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

Abstract

Dynamic affinity load balancing of multi-type tasks on multi-skilled servers, when the service rate of each task type on each of the servers is known and can possibly be different from each other, is an open problem for over three decades. The goal is to do task assignment on servers in a real time manner so that the system becomes stable, which means that the queue lengths do not diverge to infinity in steady state (throughput optimality), and the mean task completion time is minimized (delay optimality). The fluid model planning, Max-Weight, and c-µ-rule algorithms have theoretical guarantees on optimality in some aspects for the affinity problem, but they consider a complicated queueing structure and either require the task arrival rates, the service rates of tasks on servers, or both. In many cases that are discussed in the introduction section, both task arrival rates and service rates of different task types on different servers are unknown. In this work, the Blind GB-PANDAS algorithm is proposed which is completely blind to task arrival rates and service rates. Blind GB-PANDAS uses an exploration-exploitation approach for load balancing. We prove that Blind GB-PANDAS is throughput optimal under arbitrary and unknown distributions for service times of different task types on different servers and unknown task arrival rates. Blind GB-PANDAS desires to route an incoming task to the server with the minimum weighted-workload, but since the service rates are unknown, such routing of incoming tasks is not guaranteed which makes the throughput optimality analysis more complicated than the case where service rates are known. Our extensive experimental results reveal that Blind GB-PANDAS significantly outperforms existing methods in terms of mean task completion time at high loads.

Performance Analysis of Hybrid MTS/MTO Systems with Stochastic Demand and Production

“…For an accurate performance assessment, it is however essential that the stochastic characteristics of the production processes and of the demand are accurately estimated. The statistical inference of the model parameters can either be based on prior measurements or can be learned while the production system is running using an exploration-exploitation approach [40,41], and this will be considered in future work.…”

Load Balancing Under Strict Compatibility Constraints

“…On the scheduling side, there has been significant development in the analysis of multiserver input-queued systems with multiple task types; see [1,12,15,32,33,45,46] and the references therein. In this area, the work that is closest, in spirit, to our setup, is by Tsitsiklis and Xu [32,33].…”

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