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.
Our work presents a fresh perspective on scheduling for real-time systems. Only Lehoczky, Sha and Ding @cite_1 have attempted to obtain average-case results. For rate monotonic scheduling, they characterized the breakdown utilization of the rate monotonic policy for the Liu and Layland model of real-time tasks as @math . Breakdown utilization, however, is not the same as a utilization threshold, and the connection between the two needs to be examined more closely. The methodology we employ in obtaining our results is new and extremely general. It was not possible to reason in a rather abstract sense about the average-case behavior of scheduling policies with the more traditional analysis techniques of time demand and resource supply. Furthermore, our abstraction allows for reasoning about multi-stage and multiprocessor systems. Dutertre @cite_30 identified phase transitions in a non-preemptive recurring task scheduling problem. While Dutertre's work emphasized the empirical evidence for sharp thresholds, we have provided the mathematical basis for the existence of sharp thresholds.
@cite_30 @cite_1
2166440675 2141663593 2167754005 2096989632
An exact characterization of the ability of the rate monotonic scheduling algorithm to meet the deadlines of a periodic task set is represented. In addition, a stochastic analysis which gives the probability distribution of the breakdown utilization of randomly generated task sets is presented. It is shown that as the task set size increases, the task computation times become of little importance, and the breakdown utilization converges to a constant determined by the task periods. For uniformly distributed tasks, a breakdown utilization of 88 is a reasonable characterization. A case is shown in which the average-case breakdown utilization reaches the worst-case lower bound of C.L. Liu and J.W. Layland (1973). > We consider the problem of makespan minimization on m unrelated machines in the context of algorithmic mechanism design, where the machines are the strategic players. This is a multidimensional scheduling domain, and the only known positive results for makespan minimization in such a domain are O(m)-approximation truthful mechanisms [22, 20]. We study a well-motivated special case of this problem, where the processing time of a job on each machine may either be "low" or "high", and the low and high values are public and job-dependent. This preserves the multidimensionality of the domain, and generalizes the restricted-machines (i.e., pj,∞ ) setting in scheduling. We give a general technique to convert any c-approximation algorithm to a 3c-approximation truthful-in-expectation mechanism. This is one of the few known results that shows how to export approximation algorithms for a multidimensional problem into truthful mechanisms in a black-box fashion. When the low and high values are the same for all jobs, we devise a deterministic 2-approximation truthful mechanism. These are the first truthful mechanisms with non-trivial performance guarantees for a multidimensional scheduling domain. Our constructions are novel in two respects. First, we do not utilize or rely on explicit price definitions to prove truthfulness; instead we design algorithms that satisfy cycle monotonicity. Cycle monotonicity [23] is a necessary and sufficient condition for truthfulness, is a generalization of value monotonicity for multidimensional domains. However, whereas value monotonicity has been used extensively and successfully to design truthful mechanisms in single-dimensional domains, ours is the first work that leverages cycle monotonicity in the multidimensional setting. Second, our randomized mechanisms are obtained by first constructing a fractional truthful mechanism for a fractional relaxation of the problem, and then converting it into a truthful-in-expectation mechanism. This builds upon a technique of [16], and shows the usefulness of fractional mechanisms in truthful mechanism design. 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.