On Optimal Strategies for Cycle-Stealing in Networks of Workstations

  • Authors:

  • Sandeep N. Bhatt;Fan R. K. Chung;F. Thomson Leighton;Arnold L. Rosenberg

  • Affiliations:

  • -;-;-;-

  • Venue:
  • IEEE Transactions on Computers
  • Year:
  • 1997

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Abstract

We study 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 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 the owner of B reclaims the workstation militates in favor of supplying B with a sequence of small packets of work. The challenge is to 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 expected 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 that stealer can accomplish. We derive optimal scheduling strategies for sample scenarios within each of these models.Perhaps our most important discovery is the as-yet unexplained coincidence that two quite distinct scenarios lead to almost identical unique optimizing schedules. One scenario falls within our first model; it assumes that the probability of the return of B's owner is uniform across the lifespan of the episode; the optimizing schedule maximizes the expected amount of work accomplished during the episode. The other scenario 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; the optimizing schedule maximizes the amount of work that one is guaranteed to accomplish during the lifespan.