Gb-Pandas:

Abstract

Dynamic affinity scheduling has been an open problem for nearly three decades. The problem is to dynamically schedule multi-type tasks to multi-skilled servers such that the resulting queueing system is both stable in the capacity region (throughput optimality) and the mean delay of tasks is minimized at high loads near the boundary of the capacity region (heavy-traffic optimality). As for applications, dataintensive analytics like MapReduce, Hadoop, and Dryad fit into this setting, where the set of servers is heterogeneous for different task types, so the pair of task type and server determines the processing rate of the task. The load balancing algorithm used in such frameworks is an example of affinity scheduling which is desired to be both robust and delay optimal at high loads when hot-spots occur. Fluid model planning, the MaxWeight algorithm, and the generalized c?-rule are among the first algorithms proposed for affinity scheduling that have theoretical guarantees on being optimal in different senses, which will be discussed in the related work section. All these algorithms are not practical for use in data center applications because of their non-realistic assumptions. The join-the-shortest-queue-MaxWeight (JSQMaxWeight), JSQ-Priority, and weighted-workload algorithms are examples of load balancing policies for systems with two and three levels of data locality with a rack structure. In this work, we propose the Generalized-Balanced-Pandas algorithm (GB-PANDAS) for a system with multiple levels of data locality and prove its throughput optimality. We prove this result under an arbitrary distribution for service times, whereas most previous theoretical work assumes geometric distribution for service times. The extensive simulation results show that the GB-PANDAS algorithm alleviates the mean delay and has a better performance than the JSQMaxWeight algorithm by up to twofold at high loads. We believe that the GB-PANDAS algorithm is heavy-traffic optimal in a larger region than JSQ-MaxWeight, which is an interesting problem for future work.

Optimal Placement of Remote-Controlled Switches in Distribution Networks in the Presence of Distributed Generators

“…The DNs are radial and during the restoration should remain radial. The graph representation of the system can guarantee that after any restoration step the network remain radial [25][26][27]. NO switches connect either two nodes within the network or DGs (alternative sources) to network nodes.…”

Overlap times in the infinite server queue

“…These jobs are then served by each being processed individually and the results are returned to the user. For more discussion, see works such as Lu et al [10], Pender and Phung-Duc [19], Xie et al [23], Yekkehkhany et al [24] and references therein. Another relevant application in the context of infectious disease modeling is modeling the number infections of COVID-19.…”