We investigate the problem of online scheduling of jobs to minimize flow time and stretch on m identical machines. We consider the case where the algorithm is given either (1 + )m machines or m machines of speed (1 + ), for arbitrarily small > 0. We show that simple randomized and deterministic load balancing algorithms, coupled with simple single machine scheduling strategies such as SRPT (shortest remaining processing time) and SJF (shortest job first), are O(poly(1/ ))-competitive for both flow time and stretch. These are the first results which prove constant factor competitive ratios for flow time or stretch with arbitrarily small resource augmentation. Both the randomized and the deterministic load balancing algorithms are nonmigratory and do immediate dispatch of jobs. The randomized algorithm just allocates each incoming job to a random machine. Hence this algorithm is nonclairvoyant, and coupled with SETF (shortest elapsed time first), yields the first non-clairvoyant algorithm which is constant competitive for minimizing flow time with arbitrarily small resource augmentation. The deterministic algorithm that we analyze is due to Avrahami and Azar. For this algorithm, we show O(1/ )- *
Chekuri et al. then show that simple uniprocessor scheduling algorithms such as SRPT combined with simple load balancing algorithms are also (1 + )-speed O(1)-competitive for minimizing the p norms of flow and stretch on m identical machines REF .
Multi-processor scheduling to minimize flow time with ε resource augmentation
STOC '04
Computer Science