Task Reallocation for Maximal Reliability in Distributed Computing Systems with Uncertain Topologies and Non-Markovian Delays

The ability to model and optimize reliability is central in designing survivable distributed computing systems (DCSs) where servers are prone to fail permanently. In this paper the service reliability of a DCS in uncertain topologies is analytically characterized by using a novel regeneration-based probabilistic analysis. The analysis takes into account the stochastic failure times of servers, the heterogeneity and randomness of both service times and communication delays, as well as arbitrary task-reallocation policies. Auxiliary age variables are introduced in the analysis to capture the memory associated with the non-Markovian (non-exponential) communication and service random times, thereby enabling the recursive analytical characterization of reliability. Implications of the non-exponential times on reliability are studied, and the results are compared to those obtained using a Markovian formulation; in particular, the effect of increasing the mean communication times is investigated. The model is further used to solve the optimization problem of task-reallocation for maximal reliability, and the results are compared to those from Monte-Carlo simulations and actual experiments conducted on a small-scale DCS over the Internet.