Automated analysis of real-time scheduling using graph games

Abstract

In this paper, we introduce the powerful framework of graph games for the analysis of real-time scheduling with firm deadlines. We introduce a novel instance of a partialobservation game that is suitable for this purpose, and prove decidability of all the involved decision problems. We derive a graph game that allows the automated computation of the competitive ratio (along with an optimal witness algorithm for the competitive ratio) and establish an NP-completeness proof for the graph game problem. For a given on-line algorithm, we present polynomial time solution for computing (i) the worst-case utility; (ii) the worst-case utility ratio w.r.t. a clairvoyant off-line algorithm; and (iii) the competitive ratio. A major strength of the proposed approach lies in its flexibility w.r.t. incorporating additional constraints on the adversary and/or the algorithm, including limited maximum or average load, finiteness of periods of overload, etc., which are easily added by means of additional instances of standard objective functions for graph games.

The impact of resource heterogeneity on the timeliness of hard real-time complex jobs

“…Real-time scheduling is a domain that gains an ever increasing momentum and therefore has been studied extensively in the literature [5,6,7,8,9,10]. The most commonly used scheduling algorithm for hard real-time jobs is the Earliest Deadline First (EDF) [11].…”

“…Comp(ni, pn) ≤ T data (nj , pn) − EST (ni, pn) (10) where Comp(ni, pn) and EST (ni, pn) are the computational cost and the estimated start time of the ready task ni on processor pn, respectively. T data (nj , pn) is the time at which all input data of the succeeding task nj in the queue will be available on processor pn.…”

A Framework for Automated Competitive Analysis of On-line Scheduling of Firm-Deadline Tasks

“…The objective is also satisfied in conjuction with Safe({4}) or Live({4}). In the latter case, a witness path additionally traverses the edges (3,4) and (4, 5) before transitioning from C 1 to C 2 .…”

“…There are two relevant problems for the automated competitive analysis for a given taskset: (1) The synthesis question asks to find an algorithm with optimal competitive ratio; and (2) the analysis question asks to compute the competitive ratio of a given on-line algorithm. In [4], we studied the synthesis problem and presented a reduction to a problem in graph games [5], which we showed to be NP-complete.…”

“…A partialinformation game variant of their approach also allows to synthesize an optimal scheduling algorithm for a given taskset (albeit not in polynomial time). As these approaches do not generalize to competitive analysis of tasks with firm deadlines, we studied the related synthesis problem in [4]. Regarding firm deadline task scheduling in general, starting out from [3], classic real-time systems research has studied the competitive factor of both simple and extended real-time scheduling algorithms.…”