Priority algorithm for near-data scheduling: Throughput and heavy-traffic optimality

Abstract

The prevalence of data-parallel applications has made near-data scheduling an important problem. An example is the map task scheduling in the map-reduce framework. Wang et. al. [13] was the first to identify its capacity region and proposed a throughput-optimal algorithm based on MaxWeight. However, the study of the algorithm's delay performance revealed that it is only heavy-traffic optimal for a very special traffic scenario, where all traffic concentrates on a subset of servers. We propose a simple "local-tasks first" priority algorithm and show that it is throughput-optimal and heavy-traffic optimal for all traffic scenarios, i.e., it asymptotically minimizes the average delay as the arrival rate vector approaches the boundary of the capacity region. So far, it is the only known heavy-traffic optimal algorithm for this setting. As the algorithm is based on pre-determined priority, a direct application of the Lyapunov drift technique does not work. The main proof ideas are the construction of an ideal load decomposition and the separate treatment of two subsystems based on their ideal load. To the best of our knowledge, this is the only setup of affinity scheduling where a simple priority algorithm is shown to be heavy-traffic optimal. Simulation shows that our algorithm also significantly outperforms existing algorithms at loads away from the boundary of the capacity region.

Blind GB-PANDAS: A Blind Throughput-Optimal Load Balancing Algorithm for Affinity Scheduling

“…Although some of these heuristic algorithms are being used in real applications, simple facts about their optimality are not investigated. Recent works including the priority algorithm [22], Join-the-Shortest-Queue-Max-Weight (JSQ-MW) [10] and Weighted-Workload algorithm [6] study the capacity region and throughput optimality for a system with two and three levels of data locality.…”

“…where (a) follows by upper bounding 1 − δ , 1 (1− ) 2 (1+ ) 2 , and 1 t δ by 1, 16 9 , and 1 T δ 0 , respectively, and (b) is true by the fact that the number of arriving tasks is bounded by C A , the number of task types is N T , and the maximum arrival rate of task types, max i {λ i }, is bounded by the number of servers. Inequality (c) is true by doing simple calculations and using the fact that min i,m { µ i,m (t)} is lower bounded by a constant for any t ≥ t 0 as discussed in (f ) of (22). Remark.…”

Heavy-traffic Delay Optimality in Pull-based Load Balancing Systems

“…At the central dispatcher, there is also a local memory denoted as m(t), through which the dispatcher can have limited information about the system. In each timeslot, the central dispatcher routes the new incoming tasks to one of the servers, immediately upon arrival as in [7,19,25,27,28,30]. Once a task joins a queue, it will remain in that queue until its service is completed.…”

“…It should be noted that besides being a key step in proving the sufficient conditions in Theorem 2, Proposition 1 has its own contributions. (i) First, the region of state-space collapse in this paper, i.e., R (r) is not a single dimensional line as in [7,19,25,27,28,30], nor a multi-dimensional convex cone as in [18,17,29,24]. This not only brings new challenges in proving state-space collapse itself, but also requires new methods to relate the collapse result to heavy-traffic delay optimality.…”

Flexible load balancing with multi-dimensional state-space collapse: Throughput and heavy-traffic delay optimality

“…Moreover, it has been shown in [26] that a joint JSQ and MaxWeight policy is heavy-traffic delay optimal for MapReduce clusters under a specific traffic scenario. For all traffic scenarios, a heavy-traffic delay optimal policy called 'local-task-first' policy was proposed in [27] based on this new framework. However, it is worth noting that the state-space collapse of all the aforementioned heavy-traffic optimal load balancing policies is only one-dimensional.…”