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تسجيل مستخدم جديدGB-PANDAS: Throughput and heavy-traffic optimality analysis for affinity scheduling
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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, data-intensive 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 $cmu$-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 (JSQ-MaxWeight), 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 JSQ-MaxWeight algorithm by twofold
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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 i
s 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-$mu$-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.
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