Guidelines for Data-Parallel Cycle-Stealing in Networks of Workstations

We derive guidelines for nearly optimally scheduling data-parallel computations within a draconian mode of cycle-stealing in NOWs. In this computing regimen, workstation A takes control of workstation B’s processor whenever B is idle, with the promise of relinquishing control immediately upon demand—thereby losing work in progress. The typically high communication overhead for supplying workstation B with work and receiving its results militates in favor of supplying B with large amounts of work at a time; the risk of losing work in progress when B is reclaimed militates in favor of supplying B with a succession of small bundles of work. The challenge is to balance these two pressures in a way that maximizes (some measure of) the amount of work accomplished. Our guidelines attempt to maximize the expected work accomplished by workstation B in an episode of cycle-stealing, assuming knowledge of the instantaneous probability of workstation B’s being reclaimed. Our study is a step toward rendering prescriptive the descriptive study of cycle-stealing in [3]. 1. The Cycle-Stealing Problem We derive guidelines for (almost) optimally scheduling data-parallel computations on “borrowed” workstations, within the model developed in [3]. The phenomenological study in that paper builds on the following rather draconian version of cycle-stealing—the use by one workstation of idle computing cycles of another. The owner of workstation A contracts to take control of workstation B whenever its owner is absent. When the owner of B reclaims that workstation, workstation A immediately relinquishes control of B, killing any active job(s)—thereby destroying all work since the last checkpoint. This research was supported in part by NSF Grant CCR-97-10367. Such draconian “contracts” are inevitable, for instance, when a returning owner unplugs a laptop from a network; one encounters such contracts also at several institutions where cycle-stealing is supported. Such a “contract” creates a tension between the following inherently conflicting aspects of cycle-stealing. On the one hand, since any work in progress on workstation B when it is reclaimed is lost, a cycle-stealer wants to break a cyclestealing episode into many short periods, supplying small amounts of work to the borrowed workstation each time. On the other hand, since each of the inter-workstation communications that bracket every period in a cycle-stealing episode—to supply work to workstation B and to reclaim the results of that work—involves an expensive setup protocol, the cycle-stealer wants to break each cycle-stealing episode into a few long periods, supplying large amounts of work to workstation B each time. Clearly, the challenge in scheduling episodes of cycle-stealing is to balance these conflicting factors in a way that maximizes the productive output of the episode. The research we report on here resolves the preceding conflict by deriving scheduling guidelines that (approximately) maximize the expected work1 accomplished within an episode of cycle-stealing, within the following setting. We focus on computations that are dataparallel, in that they consist of a massive number of independent repetitive tasks of known durations. Many scientific computations have this form. We develop schedules assuming that we know the instantaneous probability of workstation B’s being reclaimed and that the function yielding this information is “smooth.” Although our results are stated as though we had exact knowledge of these probabilities, they extend easily to situations wherein this knowledge is approximate, 1In a forthcoming sequel, we focus on (nearly) optimizing other measures of a cycle-stealing episode’s work output.