A Bi-Objective Scheduling Algorithm for Desktop Grids with Uncertain Resource Availabilities

Abstract

In this work, we consider the execution of applications on desktop grids. Such parallel systems use idle computing resources of desktops distributed over the Internet for running massively parallel computations. The applications are composed of workflows of independent non-preemptive sequential jobs that are submitted by successive batches. Then, the corresponding jobs are executed on the distributed available resources according to some scheduling policy. However, most resources are not continuously available over time since the users give their idle CPU time only for some time when they are not using their desktops. Moreover, even if the dates of unavailability periods are estimated in advance, they are subject to uncertainties. This may drastically impact the global performances by delaying the completion time of the applications. The aim of this paper is to study how to schedule efficiently a set of jobs in the presence of unavailability periods on identical machines. In the same time, we are interested in reducing the impact of disturbances on the unavailability periods. This is achieved by maximizing the stability that measures the distance between the makespan of the disturbed instance over the initial one. Our main contribution is the design of a new parametrized algorithm and the analysis of its performance through structural properties. This algorithm reduces the impact of disturbances on availability periods without worsening too much the makespan. Its interest is assessed by running simulations based on realistic workflows. Moreover, theoretical results are obtained under the assumption that the size of every availability interval is at least twice the size of the largest job.

A proactive approach for coping with uncertain resource availabilities on desktop grids

“…We developed a preliminary study of scheduling under unavailability constraints with uncertainties in [3]. Each interrupted job was restarted from the beginning, without migration, but the unavailability constraints were only allowed to advance forward.…”

“…Since jobs allocated to any interval must fit in the availability, the horizon is then greater than or equal to the makespan without uncertainties (C max max 1≤j≤n C j where C j is the completion time of job j in a given schedule [17]). In [3], we have considered the makespan instead of an horizon. As a consequence, we assumed that at least one processor did not have any unavailability which is unrealistic and not required anymore.…”

“…Thus, Proposition 1 holds for any kind of parallel platforms (identical, uniform and unrelated). Additionally, the problem of generating a schedule that respects the slack rule with an optimal makespan can be proven to be NP-Hard using the same proof as in [3].…”

“…To the best of our knowledge, there is no related work studying scheduling with unavailability under uncertainties except our previous contribution [3] which provided a preliminary analysis for restricted disturbance patterns. Our proposed approach relies on a slack-based proactive approach (with temporal protection).…”

“…We characterize general conditions that any schedule must verify to obtain an optimal stability (i.e., with a disturbed completion time not worse than the predicted one). The processors are assumed to be uniform whereas they were identical in our previous work [3]. Moreover, we consider that unavailabilities can start not only earlier than expected but also later.…”