Random Walk Based Sampling for Load Balancing in Multi-Server Systems

Abstract

In multi-server systems, a classical job assignment algorithm works as follows: at the arrival of each job, pick d servers independently and uniformly at random and send the job to the least loaded server among the d servers. This model is known as the powerof- d choices algorithm. In this paper, we analyze a variant of this algorithm, where d servers are sampled through d independent non-backtracking random walks on a k-regular graph. The random walkers are periodically reset to independent uniform random positions. Under some assumptions on the underlying graph, we show that the system dynamics under this new algorithm converges to the solution of a deterministic ordinary differential equation (ODE), which is the same ODE as the classical power-of-d choices. We also show that the new algorithm stablizes the system, and the stationary distribution of the system converges to the stationary solution of the ODE. The new scheme can be considered as a derandomized version of power-of-d choices as it reduces the use of randomness while maintaining the performance of power-of-d choices.