We derive efficient guidelines for scheduling data-parallel computations within a draconian mode of cycle-stealing in networks of workstations. In this computing regimen, (the owner of) workstation A contracts with (the owner of) workstation B to take control of B's processor for a guaranteed total of U time units, punctuated by up to some prespecified number p of interrupts which kill any work A has in progress on B. On the one hand, the high overhead — of c time units — for setting up the communications that supply workstation B with work and receive its results recommends that A communicate with B infrequently, supplying B with large amounts of work each time. On the other hand, the risk of losing work in progress when workstation B is interrupted recommends that A supply B with a long sequence of small bundles of work. In this paper, we derive two sets of scheduling guidelines that balance these conflicting pressures in a way that optimizes, up to low-order additive terms, the amount of work that A is guaranteed to accomplish during the cycle-stealing opportunity. Our non-adaptive guidelines, which employ a single fixed strategy until all p interrupts have occurred, produce schedules that achieve at least [Formula: see text] units of work. Our adaptive guidelines, which change strategy after each interrupt, produce schedules that achieve at least [Formula: see text] (low-order terms) units of work. By deriving the theoretical underpinnings of our guidelines, we show that our non-adaptive schedules are optimal in guaranteed work-output and that our adaptive schedules are within low-order additive terms of being optimal.
Scheduling data-parallel computations on heterogeneous and time-shared environments
