Tardiness Bounds for Global EDF with Deadlines Different from Periods

Abstract

Abstract. The Earliest Deadline First (EDF) scheduling algorithm is known to be suboptimal for meeting all deadlines under global scheduling on multiprocessor platforms. However, EDF is an attractive choice for scheduling soft-real-time systems on multiprocessors. Previous work has demonstrated that the maximum tardiness is bounded, and has derived formulas for computing tardiness bounds, in EDF-scheduled real-time systems that can be modeled as collections of recurrent tasks modeled using the well-known implicit-deadline (Liu and Layland) task model. This research extends the applicability of previous techniques to systems that are modeled using the more general arbitrary sporadic task model. It also improves on prior work even for implicit-deadline systems. An algorithm is derived here that computes tardiness bounds in polynomial time. Previously, these bounds could only have been approximated in sub-exponential time.

Response Time Bounds for G-EDF without Intra-Task Precedence Constraints

“…No job may run concurrently with itself, but distinct jobs within the same task may run concurrently. In addition, we define a task's utilization U i def = C i T i , the task system utilization U (τ ) def = τ i ∈τ U i , and Under the traditional task model with implicit precedence constraints, providing bounded response time required that no τ i had U i > 1 and that U (τ ) ≤ m [3]. However, under the task model considered here, a job with U i > 1 can have bounded response time if subsequent invocations run on separate processors, as depicted for τ 1 in Fig.…”

“…Each x i value depends upon the other x i values. Therefore, we initially define the vectors using an implicit criterion, and as in [2,3] we define the notion of a compliant vector as one that meets this criterion. Definition 1.…”

“…Our definition differs from that of [3] both in the definition of L(x) and in the additional U (τ )D i term.…”

“…We will say that a job J is "executing at time instant t − i+1 " if there is an greater than 0 such that J is executing over the entire interval [t i+1 − , t i+1 ). In [3], the presence of an idle CPU implied that at most m + − 1 tasks have work available for execution at time instant t − i+1 , whereas here the same condition implies that at most m + −1 jobs are available for execution. In [3] it was necessary to account for released jobs that were not running due to a precedence constraint, despite the presence of an idle CPU.…”

“…Multicore processors have been shown to be useful for supporting traditional soft real-time (SRT) workloads when bounded deadline tardiness is acceptable [1][2][3][4]. In this paper we extend these works to a broader class of workloads in which jobs are independent of each other and can be executed in parallel, such as servers handling independent requests.…”