A Framework for Task Reallocation in Distributed Computing Systems with Non-Markovian Communication Delays

This paper presents a general framework for optimal task reallocation in heterogeneous distributed computing systems (DCSs). The framework relies on a rigorous analytical model for the stochastic execution time of a workload. The model takes into account the heterogeneity and randomness of both service times and communication delays, an arbitrary task-reallocation policy as well as the stochastic failure times of servers. Auxiliary age variables are introduced in the analysis to capture the memory associated with the non-Markovian (nonexponential) communication and service random times, thereby enabling a recursive analytical characterization for the execution time of a workload. The framework is employed to devise task reallocation policies that optimize three metrics: average execution time of a workload, quality-of-service guarantees and reliability in executing a workload. Implications of the nonexponential times on these metrics are studied, and results are compared to those obtained using a Markovian formulation; in particular, the effect of increasing the mean communication times is investigated.