Minimizing the Flow Time Without Migration

Minimizing Total Flow Time and Total Completion Time with Immediate Dispatching

“…This solves an open problem suggested by Awerbuch et al [2]. • The total completion time of algorithm IMD is at most seven times the total completion time of the optimal migratory offline algorithm.…”

“…In addition it decides to assign a job from a central pool only when a machine becomes empty. Awerbuch et al [2] presented an online non-migratory algorithm, which performs almost as well as the best known offline algorithm (SRPT) for the preemptive problem that uses migration. Specifically, this algorithm performs by at most an O(min{log P, log n}) factor of the optimal total flow time of any (possibly migratory) schedule.…”

“…Aside from the assignment strategy, which is the core of the algorithm, we also use a different (less effective) scheduling approach for each machine separately, in order to simplify the analysis of the flow time performance. The total flow time analysis basically combines new ideas with ideas used in [2] and [5]. The algorithm of [2] also uses classification of jobs to classes.…”

“…The total flow time analysis basically combines new ideas with ideas used in [2] and [5]. The algorithm of [2] also uses classification of jobs to classes. However, that classification is done according to the residual sizes of the jobs at any given time, meaning that the classification of a job changes along the process.…”

Non-Clairvoyant Scheduling for Minimizing Mean Slowdown

“…It is the ratio of the flow time of a job to its size. Slowdown as a metric has received much attention lately [10], [16], [14], [4], [5], [1], [7], since it captures the notion of "fairness". Note that a low slowdown implies that jobs are delayed in proportion to their size, hence smaller jobs are delayed less and large jobs are delayed proportionately more.…”