Power of
            <i>d</i>
            Choices for Large-Scale Bin Packing

Xie, Qiaomin; Dong, Xiaobo; Lu, Yi; Srikant, R.

doi:10.1145/2745844.2745849

Cited by 42 publications

(53 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we will demonstrate the novelty of Theorem 1 by considering two applications in data center networks: the power of two choices (Mitzenmacher 1996, Vvedenskaya et al 1996 and the virtual machine placement problem (Xie et al 2015). For both problems, mean-field models have been used to analyze the performance of the systems in an infinite server regime, but the approximation errors of the mean-field limits for systems with finite number of servers were unknown.…”

Section: Applications In Data Center Networkmentioning

confidence: 99%

“…In Xie et al (2015), the authors considered a data center network with M identical servers where each server has B units of resources and can host at most B virtual machines (VMs) as shown in Figure 4. Assume VM requests arrive according to a Poisson process with rate λM and the lifetime of each VM is exponentially distributed with mean μ 1.…”

Section: Virtual Machine Placement In Cloud Computing Systemsmentioning

confidence: 99%

“…Let s k (t) denote the fraction of servers with at least k VMs. Based on the mean-field analysis, it has been shown in Xie et al (2015) that s k (∞) weakly converges to s * k , where s * k is the equilibrium point of the following mean-field system:…”

Section: Virtual Machine Placement In Cloud Computing Systemsmentioning

confidence: 99%

“…The equilibrium point in this case can be recursively solved but the closed-form expression is difficult to obtain. The asymptotic stability of the system has been proved in Xie et al (2015). We now consider the linearized system at the equilibrium, which is Therefore, the equilibrium point is (locally) exponentially stable.…”

Section: Virtual Machine Placement In Cloud Computing Systemsmentioning

confidence: 99%

“…The 127 algorithm achieves similar delay performance as the power of two choices with a sampling ratio slightly larger than one (i.e., it only samples slightly more than one server on average for each incoming task). In Xie et al (2015) and Mukhopadhyay et al (2015), the mean-field analysis has been used to study the loss model, which is related to the virtual machine placement problem in data center networks. In these applications, the systems under consideration are modeled as CTMCs, and the solutions (equilibrium points) of the corresponding mean-field models are then used to approximate the stationary distributions of the CTMCs.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On the Approximation Error of Mean-Field Models

Lü

2018

Stochastic Systems

View full text Add to dashboard Cite

Abstract. Mean-field models have been used to study large-scale and complex stochastic systems, such as large-scale data centers and dense wireless networks, using simple deterministic models (dynamical systems). This paper analyzes the approximation error of mean-field models for continuous-time Markov chains (CTMCs) and focuses on mean-field models that are represented as finite-dimensional dynamical systems with a unique equilibrium point. By applying Stein's method and the perturbation theory, the paper shows that under some mild conditions, if the mean-field model is globally asymptotically stable and locally exponentially stable, the mean-square difference between the stationary distribution of the stochastic system of size M (i.e., with M nodes/particles) and the equilibrium point of the corresponding mean-field system is O(1/M). The result of this paper establishes a general theorem for establishing the convergence and the approximation error (i.e., the rate of convergence) of a large class of CTMCs to their mean-field limits by mainly looking into the stability of the mean-field model, which is a deterministic system and is often easier to analyze than the CTMCs. Two applications of mean-field models in data center networks are presented to demonstrate the novelty of our results.

show abstract

Section: Applications In Data Center Networkmentioning

confidence: 99%

Section: Virtual Machine Placement In Cloud Computing Systemsmentioning

confidence: 99%

Section: Virtual Machine Placement In Cloud Computing Systemsmentioning

confidence: 99%

Section: Virtual Machine Placement In Cloud Computing Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On the Approximation Error of Mean-Field Models

Lü

2018

Stochastic Systems

View full text Add to dashboard Cite

show abstract

Two-choice regulation in heterogeneous closed networks

Fricker

Servel

2015

Queueing Syst

View full text Add to dashboard Cite

show abstract

Choosing among heterogeneous server clouds

2016

View full text Add to dashboard Cite

This paper considers a model of interest in cloud computing applications. We consider a multiserver system consisting of N heterogeneous servers. The servers are categorized into M( N ) different types according to their service capabilities. Jobs having specific resource requirements arrive at the system according to a Poisson process with rate N λ. Upon each arrival, a small number of servers are sampled uniformly at random from each server type. The job is then routed to the sampled server with maximum vacancy per server capacity. If a job cannot obtain the required amount of resources from the server to which it is assigned, then the job is discarded. We analyze the system in the limit as N → ∞. This gives rise to a mean field, which we show has a unique fixed point and is globally attractive. Furthermore, as N → ∞, the servers behave independently. The stationary tail probabilities of server occupancies are obtained from the stationary solution of the mean field. Numerical results suggest that the proposed scheme significantly reduces the average blocking probability compared to static schemes that probabilistically route jobs to servers in proportion to the number of servers of each type. Moreover, the reduction in blocking holds even for systems at high load. For the limiting system in statistical equilibrium, our simulation results indicate that the occupancy distribution is insensitive to the holding time distribution and only depends on its mean.

show abstract

Power of d Choices for Large-Scale Bin Packing

Cited by 42 publications

References 23 publications

On the Approximation Error of Mean-Field Models

On the Approximation Error of Mean-Field Models

Two-choice regulation in heterogeneous closed networks

Choosing among heterogeneous server clouds

Contact Info

Product

Resources

About