NPSCS: Non-Preemptive Stochastic Coflow Scheduling With Time-Indexed LP Relaxation

Abstract

Coflows model a scheduling setting that is commonly found in a variety of applications in distributed and cloud computing. A stochastic coflow task contains a set of parallel flows with randomly distributed sizes. Further, many applications require non-preemptive scheduling of coflow tasks. This article gives an approximation algorithm on the weighted expected completion time for non-preemptive stochastic coflow scheduling. The proposed approach uses a time-indexed linear program relaxation, and uses its solution to come up with a feasible schedule. This algorithm is shown to achieve an approximation ratio of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(2\log {m}{+}1)(1{+}\sqrt {m {\Delta }})(1{+}m\sqrt {{\Delta }}){(1{+}{\Delta })}$ </tex-math></inline-formula> for zero-release times, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2(2\log {m}{+}1)(1{+}\sqrt {m{\Delta }})(1{+}m\sqrt {{\Delta }})(1{+}{\Delta })$ </tex-math></inline-formula> for general release times, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${\Delta }$ </tex-math></inline-formula> represents the upper bound of squared coefficient of variation of processing times, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${m}$ </tex-math></inline-formula> is the number of servers.