A gravitational task model with arbitrary anchor points for target sensitive real-time applications

Abstract

Classic task models for real-time systems focus on execution windows expressing earliest start times and deadlines of tasks for feasibility. Only within these windows the execution of tasks is feasible, and it is considered of uniform utility.Some tasks, however, have target demands in addition: a task should preferably execute at a specific target point within its execution window, but can execute around this point, albeit at lower utility. Examples of such applications include control and media processing.In this paper, we present a task model based on a gravitational analogy to address these issues. Tasks are considered as massive bobs hanging on a pendulum: a single task, left to itself, will execute at the bottom, the target point. If a force, such as the weight of other tasks, is applied, it can be shifted around this point. Thus, tasks' importance and their utility around target points can be expressed. Since the execution of a task cannot be mapped to a point in time, the model allows tasks to express an arbitrary point with its execution to represent the whole execution. This point is called the anchor point.Moreover, we show an example of a scheduling algorithm for this model which finds an approximation to the best compromise of tasks' interests based on the equilibrium state of a pendulum. Nonetheless, this task model is not restricted to a particular scheduling algorithm.Results from a simulation study show the effectiveness of the approach. This is an extended version of the ECRTS'08 paper (Guerra and Fohler 2008).

On-Line Scheduling Algorithm for the Gravitational Task Model

“…This scheduler achieves higher acceptance ratio and utility accrual than the scheduling example proposed in [1], [2], at the same time decreasing the complexity. Moreover, the complexities of the ordering and timing phases presented here are lower than in any other utility aware schedulers that are based in different task models.…”

“…The gravitational task model, which we presented in [1], [2] allows a task to express an execution window for feasibility, a target point where its utility is maximized, importance, and utility decay as a function of its deviation from its target point. In this model, tasks are considered as massive bobs hanging on a pendulum: a single task, left to itself, will execute at the bottom, the target point.…”

“…An approximation to this compromise is solved with linear complexity based on the equilibrium of physical pendulums. In [1], [2] we presented the equilibrium and showed its applicability with a simple adhoc scheduler as proof of concept. This scheduler was divided into 2 phases, ordering and timing, both with complexity O(n 2 ).…”

Optimizing Expected Time Utility in Cyber-Physical Systems Schedulers

“…Time utility functions can also be used in control systems to specify the sensitivity of the control loop to inter-job jitter [9]. Deploying each job at a precise point in time gains maximal utility while deploying the job early or late can result in control instabilities [10].…”

“…The Utility Accrual Packet Scheduling Algorithm (UPA) [15], which extends an algorithm presented by Chen and Muhlethaler [16], assumes time utility functions can be approximated using a strictly linearly decreasing function. Gravitational task models [9] assume that the shapes of the time utility functions are symmetric and unimodal. In addition it is assumed that utility is gained when the non-preemptable job is scheduled, which is equivalent to assuming deterministic job durations with utility gained on job completion.…”