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 our work, we explore some interesting aspects surrounding task set utilization and schedulability for real-time systems. There has been extensive work on deriving utilization bounds for periodic task systems starting with the work of Liu and Layland @cite_31 . Kuo and Mok @cite_19 made significant improvements on Liu and Layland's bound for rate monotonic scheduling by showing that schedulability is a function, not of the number of individual tasks but, of the number of harmonic chains. Bini, Buttazzo and Buttazzo @cite_20 have shown, using the hyperbolic bound , that the feasible region for schedulability using the rate monotonic scheduling policy can be larger if the product of individual task utilizations (and not their sum) is bounded. Wu, Liu and Zhao used techniques inspired by network calculus to derive schedulability bounds @cite_16 for static priority scheduling. Their contribution is an alternative framework for deriving utilization bounds.
@cite_19 @cite_31 @cite_16 @cite_20
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We propose a novel schedulability analysis for verifying the feasibility of large periodic task sets under the rate monotonic algorithm when the exact test cannot be applied on line due to prohibitively long execution times. The proposed test has the same complexity as the original Liu and Layland (1973) bound, but it is less pessimistic, thus allowing it to accept task sets that would be rejected using the original approach. The performance of the proposed approach is evaluated with respect to the classical Liu and Layland method and theoretical bounds are derived as a function of n (the number of tasks) and for the limit case of n tending to infinity. The analysis is also extended to include aperiodic servers and blocking times due to concurrency control protocols. Extensive simulations on synthetic tasks sets are presented to compare the effectiveness of the proposed test with respect to the Liu and Layland method and the exact response time analysis. 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. While utilization bound based schedulability test is simple and effective, it is often difficult to derive the bound itself. For its analytical complexity, utilization bound results are usually obtained on a case-by-case basis. In this paper, we develop a general framework that allows one to effectively derive schedulability bounds for a wide range of real-time systems with different workload patterns and schedulers. Our analytical model is capable of describing a wide range of tasks and schedulers' behaviors. We propose a new definition of utilization, called workload rate. While similar to utilization, workload rate enables flexible representation of different scheduling and workload scenarios and leads to uniform derivation of schedulability bounds. We derive a parameterized schedulability bound for static priority schedulers with arbitrary priority assignment. Existing utilization bounds for different priority assignments and task releasing patterns can be derived from our closed-form formula by simple assignments of proper parameters.