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.

中文翻译：

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二部图中的最佳负载平衡

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有效负载平衡的研究。在本文中，我们研究了二部图上的负载平衡，其中左节点对应于作业类型，右节点对应于服务器，每条边表示一个作业类型可以由服务器提供服务。因此，边代表局部性约束，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服务。该系统中的服务器可以具有异构服务费率。在此设置中，我们调查了名为 Join-the-Fastest-of-the-Shortest-Queue (JFSQ) 和 Join-the-Fastest-of-the-Idle-Queue (JFIQ) 的两个策略的性能，它们是简单的变体加入最短队列和加入空闲队列，其中关系被打破以支持最快的服务器。在“连接良好”的图形条件下，我们表明当服务器数量趋于无穷大时，JFSQ 和 JFIQ 在平均响应时间上是渐近最优的。除了渐近最优性之外，我们还获得了有限大小系统的平均响应时间的上限。我们进一步表明，连接性相对稀疏的随机二部图构造可以满足连接良好的条件。