On the Effect of Task-to-Worker Assignment in Distributed Computing Systems with Stragglers

Abstract

We study the expected completion time of some recently proposed algorithms for distributed computing which redundantly assign computing tasks to multiple machines in order to tolerate a certain number of machine failures. We analytically show that not only the amount of redundancy but also the task-to-machine assignments affect the latency in a distributed system. We study systems with a fixed number of computing tasks that are split in possibly overlapping batches, and independent exponentially distributed machine service times. We show that, for such systems, the uniform replication of non-overlapping (disjoint) batches of computing tasks achieves the minimum expected computing time.

Data Replication for Reducing Computing Time in Distributed Systems with Stragglers

“…Moreover, for the given system model, with overlapping batches System1 always has higher average completion time compared to balanced assignment of non-overlapping batches. Interested reader may find further discussions in [4]. It is proved in the original work [4] that, the balanced assignment of non-overlapping batches minimized the expected completion time if the workers' service time is stochastically decreasing and convex random variable.…”

“…Interested reader may find further discussions in [4]. It is proved in the original work [4] that, the balanced assignment of non-overlapping batches minimized the expected completion time if the workers' service time is stochastically decreasing and convex random variable. Both Exponential and Shifted-Exponential random variables are stochastically decreasing (in the sense of usual stochastic ordering) and convex random variables.…”

“…Redundancy enables a task master to generate the overall result form the computations of only a subset of all computing nodes, instead of all of them. Thus, slow workers, known as stragglers, can be mitigated [4].…”

Redundancy Scheduling in Systems with Bi-Modal Job Service Time Distributions

“…This problem, which is caused by "stragglers" [8], can significantly increase the average service time and its variability [9]. By letting jobs be served concurrently at multiple servers, jobs experience the minimum service time across the servers [10].…”

Scheduling in the Presence of Data Intensive Compute Jobs

“…In distributed computing systems, redundancy can reduce fluctuations in the service time of the jobs [2], and has gained attention both in theoretical works [3]- [5] and in practical systems [6], [7]. Redundancy is particularly beneficial in systems with high variability in job service times [8].…”