In modern distributed computing systems, unpredictable and unreliable infrastructures result in high variability of computing resources. Meanwhile, there is significantly increasing demand for timely and event-driven services with deadline constraints. Motivated by measurements over Amazon EC2 clusters, we consider a two-state Markov model for variability of computing speed in cloud networks. In this model, each worker can be either in a good state or a bad state in terms of the computation speed, and the transition between these states is modeled as a Markov chain which is unknown to the scheduler. We then consider a Coded Computing framework, in which the data is possibly encoded and stored at the worker nodes in order to provide robustness against nodes that may be in a bad state. With timely computation requests submitted to the system with computation deadlines, our goal is to design the optimal computation-load allocation scheme and the optimal data encoding scheme that maximize the timely computation throughput (i.e, the average number of computation tasks that are accomplished before their deadline). Our main result is the development of a dynamic computation strategy called Lagrange Estimate-and Allocate (LEA) strategy, which achieves the optimal timely computation throughput. It is shown that compared to the static allocation strategy, LEA increases the timely computation throughput by 1.4X - 17.5X in various scenarios via simulations and by 1.27X - 6.5X in experiments over Amazon EC2 clusters
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