二部图中的最优负载均衡
Optimal Load Balancing in Bipartite Graphs
摘要：
云平台中的应用激发了对作业服务器约束和服务器异构性下的高效负载均衡的研究。在本文中，我们研究了负载均衡的二分图，其中左节点对应的作业类型和右节点对应的服务器，与每一个边缘表示的作业类型可以由一个服务器。因此，边表示局部约束，即，每个作业只能在包含某些数据和/或机器学习（ML）模型的服务器上提供。该系统中的服务器可以具有不同的服务速率。在此设置中，我们调查了两个名为Join-the-Fastest-of-the-Shortest-Queue（JFSQ）和Join-the-Fastest-of-the-Idle-Queue（JFIQ）的策略的性能，这两个策略是Join-the-Shortest-Queue和Join-the-Idle-Queue的简单变体，其中关系被打破以支持最快的服务器。在“良好连通”图的条件下，我们证明了JFSQ和JFIQ是渐近最优的平均响应时间时，服务器的数量趋于无穷大。除了渐近最优性，我们还获得了有限大小系统的平均响应时间的上界。我们进一步表明，良好的连通性条件可以满足随机二部图的建设与相对稀疏的连接。
英文摘要：
Applications in cloud platforms motivate the study of efficient load balancing under job-server constraints and server heterogeneity. In this paper, we study load balancing on a bipartite graph where left nodes correspond to job types and right nodes correspond to servers, with each edge indicating that a job type can be served by a server. Thus edges represent locality constraints, i.e., each job can only be served at servers which contained certain data and/or machine learning (ML) models. Servers in this system can have heterogeneous service rates. In this setting, we investigate the performance of two policies named Join-the-Fastest-of-the-Shortest-Queue (JFSQ) and Join-the-Fastest-of-the-Idle-Queue (JFIQ), which are simple variants of Join-the-Shortest-Queue and Join-the-Idle-Queue, where ties are broken in favor of the fastest servers. Under a "well-connected" graph condition, we show that JFSQ and JFIQ are asymptotically optimal in the mean response time when the number of servers goes to infinity. In addition to asymptotic optimality, we also obtain upper bounds on the mean response time for finite-size systems. We further show that the well-connectedness condition can be satisfied by a random bipartite graph construction with relatively sparse connectivity.
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