On Optimal Strategies for Stealing Cycles in Clusters of Workstations

We study aspects of the parallel scheduling problem for a new modality of parallel computing: having one workstation “steal cycles” from another. We focus on a draconian mode of cycle-stealing, in which the owner of workstation B allows workstation A to take control of B’s processor whenever it is idle, with the promise of relinquishing control immediately upon demand. The costs for such cycle-stealing reside in the (typically high) communication overhead for supplying workstation B with work and receiving its results, coupled with the risk that work in progress when the owner of B reclaims the workstation is lost to the owner of A. The first of these costs militates toward supplying B with a large amount of work at once; the second of these costs militates toward repeatedly supplying B with many small packets of work. The challege is to find balance these two pressures in a way that maximizes the amount of work accomplished. We formulate two models of cycle-stealing. The first attempts to maximize the work accomplished during a single episode, when one knows the probability distribution of the return of B’s owner. The second attempts to match the productivity of an omniscient cycle-stealer, when one knows how much work the stealer can accomplish. We study cycle-stealing scenarios within each of these models, deriving optimal scheduling strategies for each studied scenario. We uncover an as-yet unexplained coincidence, two quite distinct scenarios which lead to almost identical unique optimizing schedules. The first of these scenarios falls within our first model: it assumes that the probability of the return of B’s owner is distributed uniformly across the lifespan of the episode. The second of these scenarios falls within our second model: it assumes that B’s owner will interrupt our cycle-stealing at most once during the lifespan of the opportunity.