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

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
$(2\log {m}{+}1)(1{+}\sqrt {m {\Delta }})(1{+}m\sqrt {{\Delta }}){(1{+}{\Delta })}$
for zero-release times, and
$2(2\log {m}{+}1)(1{+}\sqrt {m{\Delta }})(1{+}m\sqrt {{\Delta }})(1{+}{\Delta })$
for general release times, where
${\Delta }$
represents the upper bound of squared coefficient of variation of processing times, and
${m}$
is the number of servers.