Order of Servers for Periodic Multi-Installment Scheduling

Periodic multi-installment scheduling (PMIS) has been the most effective model for large-scale divisible-load scheduling on distributed systems. In practice, the decreasing order of communication speeds, denoted as IZ, has always been used as the scheduling sequence of servers because it has been proven that IZ is the optimal sequence to achieve minimum makespan for single-installment scheduling and studies available have shown that IZ is the near-optimal sequence for multi-installment scheduling. In this paper, however, we illustrate by an example that IZ unfortunately causes time conflicts for servers between the last installment but one and the last installment, thus it is definitely not a feasible sequence for PMIS, not to mention an optimal or near-optimal sequence. Further, to obtain a feasible order of servers, we provide rigorous proof in this paper that there is no time conflict when servers follow the increasing order of communication speeds.