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We consider a large-scale parallel-server loss system with an unknown arrival rate, where each server is able to adjust its processing speed. The objective is to minimize the system cost, which consists of a power cost to maintain the servers' processing speeds and a quality of service cost depending on the tasks' processing times, among others. We draw on ideas from stochastic approximation to design a novel speed scaling algorithm and prove that the servers' processing speeds converge to the globally asymptotically optimum value. Curiously, the algorithm is fully distributed and does not require any communication between servers. Apart from the algorithm design, a key contribution of our approach lies in demonstrating how concepts from the stochastic approximation literature can be leveraged to effectively tackle learning problems in large-scale, distributed systems. En route, we also analyze the performance of a fully heterogeneous parallel-server loss system, where each server has a distinct processing speed, which might be of independent interest. 

We consider large-scale load balancing systems where processing time distribution of tasks depend on both task and server types. We analyze the system in the asymptotic regime where the number of task and server types tend to infinity proportionally to each other. In such heterogeneous setting, popular policies like Join Fastest Idle Queue (JFIQ), Join Fastest Shortest Queue (JFSQ) are known to perform poorly and they even shrink the stability region. Moreover, to the best of our knowledge, in this setup, finding a scalable policy with provable performance guarantee has been an open question prior to this work. In this paper, we propose and analyze two asymptotically delay-optimal dynamic load balancing approaches: (a) one that efficiently reserves the processing capacity of each server for good tasks and route tasks under the Join Idle Queue policy; and (b) a speed-priority policy that increases the probability of servers processing tasks at a high speed. Introducing a novel analytical framework and using the mean-field method and stochastic coupling arguments, we prove that both policies above achieve asymptotic zero queueing, whereby the probability that a typical task is assigned to an idle server tends to 1 as the system scales. 

We consider load balancing in large-scale heterogeneous server systems in the presence of data locality that imposes constraints on which tasks can be assigned to which servers. The constraints are naturally captured by a bipartite graph between the servers and the dispatchers handling assignments of various arrival flows. When a task arrives, the corresponding dispatcher assigns it to a server with the shortest queue among [Formula: see text] randomly selected servers obeying these constraints. Server processing speeds are heterogeneous, and they depend on the server type. For a broad class of bipartite graphs, we characterize the limit of the appropriately scaled occupancy process, both on the process level and in steady state, as the system size becomes large. Using such a characterization, we show that imposing data locality constraints can significantly improve the performance of heterogeneous systems. This is in stark contrast to either heterogeneous servers in a full flexible system or data locality constraints in systems with homogeneous servers, both of which have been observed to degrade the system performance. Extensive numerical experiments corroborate the theoretical results. Funding: This work was partially supported by the National Science Foundation [CCF. 07/2021–06/2024]. 

Modern data centers suffer from immense power consumption. As a result, data center operators have heavily invested in capacity-scaling solutions, which dynamically deactivate servers if the demand is low and activate them again when the workload increases. We analyze a continuous-time model for capacity scaling, where the goal is to minimize the weighted sum of flow time, switching cost, and power consumption in an online fashion. We propose a novel algorithm, called adaptive balanced capacity scaling (ABCS), that has access to black-box machine learning predictions. ABCS aims to adapt to the predictions and is also robust against unpredictable surges in the workload. In particular, we prove that ABCS is [Formula: see text] competitive if the predictions are accurate, and yet, it has a uniformly bounded competitive ratio even if the predictions are completely inaccurate. Finally, we investigate the performance of this algorithm on a real-world data set and carry out extensive numerical experiments, which positively support the theoretical results. Funding: This work was partially supported by the Division of Computing and Communication Foundations [Grant 2113027]. The authors also acknowledge financial support for this project from the Algorithm and Randomness Center–Transdisciplinary Research Institute for Advancing Data Science Fellowship at Georgia Tech. 

Consider a system with N identical single-server queues and a number of task types, where each server is able to process only a small subset of possible task types. Arriving tasks select [Formula: see text] random compatible servers and join the shortest queue among them. The compatibility constraints are captured by a fixed bipartite graph between the servers and the task types. When the graph is complete bipartite, the mean-field approximation is accurate. However, such dense compatibility graphs are infeasible for large-scale implementation. We characterize a class of sparse compatibility graphs for which the mean-field approximation remains valid. For this, we introduce a novel notion, called proportional sparsity, and establish that systems with proportionally sparse compatibility graphs asymptotically match the performance of a fully flexible system. Furthermore, we show that proportionally sparse random compatibility graphs can be constructed, which reduce the server degree almost by a factor [Formula: see text] compared with the complete bipartite compatibility graph. 

We consider a large-scale service system where incoming tasks have to be instantaneously dispatched to one out of many parallel server pools. The user-perceived performance degrades with the number of concurrent tasks and the dispatcher aims at maximizing the overall quality of service by balancing the load through a simple threshold policy. We demonstrate that such a policy is optimal on the fluid and diffusion scales, while only involving a small communication overhead, which is crucial for large-scale deployments. In order to set the threshold optimally, it is important, however, to learn the load of the system, which may be unknown. For that purpose, we design a control rule for tuning the threshold in an online manner. We derive conditions that guarantee that this adaptive threshold settles at the optimal value, along with estimates for the time until this happens. In addition, we provide numerical experiments that support the theoretical results and further indicate that our policy copes effectively with time-varying demand patterns. Summary of Contribution: Data centers and cloud computing platforms are the digital factories of the world, and managing resources and workloads in these systems involves operations research challenges of an unprecedented scale. Due to the massive size, complex dynamics, and wide range of time scales, the design and implementation of optimal resource-allocation strategies is prohibitively demanding from a computation and communication perspective. These resource-allocation strategies are essential for certain interactive applications, for which the available computing resources need to be distributed optimally among users in order to provide the best overall experienced performance. This is the subject of the present article, which considers the problem of distributing tasks among the various server pools of a large-scale service system, with the objective of optimizing the overall quality of service provided to users. A solution to this load-balancing problem cannot rely on maintaining complete state information at the gateway of the system, since this is computationally unfeasible, due to the magnitude and complexity of modern data centers and cloud computing platforms. Therefore, we examine a computationally light load-balancing algorithm that is yet asymptotically optimal in a regime where the size of the system approaches infinity. The analysis is based on a Markovian stochastic model, which is studied through fluid and diffusion limits in the aforementioned large-scale regime. The article analyzes the load-balancing algorithm theoretically and provides numerical experiments that support and extend the theoretical results.