Clairvoyant Dynamic Bin Packing for Job Scheduling with Minimum Server Usage Time

The MinUsageTime Dynamic Bin Packing (DBP) problem targets at minimizing the accumulated usage time of all the bins in the packing process. It models the server acquisition and job scheduling issues in many cloud-based systems. Earlier work has studied MinUsageTime DBP in the non-clairvoyant setting where the departure time of each item is not known at the time of its arrival. In this paper, we investigate MinUsageTime DBP in the clairvoyant setting where the departure time of each item is known for packing purposes. We study both the offline and online versions of Clairvoyant MinUsageTime DBP. We present two approximation algorithms for the offline problem, including a 5-approximation Duration Descending First Fit algorithm and a 4-approximation Dual Coloring algorithm. For the online problem, we establish a lower bound of 1+√5/2 on the competitive ratio of any online packing algorithm. We propose two strategies of item classification for online packing, including a classify-by-departure-time strategy and a classify-by-duration strategy. We analyze the competitiveness of these strategies when they are applied to the classical First Fit packing algorithm. It is shown that both strategies can substantially reduce the competitive ratio for Clairvoyant MinUsageTime DBP compared to the original First Fit algorithm.