arXiv subjects

Xingyu Zhou

Publications and source records attributed to Xingyu Zhou.

119 records · Page 7Linked to original sources

arXiv2020

Optimal Load Balancing in Bipartite Graphs

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 performance of two policies named Join-the-Fastest-of-the-Shortest-Queue (JFSQ) and Join-the-Fastest-of-the-Idle-Queue (JFIQ), which are simple variants of Join-the-Shortest-Queue and Join-the-Idle-Queue, where ties are broken in favor of the fastest servers. Under a "well-connected" graph condition, we show that JFSQ and JFIQ are asymptotically optimal in the mean response time when the number of servers goes to infinity. In addition to asymptotic optimality, we also obtain upper bounds on the mean response time for finite-size systems. We further show that the well-connectedness condition can be satisfied by a random bipartite graph construction with relatively sparse connectivity.

cs.PF↗

arXiv2020

Experimental review of the $Υ(1S,2S,3S)$ physics at $e^+e^-$ colliders and the LHC

The three lowest-lying $Υ$ states, i.e. $Υ(1S)$, $Υ(2S)$, and $Υ(3S)$, composed of $b\bar b$ pairs and below the $B\bar B$ threshold, provide a good platform for the researches of hadronic physics and physics beyond the Standard Model. They can be produced directly in $e^+e^-$ colliding experiments, such as CLEO, Babar, and Belle, with low continuum backgrounds. In these experiments, many measurements of the exclusive $Υ(1S)$ and $Υ(2S)$ decays into light hadrons, which shed light on the "80\% rule" for the Okubo-Zweig-Iizuka suppressed decays in the bottomonium sector, were carried out. Meanwhile, many studies of the charmonium and bottomonium productions in $Υ(1S,2S,3S)$ decays were performed, to distinguish different Quantum Chromodynamics (QCD) models. Besides, exotic states and new physics were also extensively explored in $Υ(1S,2S,3S)$ decays at CLEO, BaBar, and Belle. The $Υ(1S,2S,3S)$ states can also be produced in $pp$ collisions and in collisions involving heavy ions. The precision measurements of their cross sections and polarizations at the large hadron collider (LHC), especially in the CMS, ATLAS, and LHCb experiments, help to understand $Υ$ production mechanisms in $pp$ collisions. The observation of the sequential $Υ$ suppression in heavy ion collisions at CMS is of great importance for verifying the quark-gluon plasma predicted by QCD. In this article, we review the experimental results on $Υ(1S,2S,3S)$ at $e^+e^-$ colliders and the LHC, and summarize their prospects at Belle II and the LHC.

hep-ex↗

arXiv2020

Multi-Armed Bandits with Local Differential Privacy

This paper investigates the problem of regret minimization for multi-armed bandit (MAB) problems with local differential privacy (LDP) guarantee. In stochastic bandit systems, the rewards may refer to the users' activities, which may involve private information and the users may not want the agent to know. However, in many cases, the agent needs to know these activities to provide better services such as recommendations and news feeds. To handle this dilemma, we adopt differential privacy and study the regret upper and lower bounds for MAB algorithms with a given LDP guarantee. In this paper, we prove a lower bound and propose algorithms whose regret upper bounds match the lower bound up to constant factors. Numerical experiments also confirm our conclusions.

cs.LG↗

arXiv2020

A Note on Load Balancing in Many-Server Heavy-Traffic Regime

In this note, we apply Stein's method to analyze the performance of general load balancing schemes in the many-server heavy-traffic regime. In particular, consider a load balancing system of $N$ servers and the distance of arrival rate to the capacity region is given by $N^{1-α}$ with $α> 1$. We are interested in the performance as $N$ goes to infinity under a large class of policies. We establish different asymptotics under different scalings and conditions. Specifically, (i) If the second moments linearly increase with $N$ with coefficients $σ_a^2$ and $ν_s^2$, then for any $α> 4$, the distribution of the sum queue length scaled by $N^{-α}$ converges to an exponential random variable with mean $\frac{σ_a^2 + ν_s^2}{2}$. (3) If the second moments quadratically increase with $N$ with coefficients $\tildeσ_a^2$ and $\tildeν_s^2$, then for any $α> 3$, the distribution of the sum queue length scaled by $N^{-α-1}$ converges to an exponential random variable with mean $\frac{\tildeσ_a^2 + \tildeν_s^2}{2}$. Both results are simple applications of our previously developed framework of Stein's method for heavy-traffic analysis in \cite{zhou2020note}.

math.PR↗

arXiv2020

Asymptotically Optimal Load Balancing in Large-scale Heterogeneous Systems with Multiple Dispatchers

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. These conditions directly imply delay optimality for many previous local-memory based policies in heavy traffic. Moreover, the results enable us to design new delay optimal policies for heterogeneous systems with multiple dispatchers. Finally, the heavy-traffic delay optimality of the LED framework directly resolves a recent open problem on how to design optimal load balancing schemes using delayed information.

cs.PF↗

arXiv2019

An initial overview of the extent and structure of recent star formation within the Serpens Molecular Cloud using Gaia Data Release 2

The dense clusters within the Serpens Molecular Cloud are among the most active regions of nearby star formation. In this paper, we use Gaia DR2 parallaxes and proper motions to statistically measure 1167 kinematic members of Serpens, few of which were previously identified, to evaluate the star formation history of the complex. The optical members of Serpens are concentrated in three distinct groups located at 380 to 480 pc; the densest clusters are still highly obscured by optically-thick dust and have few optical members. The total population of young stars and protostars in Serpens is at least 2000 stars, including past surveys that were most sensitive to protostars and disks, and may be far higher. Distances to dark clouds measured from deficits in star counts are consistent with the distances to the optical star clusters. The Serpens Molecular Cloud is seen in the foreground of the Aquila Rift, dark clouds located at 600 to 700 pc, and behind patchy extinction, here called the Serpens Cirrus, located at ~250 pc. Based on the lack of a distributed population of older stars, the star formation rate throughout the Serpens Molecular Cloud increased by at least a factor of 20 within the past ~5 Myr. The optically bright stars in Serpens Northeast are visible because their natal molecular cloud has been eroded and not because they were flung outwards from a central factory of star formation. The separation between subclusters of 20 to 100 pc and the absence of an older population leads to speculation that an external forcing was needed to trigger the active star formation.

astro-ph.SR↗

arXiv2019

Asymmetric sending or not-sending twin-field quantum key distribution in practice

Quantum key distribution (QKD) offers a secret way to share keys between legitimate users which is guaranteed by the law of quantum mechanics. Most recently, the limitation of transmission distance without quantum repeaters was broken through by twin-field QKD [Nature (London) 557, 400 (2018)]. Based on its main idea, sending or not-sending (SNS) QKD protocol was proposed [Phys. Rev. A 98, 062323 (2018)], which filled the remaining security loopholes and can tolerate large misalignment errors. In this paper, we give a more general model for SNS QKD, where the two legitimate users, Alice and Bob, can possess asymmetric quantum channels. By applying the method present in the work, the legitimate users can achieve dramatically increased key generation rate and transmission distance compared with utilizing the original symmetric protocol. Therefore, our present work represents a further step along the progress of practical QKD.

quant-ph↗

arXiv2018

Heavy-traffic Delay Optimality in Pull-based Load Balancing Systems: Necessary and Sufficient Conditions

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 arrival rate approaches the boundary of the capacity region (i.e., the load intensity approaches one) but the growth rate should be slower than a polynomial function of the mean number of tasks in the system. As a special case of this result, we directly show that the delay performance of the popular pull-based policy Join-Idle-Queue (JIQ) lies strictly between that of any heavy-traffic delay optimal policy and that of random routing. We further show that a sufficient condition for heavy-traffic delay optimality is that the threshold grows logarithmically with the mean number of tasks in the system. This result directly resolves a generalized version of the conjecture by Kelly and Laws.

cs.PF↗

arXiv2018

Flexible Load Balancing with Multi-dimensional State-space Collapse: Throughput and Heavy-traffic Delay Optimality

Heavy traffic analysis for load balancing policies has relied heavily on the condition of state-space collapse onto a single-dimensional line in previous works. In this paper, via Lyapunov-drift analysis, we rigorously prove that even under a multi-dimensional state-space collapse, steady-state heavy-traffic delay optimality can still be achieved for a general load balancing system. This result directly implies that achieving steady-state heavy-traffic delay optimality simply requires that no server is idling while others are busy at heavy loads, thus complementing and extending the result obtained by diffusion approximations. Further, we explore the greater flexibility provided by allowing a multi-dimensional state-space collapse in designing new load balancing policies that are both throughput optimal and heavy-traffic delay optimal in steady state. This is achieved by overcoming various technical challenges, and the methods used in this paper could be of independent interest.

cs.DC↗

arXiv2018

On the Fenchel Duality between Strong Convexity and Lipschitz Continuous Gradient

We provide a simple proof for the Fenchel duality between strong convexity and Lipschitz continuous gradient. To this end, we first establish equivalent conditions of convexity for a general function that may not be differentiable. By utilizing these equivalent conditions, we can directly obtain equivalent conditions for strong convexity and Lipschitz continuous gradient. Based on these results, we can easily prove Fenchel duality. Beside this main result, we also identify several conditions that are implied by strong convexity or Lipschitz continuous gradient, but are not necessarily equivalent to them. This means that these conditions are more general than strong convexity or Lipschitz continuous gradient themselves.

math.OC↗

arXiv2017

Designing Low-Complexity Heavy-Traffic Delay-Optimal Load Balancing Schemes: Theory to Algorithms

We establish a unified analytical framework for load balancing systems, which allows us to construct a general class $Π$ of policies that are both throughput optimal and heavy-traffic delay optimal. This general class $Π$ includes as special cases popular policies such as join-shortest-queue and power-of-$d$, but not the join-idle-queue (JIQ) policy. In fact, we show that JIQ, which is not in $Π$, is actually not heavy-traffic delay optimal. Owing to the significant flexibility offered by class $Π$, we are able to design a new policy called join-below-threshold (JBT-d), which maintains the simplicity of pull-based policies such as JIQ, but updates its threshold dynamically. We prove that JBT-$d$ belongs to the class $Π$ when the threshold is picked appropriately and thus it is heavy-traffic delay optimal. Extensive simulations show that the new policy not only has a low complexity in message rates, but also achieves excellent delay performance, comparable to the optimal join-shortest-queue in various system settings.

cs.DC↗