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Scheduling in Bandwidth Constrained Tree Networks

In this paper we introduce a new network scheduling model. Here jobs need to be sent via routers on a tree to machines to be scheduled, and the communication is constrained by network bandwidth. The scheduler coordinates network communication and job machine scheduling. This type of scheduler is highly desirable in practice; yet few works have considered combing networking with job processing. We consider the popular objective of total flow time in the online setting. We give a (1+ε)-speed O(1/ε7)-competitive algorithm when all routers are identical and all machines are identical for any fixed eps >0. Then we go on to show a (2+ε)-speed O(1/ε7)-competitive algorithm when the routers are identical and the machines are unrelated. To show these results we introduce an interesting combination of potential function and dual fitting techniques as well as a reduction of general tree scheduling to a special case of trees.