具有最小干扰的动态加权公平性
Dynamic Weighted Fairness with Minimal Disruptions
摘要：
在本文中，我们考虑以下动态公平分配问题：给定一个序列的工作到达和离开，目标是保持一个近似公平分配的资源对目标公平分配政策，同时最小化的总中断次数，这是任何工作的分配被改变的次数。我们考虑了丰富的公平分配政策，显着概括那些考虑在以前的工作。我们首先考虑工作只到达或工作只离开的模型。我们提出了严格的上限和下限的中断所需的数量，以保持一个恒定的近似公平分配的每一个时间步。特别是，对于典型的情况下，工作的权重和资源分配是成比例的工作的重量，我们表明，保持一个恒定的近似公平分配需要$Θ(\log^* n)$中断每个工作，几乎匹配的边界在以前的工作单位重量的情况下。对于更一般的设置，分配政策只减少分配到一个工作时，新的工作到达，我们表明，保持一个恒定的近似公平分配需要$Θ(\log n)$中断每个作业。然后，我们考虑模型中的工作都可以到达和离开。我们首先显示出强大的下限所需的中断的数量，以保持恒定的近似公平的任意实例。与此相反，我们然后表明，有一个算法，可以保持恒定的近似公平性与$O(1)$预期中断每个工作，如果工作的权重是独立的工作的到达和离开顺序。最后，我们展示了如何将我们的结果扩展到具有多个资源的设置。
英文摘要：
In this paper, we consider the following dynamic fair allocation problem: Given a sequence of job arrivals and departures, the goal is to maintain an approximately fair allocation of the resource against a target fair allocation policy, while minimizing the total number of disruptions, which is the number of times the allocation of any job is changed. We consider a rich class of fair allocation policies that significantly generalize those considered in previous work. We first consider the models where jobs only arrive, or jobs only depart. We present tight upper and lower bounds for the number of disruptions required to maintain a constant approximate fair allocation every time step. In particular, for the canonical case where jobs have weights and the resource allocation is proportional to the job's weight, we show that maintaining a constant approximate fair allocation requires $Θ(\log^* n)$ disruptions per job, almost matching the bounds in prior work for the unit weight case. For the more general setting where the allocation policy only decreases the allocation to a job when new jobs arrive, we show that maintaining a constant approximate fair allocation requires $Θ(\log n)$ disruptions per job. We then consider the model where jobs can both arrive and depart. We first show strong lower bounds on the number of disruptions required to maintain constant approximate fairness for arbitrary instances. In contrast we then show that there there is an algorithm that can maintain constant approximate fairness with $O(1)$ expected disruptions per job if the weights of the jobs are independent of the jobs arrival and departure order. We finally show how our results can be extended to the setting with multiple resources.
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。
