case of distributed resource systems. In the basic model, aperiodically arriving tasks are processed by multiple stages of a resource pipeline within end-to-end deadlines. The authors consider a multidimensional space in which each dimension represents the instantaneous utilization of a single stage. A feasible region is derived in this space such that all tasks meet their deadlines as long as pipeline resource consumption remains within the feasible region. The feasible region is a multidimensional extension of the single-resource utilization bound giving rise to a bounding surface in the utilization space rather than a scalar bound. Extensions of the analysis are provided to nonindependent tasks and arbitrary task graphs. We evaluate the performance of admission control using simulation, as well as demonstrate the applicability of these results to task schedulability analysis in the total ship computing environment envisioned by the US navy. The proliferation of high-volume time-critical Web services such as online trading calls for a scalable server design that allows meeting individual response-time guarantees of real time transactions. A main challenge is to honor these guarantees despite unpredictability in incoming server load. The extremely high volume of real-time service requests mandates constant-time scheduling and schedulability analysis algorithms (as opposed to polynomial or logarithmic ones in the number of current requests). The paper makes two major contributions towards developing an architecture and theoretical foundations for scalable real-time servers operating in dynamic environments. First, we derive a tight utilization bound for schedulability of aperiodic tasks (requests) that allows implementing a constant time schedulability test on the server. We demonstrate that Liu and Layland's schedulable utilization bound of ln 2 does not apply to aperiodic tasks, and prove that an optimal arrival-time independent scheduling policy will meet all aperiodic task deadlines if utilization is maintained below 1 1+ spl radic (1 2). Second, we show that aperiodic deadline-monotonic scheduling is the optimal arrival-time-independent scheduling policy for aperiodic tasks. This result is used to optimally prioritize server requests. Evaluation of a utilization control loop that maintains server utilization below the bound shows that the approach is effective in meeting all individual deadlines in a high performance real-time server. Real-time scheduling theory offers constant-time schedulability tests for periodic and sporadic tasks based on utilization bounds. Unfortunately, the periodicity or the minimal interarrival-time assumptions underlying these bounds make them inapplicable to a vast range of aperiodic workloads such as those seen by network routers, Web servers, and event-driven systems. This paper makes several important contributions toward real-time scheduling theory and schedulability analysis. We derive the first known bound for schedulability of aperiodic tasks. The bound is based on a utilization-like metric we call synthetic utilization, which allows implementing constant-time schedulability tests at admission control time. We prove that the synthetic utilization bound for deadline-monotonic scheduling of aperiodic tasks is 1 1+ spl radic 1 2. We also show that no other time-independent scheduling policy can have a higher schedulability bound. Similarly, we show that EDF has a bound of 1 and that no dynamic-priority policy has a higher bound. We assess the performance of the derived bound and conclude that it is very efficient in hit-ratio maximization.