Stochastic Systems最新文献_第4页

Greedy Matching in Bipartite Random Graphs 二部随机图中的贪婪匹配

Stochastic Systems Pub Date : 2021-11-02 DOI: 10.1287/stsy.2021.0082

N. Arnosti

{"title":"Greedy Matching in Bipartite Random Graphs","authors":"N. Arnosti","doi":"10.1287/stsy.2021.0082","DOIUrl":"https://doi.org/10.1287/stsy.2021.0082","url":null,"abstract":"This paper studies the performance of greedy matching algorithms on bipartite graphs [Formula: see text]. We focus primarily on three classical algorithms: [Formula: see text], which sequentially selects random edges from [Formula: see text]; [Formula: see text], which sequentially matches random vertices in [Formula: see text] to random neighbors; and [Formula: see text], which generates a random priority order over vertices in [Formula: see text] and then sequentially matches random vertices in [Formula: see text] to their highest-priority remaining neighbor. Prior work has focused on identifying the worst-case approximation ratio for each algorithm. This guarantee is highest for [Formula: see text] and lowest for [Formula: see text]. Our work instead studies the average performance of these algorithms when the edge set [Formula: see text] is random. Our first result compares [Formula: see text] and [Formula: see text] and shows that on average, [Formula: see text] produces more matches. This result holds for finite graphs (in contrast to previous asymptotic results) and also applies to “many to one” matching in which each vertex in [Formula: see text] can match with multiple vertices in [Formula: see text]. Our second result compares [Formula: see text] and [Formula: see text] and shows that the better worst-case guarantee of [Formula: see text] does not translate into better average performance. In “one to one” settings where each vertex in [Formula: see text] can match with only one vertex in [Formula: see text], the algorithms result in the same number of matches. When each vertex in [Formula: see text] can match with two vertices in [Formula: see text] produces more matches than [Formula: see text].","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66531612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 6

A Diffusion Approximation Theory of Momentum Stochastic Gradient Descent in Nonconvex Optimization 非凸优化中动量随机梯度下降的扩散逼近理论

Stochastic Systems Pub Date : 2021-10-21 DOI: 10.1287/stsy.2021.0083

Tianyi Liu, Zhehui Chen, Enlu Zhou, T. Zhao

引用次数: 0

Average Cost Brownian Drift Control with Proportional Changeover Costs 具有比例转换成本的平均成本布朗漂移控制

Stochastic Systems Pub Date : 2021-09-01 DOI: 10.1287/stsy.2021.0071

John H. Vande Vate

{"title":"Average Cost Brownian Drift Control with Proportional Changeover Costs","authors":"John H. Vande Vate","doi":"10.1287/stsy.2021.0071","DOIUrl":"https://doi.org/10.1287/stsy.2021.0071","url":null,"abstract":"This paper considers the problem of optimally controlling the drift of a Brownian motion with a finite set of possible drift rates so as to minimize the long-run average cost, consisting of fixed costs for changing the drift rate, processing costs for maintaining the drift rate, holding costs on the state of the process, and costs for instantaneous controls to keep the process within a prescribed range. We show that, under mild assumptions on the processing costs and the fixed costs for changing the drift rate, there is a strongly ordered optimal policy, that is, an optimal policy that limits the use of each drift rate to a single interval; when the process reaches the upper limit of that interval, the policy either changes to the next lower drift rate deterministically or resorts to instantaneous controls to keep the process within the prescribed range, and when the process reaches the lower limit of the interval, the policy either changes to the next higher drift rate deterministically or again resorts to instantaneous controls to keep the process within the prescribed range. We prove the optimality of such a policy by constructing smooth relative value functions satisfying the associated simplified optimality criteria. This paper shows that, under the proportional changeover cost assumption, each drift rate is active in at most one contiguous range and that the transitions between drift rates are strongly ordered. The results reduce the complexity of proving the optimality of such a policy by proving the existence of optimal relative value functions that constitute a nondecreasing sequence of functions. As a consequence, the constructive arguments lead to a practical procedure for solving the problem that is tens of thousands of times faster than previously reported methods.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48242353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Applied Probability Society Student Paper Competition: Abstracts of 2020 Finalists 应用概率学会学生论文竞赛：2020年入围者摘要

Stochastic Systems Pub Date : 2021-09-01 DOI: 10.1287/stsy.2021.0069

引用次数: 0

Large-Time Behavior of Finite-State Mean-Field Systems With Multiclasses 多类有限状态平均场系统的大时间行为

Stochastic Systems Pub Date : 2021-08-17 DOI: 10.1287/stsy.2022.0100

D. Dawson, Ahmed Sid-Ali, Yiqiang Q. Zhao

引用次数: 1

The Prelimit Generator Comparison Approach of Stein’s Method Stein方法的前置生成器比较法

Stochastic Systems Pub Date : 2021-02-24 DOI: 10.1287/stsy.2021.0085

Anton Braverman

引用次数: 7

Generalized Max-Weight Policies in Stochastic Matching 随机匹配中的广义最大权策略

Stochastic Systems Pub Date : 2020-11-09 DOI: 10.1287/stsy.2022.0098

M. Jonckheere, P. Moyal, Claudia Ram'irez, N. Soprano-Loto

引用次数: 12

Exponential Single Server Queues in an Interactive Random Environment 交互式随机环境中的指数单服务器队列

Stochastic Systems Pub Date : 2020-06-28 DOI: 10.1287/stsy.2023.0106

Sonja Otten, Ruslan K. Krenzler, H. Daduna, K. Kruse

引用次数: 1

Crowdvoting Judgment: An Analysis of Modern Peer Review 众选判断:现代同行评议的分析

Stochastic Systems Pub Date : 2020-06-02 DOI: 10.1287/stsy.2019.0053

Michael R. Wagner

{"title":"Crowdvoting Judgment: An Analysis of Modern Peer Review","authors":"Michael R. Wagner","doi":"10.1287/stsy.2019.0053","DOIUrl":"https://doi.org/10.1287/stsy.2019.0053","url":null,"abstract":"In this paper, we propose and analyze models of self policing in online communities, in which assessment activities, typically handled by firm employees, are shifted to the “crowd.” Our underlying objective is to maximize firm value by maintaining the quality of the online community to prevent attrition, which, given a parsimonious model of voter participation, we show can be achieved by efficiently utilizing the crowd of volunteer voters. To do so, we focus on minimizing the number of voters needed for each assessment, subject to service-level constraints, which depends on a voting aggregation rule. We focus our attention on classes of voting aggregators that are simple, interpretable, and implementable, which increases the chance of adoption in practice. We consider static and dynamic variants of simple majority-rule voting, with which each vote is treated equally. We also study static and dynamic variants of a more sophisticated voting rule that allows more accurate voters to have a larger influence in determining the aggregate decision. We consider both independent and correlated voters and show that correlation is detrimental to performance. Finally, we take a system view and characterize the limit of a costless crowdvoting system that relies solely on volunteer voters. If this limit does not satisfy target service levels, then costly firm employees are needed to supplement the crowd.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/stsy.2019.0053","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47714906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises 带有弱相关噪声的散粒噪声过程的泛函极限定理

Stochastic Systems Pub Date : 2020-06-01 DOI: 10.1287/stsy.2019.0051

G. Pang, Yuhang Zhou

{"title":"Functional Limit Theorems for Shot Noise Processes with Weakly Dependent Noises","authors":"G. Pang, Yuhang Zhou","doi":"10.1287/stsy.2019.0051","DOIUrl":"https://doi.org/10.1287/stsy.2019.0051","url":null,"abstract":"We study shot noise processes when the shot noises are weakly dependent, satisfying the ρ-mixing condition. We prove a functional weak law of large numbers and a functional central limit theorem for this shot noise process in an asymptotic regime with a high intensity of shots. The deterministic fluid limit is unaffected by the presence of weak dependence. The limit in the diffusion scale is a continuous Gaussian process whose covariance function explicitly captures the dependence among the noises. The model and results can be applied in financial and insurance risks with dependent claims as well as queueing systems with dependent service times. To prove the existence of the limit process, we employ the existence criterion that uses a maximal inequality requiring a set function with a superadditivity property. We identify such a set function for the limit process by exploiting the ρ-mixing condition. To prove the weak convergence, we establish the tightness property and the convergence of finite dimensional distributions. To prove tightness, we construct two auxiliary processes and apply an Ottaviani-type inequality for weakly dependent sequences.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/stsy.2019.0051","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42747297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5