云服务器租赁：等时长作业的情形
Renting Servers in the Cloud: The Case of Equal Duration Jobs
AI总结：
该研究针对云服务器租赁这一装箱推广问题，分析等时长作业下NextFit和FirstFit算法的竞争比，证明NextFit紧界为2，给出FirstFit的多组上下界，并借权重函数技术得到均匀服务器场景下的更强结果。
摘要：
云服务器租赁问题是装箱问题的推广，其研究动机来自云计算应用中的作业-服务器分配场景。作业以在线方式到达，需被分配到服务器上；作业的时长和大小在到达时即为已知。系统中有无限多台相同的服务器，每台服务器每单位时间拥有一单位计算容量。服务器可在任意时间被租赁，租赁状态会持续到分配给它的所有作业全部完成。分配方案的成本为所有服务器租赁期的时长总和。研究目标是在满足服务器容量约束的前提下，将作业分配到服务器上以最小化总成本。我们聚焦于分析两种自然算法——NextFit（下次适配）和FirstFit（首次适配）在等时长作业情形下的性能。已知在该情形下，NextFit和FirstFit的竞争比上界分别为3和4。我们证明了NextFit的竞争比紧界为2。对于FirstFit，我们确立了其竞争比的下界为2.519，即便作业仅存在两个不同的到达时刻时该下界依然成立。针对作业到达时刻为0和1、时长为2的情形，我们证明了FirstFit的严格竞争比下界为1.89、上界为2。最后，借助权重函数技术，我们在均匀服务器的情形下得到了更强的结果。
英文摘要：
Renting servers in the cloud is a generalization of the bin packing problem, motivated by job allocation to servers in cloud computing applications. Jobs arrive in an online manner, and need to be assigned to servers; their duration and size are known at the time of arrival. There is an infinite supply of identical servers, each having one unit of computational capacity per unit of time. A server can be rented at any time and continues to be rented until all jobs assigned to it finish. The cost of an assignment is the sum of durations of rental periods of all servers. The goal is to assign jobs to servers to minimize the overall cost while satisfying server capacity constraints. We focus on analyzing two natural algorithms, NextFit and FirstFit, for the case of jobs of equal duration. It is known that the competitive ratio of NextFit and FirstFit are at most 3 and 4 respectively for this case. We prove a tight bound of 2 on the competitive ratio of NextFit. For FirstFit, we establish a lower bound of 2.519 on the competitive ratio, even when jobs have only two distinct arrival times. For the case when jobs have arrival times 0 and 1 and duration 2, we show a lower bound of 1.89 and an upper bound of 2 on the strict competitive ratio of FirstFit. Finally, using the weight function technique, we obtain stronger results for the case of uniform servers.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
