Dynamic affinity load balancing of multi-type tasks on multi-skilled servers, when the service rate of each task type on each of the servers is known and can possibly be different from each other, is an open problem for over three decades. The goal is to do task assignment on servers in a real time manner so that the system becomes stable, which means that the queue lengths do not diverge to infinity in steady state (throughput optimality), and the mean task completion time is minimized (delay optimality). The fluid model planning, Max-Weight, and c-$\mu$-rule algorithms have theoretical guarantees on optimality in some aspects for the affinity problem, but they consider a complicated queueing structure and either require the task arrival rates, the service rates of tasks on servers, or both. In many cases that are discussed in the introduction section, both task arrival rates and service rates of different task types on different servers are unknown. In this work, the Blind GB-PANDAS algorithm is proposed which is completely blind to task arrival rates and service rates. Blind GB-PANDAS uses an exploration-exploitation approach for load balancing. We prove that Blind GB-PANDAS is throughput optimal under arbitrary and unknown distributions for service times of different task types on different servers and unknown task arrival rates. Blind GB-PANDAS desires to route an incoming task to the server with the minimum weighted-workload, but since the service rates are unknown, such routing of incoming tasks is not guaranteed which makes the throughput optimality analysis more complicated than the case where service rates are known. Our extensive experimental results reveal that Blind GB-PANDAS significantly outperforms existing methods in terms of mean task completion time at high loads.

中文翻译：

---

Blind GB-PANDAS：一种用于亲和性调度的盲吞吐量优化负载平衡算法

多技能服务器上的多类型任务的动态亲和性负载平衡，当每个服务器上每种任务类型的服务率是已知的并且可能彼此不同时，这是三十多年来的一个悬而未决的问题。目标是实时在服务器上进行任务分配，使系统变得稳定，这意味着稳定状态下队列长度不会发散到无穷大（吞吐量最优），并且最小化平均任务完成时间（延迟最优性）。流体模型规划、Max-Weight 和 c-$\mu$-rule 算法在某些方面对亲和性问题的最优性有理论上的保证，但它们考虑了复杂的排队结构，并且需要任务到达率、服务率服务器上的任务，或两者兼而有之。在介绍部分讨论的许多情况下，不同服务器上不同任务类型的任务到达率和服务率都是未知的。在这项工作中，提出了Blind GB-PANDAS 算法，该算法完全对任务到达率和服务率视而不见。Blind GB-PANDAS 使用探索-利用方法进行负载平衡。我们证明了 Blind GB-PANDAS 在任意和未知分布下对于不同服务器上不同任务类型的服务时间和未知任务到达率是吞吐量最优的。Blind GB-PANDAS 希望以最小的加权工作负载将传入任务路由到服务器，但由于服务速率未知，因此无法保证传入任务的这种路由，这使得吞吐量优化分析比服务速率的情况更复杂众所周知。