Distributed load balancing is the act of allocating jobs among a set of servers as evenly as possible. There are mainly two versions of the load balancing problem that have been studied in the literature: static and dynamic. The static interpretation leads to formulating the load balancing problem as a case with jobs (balls) never leaving the system and accumulating at the servers (bins) whereas the dynamic setting deals with the case when jobs arrive and leave the system after service completion. This paper designs and evaluates server proximity aware job allocation policies for treating load balancing problems with a goal to reduce the communication cost associated with the jobs. We consider a class of proximity aware Power of Two (POT) choice based assignment policies for allocating jobs to servers, where servers are interconnected as an n-vertex graph G(V, E). For the static version, we assume each job arrives at one of the servers, u. For the dynamic setting, we assume G to be a circular graph and job arrival process at each server is described by a Poisson point process with the job service time exponentially distributed. For both settings, we then assign each job to the server with minimum load among servers u and v where v is chosen according to one of the following two policies: (i) Unif-POT(k): Sample a server v uniformly at random from k-hop neighborhood of u (ii) InvSq-POT(k): Sample a server v from k-hop neighborhood of u with probability proportional to the inverse square of the distance between u and v. Our simulation results show that both the policies consistently produce a load distribution which is much similar to that of a classical proximity oblivious POT policy.

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图上基于邻近度的负载平衡策略：模拟研究

分布式负载平衡是在一组服务器之间尽可能均匀地分配作业的行为。文献中研究的负载均衡问题主要有两种版本：静态和动态。静态解释导致将负载平衡问题表述为作业（球）永远不会离开系统并在服务器（箱）上累积的情况，而动态设置则处理作业在服务完成后到达并离开系统的情况。本文设计和评估服务器邻近感知作业分配策略，用于处理负载平衡问题，目标是降低与作业相关的通信成本。我们考虑一类基于接近度感知二幂 (POT) 选择的分配策略，用于将作业分配给服务器，其中服务器互连为 n 顶点图 G(V, E)。对于静态版本，我们假设每个作业都到达其中一台服务器 u。对于动态设置，我们假设 G 是一个圆形图，每个服务器的作业到达过程由泊松点过程描述，作业服务时间呈指数分布。对于这两种设置，我们然后将每个作业分配给服务器 u 和 v 中负载最小的服务器，其中 v 根据以下两种策略之一进行选择： (i) Unif-POT(k)：随机均匀地对服务器 v 进行采样从 u 的 k 跳邻域 (ii) InvSq-POT(k)：从 u 的 k 跳邻域中采样服务器 v，概率与 u 和 v 之间的距离的平方反比成正比。