Multi-processor scheduling to minimize flow time with ε resource augmentation

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+ε)m machines or m machines of speed (1+ε), for arbitrarily small ε > 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/ε))-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 non-migratory and do immediate dispatch of jobs.The randomized algorithm just allocates each incoming job to a random machine. Hence this algorithm is non-clairvoyant, 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/ε)-competitiveness for total flow time and stretch, and also for their Lp norms, for any fixed p ≥ 1.