Derandomized Load Balancing using Random Walks on Expander Graphs
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In a computing center with a huge amount of machines, when a job arrives, a dispatcher need to decide which machine to route this job to based on limited information. A classical method, called the power-of-d choices algorithm is to pick d servers independently at random and dispatch the job to the least loaded server among the d servers. In this paper, we analyze a low-randomness variant of this dispatching scheme, where d queues are sampled through d independent non-backtracking random walks on a k-regular graph G. Under certain assumptions of the graph G we show that under this scheme, the dynamics of the queuing system converges to the same deterministic ordinary differential equation (ODE) for the power-of-d choices scheme. We also show that the system is stable under the proposed scheme, and the stationary distribution of the system converges to the fixed point of the ODE.
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