In this paper, we study the problem of job dispatching and scheduling, where each job consists of a set of tasks. Each task is processed by a set of machines simultaneously. We consider two important performance metrics, the average job completion time (JCT), and the number of deadline-aware jobs that meet their deadlines. The goal is to minimize the former and maximize the latter. We first propose OneJ to minimize the job completion time (JCT) when there is exactly one single job in the system. Then, we propose an online algorithm called MultiJ, taking OneJ as a subroutine, to minimize the average JCT, and prove it has a good competitive ratio. We then derive another online algorithm QuickJ to maximize the number of jobs that can meet their deadlines. We show that QuickJ is competitive via a worst case analysis. We also conjecture that the competitive ratio of QuickJ is likely to be the best one that any deterministic algorithm can achieve. We also shed light on several important merits of MultiJ and QuickJ, such as no severe coordination overhead, scalability, work conservation, and no job starvation.
