Asymptotically Optimal Load Balancing Topologies

Mukherjee, Debankur; Borst, Sem; Leeuwaarden, Johan S. H. van

doi:10.1145/3292040.3219674

Cited by 16 publications

(50 citation statements)

References 35 publications

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“…The expressions for the arrival terms in the derivatives of (15) and the reduced arrival rateλ should be considered more carefully due to the discontinuity at q 00 = 0. We will give a sketch of the derivation of this fluid limit in Subsection 5.2.…”

Section: Fluid Limitmentioning

confidence: 99%

“…The fluid-limit expression can be validated with simulations of the fluid-scaled stochastic process. Consider for instance Figure 3 where the solution of the fluid limit (15) is presented together with a simulated trajectory of a reasonably large system. It can be observed that the simulated trajectory fluctuates closely around the numerical solution of the fluid limit, which supports the connection between the fluid limit and the behavior of the stochastic system in a many-server setting.…”

Section: Fluid Limitmentioning

confidence: 99%

“…), rounded at four decimals. Figure 5: A comparison between the long-term behavior of a simulated trajectory for N = 2000 servers (green) and the unique fixed point (blue) of the fluid limit (15). The model parameters are given by d 1 = 3, λ = 0.8, µ 1 = 1 and µ 2 = 0.5.…”

Section: Sufficiently Small Primary Selectionsmentioning

confidence: 99%

“…Step 3: Towards fluid limits. While making the transition from integral equations to differential equations with N tending to infinity, the representation of the departure terms in (15) is straightforward. The arrival terms in the differential equations, on the other hand, are not immediately obvious.…”

mentioning

confidence: 99%

“…of the arriving jobs will be allocated as type II jobs which causes the changes in (15) for q 00 , q 01 and q 10 .…”

mentioning

confidence: 99%

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Job assignment in large-scale service systems with affinity relations

2019

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We consider load balancing in service systems with affinity relations between jobs and servers. Specifically, an arriving job can be allocated to a fast, primary server from a particular selection associated with this job or to a secondary server to be processed at a slower rate. Such job-server affinity relations can model network topologies based on geographical proximity, or data locality in cloud scenarios. We introduce load balancing schemes that allocate jobs to primary servers if available, and otherwise to secondary servers. A novel coupling construction is developed to obtain stability conditions and performance bounds using a coupling technique. We also conduct a fluid limit analysis for symmetric model instances, which reveals a delicate interplay between the model parameters and load balancing performance.

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Section: Fluid Limitmentioning

confidence: 99%

Section: Fluid Limitmentioning

confidence: 99%

Section: Sufficiently Small Primary Selectionsmentioning

confidence: 99%

mentioning

confidence: 99%

“…of the arriving jobs will be allocated as type II jobs which causes the changes in (15) for q 00 , q 01 and q 10 .…”

mentioning

confidence: 99%

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Job assignment in large-scale service systems with affinity relations

2019

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Stability of JSQ in queues with general server-job class compatibilities

2020

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We consider Poisson streams of exponentially distributed jobs arriving at each edge of a hypergraph of queues. Upon arrival, an incoming job is rooted to the shortest queue among the corresponding vertices. This generalizes many known models such as power-of-d load balancing and JSQ (join the shortest queue) on generic graphs. We provide a generic condition for stability of this model. We show that some graph topologies lead to a loss of capacity, implying more restrictive stability conditions than in, e.g., complete graphs.

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Scalable Load Balancing in Networked Systems: Universality Properties and Stochastic Coupling Methods

Boor

Borst

Leeuwaarden

et al. 2019

Proceedings of the International Congress of Mathematicians (ICM 2018)

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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 -referred to as the supermarket model -consisting of a single dispatcher where tasks arrive that must immediately be forwarded to one of N single-server queues. The supermarket model is a dynamic counterpart of the classical balls-and-bins setup where balls must be sequentially distributed across bins.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 uniformly at random. As the name reflects, this class includes the celebrated Join-the-Shortest-Queue (JSQ) policy as a special case (d = N ), which has strong stochastic optimality properties and yields a mean waiting time that vanishes as N grows large for any fixed subcritical load. However, a nominal implementation of the JSQ policy involves a prohibitive communication burden in large-scale deployments. In contrast, a simple random assignment policy (d = 1) does not entail any communication overhead, but the mean waiting time remains constant as N grows large for any fixed positive load.In order to examine the fundamental trade-off between delay performance and implementation overhead, we consider an asymptotic regime where the diversity parameter d(N ) depends on N . We investigate what growth rate of d(N ) is required to match the optimal performance of the JSQ policy on fluid and diffusion scale, and achieve a vanishing waiting time in the limit. The results demonstrate that the asymptotics for the JSQ(d(N )) policy are insensitive to the exact growth rate of d(N ), as long as the latter is sufficiently fast, implying that the optimality of the JSQ policy can asymptotically be preserved while dramatically reducing the communication overhead.Stochastic coupling techniques play an instrumental role in establishing the asymptotic optimality and universality properties, and augmentations of the coupling constructions allow these properties to be extended to infinite-server settings and network scenarios. We additionally show how the communication overhead can be reduced yet further by the so-called Join-the-Idle-Queue (JIQ) scheme, leveraging memory at the dispatcher to keep track of idle servers.In the present paper we review scalable load balancing algorithms (LBAs) which achieve excellent delay performance in large-scale systems and yet only involve low implementation overhead. LBAs play a critical role in distributing service requests or tasks (e.g. compute jobs, data base look-ups, file transfers) among servers or distributed resources in parallel-processing systems. The analysis and design of LBAs has attracted strong attention in recent years, mainly spurred by crucial scalability challenges arising in cloud networks and data centers with massive...

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Asymptotically Optimal Load Balancing Topologies

Cited by 16 publications

References 35 publications

Job assignment in large-scale service systems with affinity relations

Job assignment in large-scale service systems with affinity relations

Stability of JSQ in queues with general server-job class compatibilities

Scalable Load Balancing in Networked Systems: Universality Properties and Stochastic Coupling Methods

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