A Time-Series Model for Varying Worker Ability in Heterogeneous Distributed Computing Systems

Abstract

In this paper, we consider the problem of estimating the time-dependent ability of workers participating in distributed matrix-vector multiplication over heterogeneous clusters. Specifically, we model the workers’ ability as a latent variable and introduce a log-normally distributed working rate as a function of the latent variable with parameters so that the working rate increases as the latent ability of workers increases, and takes positive values only. This modeling is motivated by the need to reflect the impact of time-dependent external factors on the workers’ performance. We estimate the latent variable and parameters using the expectation-maximization (EM) algorithm combined with the particle method. The proposed estimation and inference on the working rates are used to allocate tasks to the workers to reduce expected latency. From simulations, we observe that our estimation and inference on the working rates are effective in reducing expected latency.