Load balancing plays a critical role in efficiently dispatching jobs in parallel-server systems such as cloud networks and data centers. A fundamental challenge in the design of load balancing algorithms is to achieve an optimal trade-off between delay performance and implementation overhead (e.g. communication or memory usage). This trade-off has primarily been studied so far from the angle of the amount of overhead required to achieve asymptotically optimal performance, particularly vanishing delay in large-scale systems. In contrast, in the present paper, we focus on an arbitrarily sparse communication budget, possibly well below the minimum requirement for vanishing delay, referred to as the hyper-scalable operating region. Furthermore, jobs may only be admitted when a specific limit on the queue position of the job can be guaranteed.
The centerpiece of our analysis is a universal upper bound for the achievable throughput of any dispatcher-driven algorithm for a given communication budget and queue limit. We also propose a specific hyper-scalable scheme which can operate at any given message rate and enforce any given queue limit, while allowing the server states to be captured via a closed product-form network, in which servers act as customers traversing various nodes. The product-form distribution is leveraged to prove that the bound is tight and that the proposed hyper-scalable scheme is throughput-optimal in a many-server regime given the communication and queue limit constraints. Extensive simulation experiments are conducted to illustrate the results.
The basic load balancing scenario involves a single dispatcher where tasks arrive that must immediately be forwarded to one of $N$ single-server queues. We discuss recent advances on scalable load balancing schemes which provide favorable delay performance when $N$ grows large, and yet only require minimal implementation overhead. Join-the-Shortest-Queue (JSQ) yields vanishing delays as $N$ grows large, as in a centralized queueing arrangement, but involves a prohibitive communication burden. In contrast, power-of-$d$ or JSQ($d$) schemes that assign an incoming task to a server with the shorte…
Applications in cloud platforms motivate the study of efficient load balancing under job-server constraints and server heterogeneity. In this paper, we study load balancing on a bipartite graph where left nodes correspond to job types and right nodes correspond to servers, with each edge indicating that a job type can be served by a server. Thus edges represent locality constraints, i.e., each job can only be served at servers which contained certain data and/or machine learning (ML) models. Servers in this system can have heterogeneous service rates. In this setting, we investigate the perfor…
Load balancing algorithms play critical roles in systems where the workload has to be distributed across multiple resources, such as cores in multiprocessor system, computers in distributed computing, and network links. In this paper, we study and evaluate four load balancing methods: random, round robin, shortest queue, and shortest queue with stale load information. We build a simulation model and compare mean delay of the systems for the load balancing methods. We also provide a method to improve shortest queue with stale load information load balancing. A performance analysis for the impro…
We present an overview of scalable load balancing algorithms which provide favorable delay performance in large-scale systems, and yet only require minimal implementation overhead. Aimed at a broad audience, the paper starts with an introduction to the basic load balancing scenario, consisting of a single dispatcher where tasks arrive that must immediately be forwarded to one of $N$ single-server queues. A popular class of load balancing algorithms are so-called power-of-$d$ or JSQ($d$) policies, where an incoming task is assigned to a server with the shortest queue among $d$ servers selected …
Joining the shortest or least loaded queue among $d$ randomly selected queues are two fundamental load balancing policies. Under both policies the dispatcher does not maintain any information on the queue length or load of the servers. In this paper we analyze the performance of these policies when the dispatcher has some memory available to store the ids of some of the idle servers. We consider methods where the dispatcher discovers idle servers as well as methods where idle servers inform the dispatcher about their state. We focus on large-scale systems and our analysis uses the cavity metho…
Load balancing in parallel infinite-server queues with action delay via phase representation
Graduate School of Science and Technology, University of Tsukuba（筑波大学理工学研究科）；Institute of Systems and Information Engineering, University of Tsukuba（筑波大学系统信息工学研究院）
In large-scale distributed systems, balancing the load in an efficient way is crucial in order to achieve low latency. Recently, some load balancing policies have been suggested which are able to achieve a bounded maximum queue length in the large-scale limit. However, these policies have thus far only been studied in case of exponential job sizes. As job sizes are more variable in real systems, we investigate how the performance of these policies (and in particular the value of these bounds) is impacted by the job size distribution. We present a unified analysis which can be used to compute t…
Heterogeneity is becoming increasingly ubiquitous in modern large-scale computer systems. Developing good load balancing policies for systems whose resources have varying speeds is crucial in achieving low response times. Indeed, how best to dispatch jobs to servers is a classical and well-studied problem in the queueing literature. Yet the bulk of existing work on large-scale systems assumes homogeneous servers; unfortunately, policies that perform well in the homogeneous setting can cause unacceptably poor performance---or even instability---in heterogeneous systems. We adapt the "power-of-d…
We consider the model of a token-based joint auto-scaling and load balancing strategy, proposed in a recent paper by Mukherjee, Dhara, Borst, and van Leeuwaarden (SIGMETRICS '17, arXiv:1703.08373), which offers an efficient scalable implementation and yet achieves asymptotically optimal steady-state delay performance and energy consumption as the number of servers $N\to\infty$. In the above work, the asymptotic results are obtained under the assumption that the queues have fixed-size finite buffers, and therefore the fundamental question of stability of the proposed scheme with infinite buffer…
Load balancing arises as a fundamental problem, underlying the dimensioning and operation of many computing and communication systems, such as job routing in data center clusters, multipath communication, Big Data and queueing systems. In essence, the decision-making agent maps each arriving job to one of the possibly heterogeneous servers while aiming at an optimization goal such as load balancing, low average delay or low loss rate. One main difficulty in finding optimal load balancing policies here is that the agent only partially observes the impact of its decisions, e.g., through the dela…
A fundamental challenge in large-scale cloud networks and data centers is to achieve highly efficient server utilization and limit energy consumption, while providing excellent user-perceived performance in the presence of uncertain and time-varying demand patterns. Auto-scaling provides a popular paradigm for automatically adjusting service capacity in response to demand while meeting performance targets, and queue-driven auto-scaling techniques have been widely investigated in the literature. In typical data center architectures and cloud environments however, no centralized queue is maintai…
We study large-scale systems operating under the JSQ$(d)$ policy in the presence of stringent task-server compatibility constraints. Consider a system with $N$ identical single-server queues and $M(N)$ task types, where each server is able to process only a small subset of possible task types. Each arriving task selects $d\geq 2$ random servers compatible to its type, and joins the shortest queue among them. The compatibility constraint is naturally captured by a fixed bipartite graph $G_N$ between the servers and the task types. When $G_N$ is complete bipartite, the meanfield approximation is…
In this paper, we derive and investigate approaches to dynamically load balance a distributed task parallel application software. The load balancing strategy is based on task migration. Busy processes export parts of their ready task queue to idle processes. Idle--busy pairs of processes find each other through a random search process that succeeds within a few steps with high probability. We evaluate the load balancing approach for a block Cholesky factorization implementation and observe a reduction in execution time on the order of 5\% in the selected test cases.
In this paper, we consider a load balancing system under a general pull-based policy. In particular, each arrival is randomly dispatched to one of the servers whose queue lengths are below a threshold, if there are any; otherwise, this arrival is randomly dispatched to one of the entire set of servers. We are interested in the fundamental relationship between the threshold and the delay performance of the system in heavy traffic. To this end, we first establish the following necessary condition to guarantee heavy-traffic delay optimality: the threshold will grow to infinity as the exogenous ar…
This paper studies the sensitivity (or insensitivity) of a class of load balancing algorithms that achieve asymptotic zero-waiting in the sub-Halfin-Whitt regime, named LB-zero. Most existing results on zero-waiting load balancing algorithms assume the service time distribution is exponential. This paper establishes the {\em large-system insensitivity} of LB-zero for jobs whose service time follows a Coxian distribution with a finite number of phases. This result suggests that LB-zero achieves asymptotic zero-waiting for a large class of service time distributions, which is confirmed in our si…
We consider the load balancing problem in large-scale heterogeneous systems with multiple dispatchers. We introduce a general framework called Local-Estimation-Driven (LED). Under this framework, each dispatcher keeps local (possibly outdated) estimates of queue lengths for all the servers, and the dispatching decision is made purely based on these local estimates. The local estimates are updated via infrequent communications between dispatchers and servers. We derive sufficient conditions for LED policies to achieve throughput optimality and delay optimality in heavy-traffic, respectively. Th…
Load balancing algorithms play a crucial role in delivering robust application performance in data centers and cloud networks. Recently, strong interest has emerged in Join-the-Idle-Queue (JIQ) algorithms, which rely on tokens issued by idle servers in dispatching tasks and outperform power-of-$d$ policies. Specifically, JIQ strategies involve minimal information exchange, and yet achieve zero blocking and wait in the many-server limit. The latter property prevails in a multiple-dispatcher scenario when the loads are strictly equal among dispatchers. For various reasons it is not uncommon howe…
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 guarant…
We consider a multi-server queueing system under the power-of-two policy with Poisson job arrivals, heterogeneous servers and a general job requirement distribution; each server operates under the first-come first-serve policy and there are no buffer constraints. We analyze the performance of this system in light traffic by evaluating the first two light traffic derivatives of the average job response time. These expressions point to several interesting structural features associated with server heterogeneity in light traffic: For unequal capacities, the average job response time is seen to de…
We address the problem of giving robust performance bounds based on the study of the asymptotic behavior of the insensitive load balancing schemes when the number of servers and the load scales jointly. These schemes have the desirable property that the stationary distribution of the resulting stochastic network depends on the distribution of job sizes only through its mean. It was shown that they give good estimates of performance indicators for systems with finite buffers, generalizing henceforth Erlang's formula whereas optimal policies are already theoretically and computationally out of r…
In the context of load balancing, Lu et al. introduced the distributed Join-Idle-Queue algorithm, where a group of dispatchers distribute jobs to a cluster of parallel servers. Each dispatcher maintains a queue of idle servers; when a job arrives to a dispatcher, it sends it to a server on its queue, or to a random server if the queue is empty. In turn, when a server has no jobs, it requests to be placed on the idle queue of a randomly chosen dispatcher. Although this algorithm was shown to be quite effective, the original asymptotic analysis makes simplifying assumptions that become increasin…
Supermarket models are a class of interesting parallel queueing networks with dynamic randomized load balancing and real-time resource management. When the parallel servers are subject to breakdowns and repairs, analysis of such a supermarket model becomes more difficult and challenging. In this paper, we apply the mean-field theory to studying four interrelated supermarket models with repairable servers, and numerically indicate impact of the different repairman groups on performance of the systems. First, we set up the systems of mean-field equations for the supermarket models with repairabl…
In recent years, enterprise Solid-State Drives (SSDs) are used in the caching layer of high-performance servers to close the growing performance gap between processing units and storage subsystem. SSD-based I/O caching is typically not effective in workloads with burst accesses in which the caching layer itself becomes the performance bottleneck because of the large number of accesses. Existing I/O cache architectures mainly focus on maximizing the cache hit ratio while they neglect the average queue time of accesses. Previous studies suggested bypassing the cache when burst accesses are ident…
Nowadays, more and more increasingly hard computations are performed in challenging fields like weather forecasting, oil and gas exploration, and cryptanalysis. Many of such computations can be implemented using a computer cluster with a large number of servers. Incoming computation requests are then, via a so-called load balancing policy, distributed over the servers to ensure optimal performance. Additionally, being able to switch-off some servers during low period of workload, gives potential to reduced energy consumption. Therefore, load balancing forms, albeit indirectly, a trade-off betw…
Load balancing is a common approach in web server farms or inventory routing problems. An important issue in such systems is to determine the server to which an incoming request should be routed to optimize a given performance criteria. In this paper, we assume the server's scheduling disciplines to be heterogeneous. More precisely, a server implements a scheduling discipline which belongs to the class of limited processor sharing (LPS-$d$) scheduling disciplines. Under LPS-$d$, up to $d$ jobs can be served simultaneously, and hence, includes as special cases First Come First Served ($d=1$) an…
We consider a system of $N$ servers inter-connected by some underlying graph topology $G_N$. Tasks arrive at the various servers as independent Poisson processes of rate $λ$. Each incoming task is irrevocably assigned to whichever server has the smallest number of tasks among the one where it appears and its neighbors in $G_N$. Tasks have unit-mean exponential service times and leave the system upon service completion. The above model has been extensively investigated in the case $G_N$ is a clique. Since the servers are exchangeable in that case, the queue length process is quite tractable, an…
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 determi…
