Stochastic Systems最新文献_第2页

Learning-Based Optimal Admission Control in a Single-Server Queuing System 单服务器队列系统中基于学习的最优接纳控制

Stochastic Systems Pub Date : 2024-01-05 DOI: 10.1287/stsy.2022.0042

Asaf Cohen, Vijay Subramanian, Yili Zhang

{"title":"Learning-Based Optimal Admission Control in a Single-Server Queuing System","authors":"Asaf Cohen, Vijay Subramanian, Yili Zhang","doi":"10.1287/stsy.2022.0042","DOIUrl":"https://doi.org/10.1287/stsy.2022.0042","url":null,"abstract":"We consider a long-term average profit–maximizing admission control problem in an M/M/1 queuing system with unknown service and arrival rates. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue length of the system. Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24] shows that, if all the parameters of the model are known, then it is optimal to use a static threshold policy: admit if the queue length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full-information model of Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24]. We show that the algorithm achieves an O(1) regret when all optimal thresholds with full information are nonzero and achieves an [Formula: see text] regret for any specified [Formula: see text] in the case that an optimal threshold with full information is 0 (i.e., an optimal policy is to reject all arrivals), where N is the number of arrivals.Funding: A. Cohen is partially supported by the National Science Foundation [Grant DMS-2006305]. V. Subramanian is supported in part by the NSF [Grants CCF-2008130, ECCS-2038416, CNS-1955777, and CMMI-2240981].","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139374276","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: 0

Solution Representations for Poisson’s Equation, Martingale Structure, and the Markov Chain Central Limit Theorem 泊松方程的解表示、马丁格尔结构和马尔可夫链中心极限定理

Stochastic Systems Pub Date : 2023-12-28 DOI: 10.1287/stsy.2022.0001

Peter W. Glynn, Alex Infanger

引用次数: 0

A Particle System with Mean-Field Interaction: Large-Scale Limit of Stationary Distributions 具有平均场相互作用的粒子系统:平稳分布的大尺度极限

Stochastic Systems Pub Date : 2023-09-01 DOI: 10.1287/stsy.2023.0108

Alexander L. Stolyar

{"title":"A Particle System with Mean-Field Interaction: Large-Scale Limit of Stationary Distributions","authors":"Alexander L. Stolyar","doi":"10.1287/stsy.2023.0108","DOIUrl":"https://doi.org/10.1287/stsy.2023.0108","url":null,"abstract":"We consider a system consisting of n particles, moving forward in jumps on the real line. System state is the empirical distribution of particle locations. Each particle “jumps forward” at some time points, with the instantaneous rate of jumps given by a decreasing function of the particle’s location quantile within the current state (empirical distribution). Previous work on this model established, under certain conditions, the convergence, as [Formula: see text], of the system random dynamics to that of a deterministic mean-field model (MFM), which is a solution to an integro-differential equation. Another line of previous work established the existence of MFMs that are traveling waves, as well as the attraction of MFM trajectories to traveling waves. The main results of this paper are: (a) We prove that, as [Formula: see text], the stationary distributions of (recentered) states concentrate on a (recentered) traveling wave; (b) we obtain a uniform across n moment bound on the stationary distributions of (recentered) states; and (c) we prove a convergence-to-MFM result, which is substantially more general than that in previous work. Results (b) and (c) serve as “ingredients” of the proof of (a), but also are of independent interest.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944526","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: 0

Optimally Scheduling Public Safety Power Shutoffs 公共安全停电的优化调度

Stochastic Systems Pub Date : 2023-06-07 DOI: 10.1287/stsy.2022.004

Antoine Lesage-Landry, Félix Pellerin, Duncan S. Callaway, Joshua A. Taylor

{"title":"Optimally Scheduling Public Safety Power Shutoffs","authors":"Antoine Lesage-Landry, Félix Pellerin, Duncan S. Callaway, Joshua A. Taylor","doi":"10.1287/stsy.2022.004","DOIUrl":"https://doi.org/10.1287/stsy.2022.004","url":null,"abstract":"In an effort to reduce power system-caused wildfires, utilities carry out public safety power shutoffs (PSPSs), in which portions of the grid are deenergized to mitigate the risk of ignition. The decision to call a PSPS must balance reducing ignition risks and the negative impact of service interruptions. In this work, we consider three PSPS scheduling scenarios, which we model as dynamic programs. In the first two scenarios, we assume that N PSPSs are budgeted as part of the investment strategy. In the first scenario, a penalty is incurred for each PSPS declared past the Nth event. In the second, we assume that some costs can be recovered if the number of PSPSs is below N while still being subject to a penalty if above N. In the third, the system operator wants to minimize the number of PSPSs such that the total expected cost is below a threshold. We provide optimal or asymptotically optimal policies for each case, the first two of which have closed-form expressions. Lastly, we establish the applicability of the first PSPS model’s policy to critical peak pricing and obtain an optimal scheduling policy to reduce the peak demand based on weather observations. Funding: This work was funded in part by the Natural Sciences and Engineering Research Council of Canada, the Institute for Data Valorization, the National Science Foundation [Award 1351900], the Advanced Research Projects Agency-Energy [Award DE-AR0001061], and the University of California Office of the President Laboratory Fees Program [Grant LFR-20-652467].","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135409508","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: 0

Optimally Scheduling Public Safety Power Shutoffs 公共安全停电的优化调度

Stochastic Systems Pub Date : 2023-06-07 DOI: 10.1287/stsy.2022.0004

Antoine Lesage-Landry, Félix Pellerin, Duncan S. Callaway, Joshua A. Taylor

{"title":"Optimally Scheduling Public Safety Power Shutoffs","authors":"Antoine Lesage-Landry, Félix Pellerin, Duncan S. Callaway, Joshua A. Taylor","doi":"10.1287/stsy.2022.0004","DOIUrl":"https://doi.org/10.1287/stsy.2022.0004","url":null,"abstract":"In an effort to reduce power system-caused wildfires, utilities carry out public safety power shutoffs (PSPSs), in which portions of the grid are deenergized to mitigate the risk of ignition. The decision to call a PSPS must balance reducing ignition risks and the negative impact of service interruptions. In this work, we consider three PSPS scheduling scenarios, which we model as dynamic programs. In the first two scenarios, we assume that N PSPSs are budgeted as part of the investment strategy. In the first scenario, a penalty is incurred for each PSPS declared past the Nth event. In the second, we assume that some costs can be recovered if the number of PSPSs is below N while still being subject to a penalty if above N. In the third, the system operator wants to minimize the number of PSPSs such that the total expected cost is below a threshold. We provide optimal or asymptotically optimal policies for each case, the first two of which have closed-form expressions. Lastly, we establish the applicability of the first PSPS model’s policy to critical peak pricing and obtain an optimal scheduling policy to reduce the peak demand based on weather observations. Funding: This work was funded in part by the Natural Sciences and Engineering Research Council of Canada, the Institute for Data Valorization, the National Science Foundation [Award 1351900], the Advanced Research Projects Agency-Energy [Award DE-AR0001061], and the University of California Office of the President Laboratory Fees Program [Grant LFR-20-652467].","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135449343","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: 0

Directed Acyclic Graph-Type Distributed Ledgers via Young-Age Preferential Attachment 基于年龄优先依附的有向无环图型分布式账本

Stochastic Systems Pub Date : 2023-06-05 DOI: 10.1287/stsy.2022.005

Christian Mönch, Amr Rizk

{"title":"Directed Acyclic Graph-Type Distributed Ledgers via Young-Age Preferential Attachment","authors":"Christian Mönch, Amr Rizk","doi":"10.1287/stsy.2022.005","DOIUrl":"https://doi.org/10.1287/stsy.2022.005","url":null,"abstract":"Distributed ledger technologies provide a mechanism to achieve ordering among transactions that are scattered on multiple participants with no prerequisite trust relations. This mechanism is essentially based on the idea of new transactions referencing older ones in a chain structure. Recently, directed acyclic graph (DAG)-type distributed ledgers that are based on DAGs were proposed to increase the system scalability through sacrificing the total order of transactions. In this paper, we develop a mathematical model to study the process that governs the addition of new transactions to the DAG-type distributed ledger. We propose a simple model for DAG-type distributed ledgers that are obtained from a recursive young-age preferential attachment scheme (i.e., new connections are made preferably to transactions that have not been in the system for very long). We determine the asymptotic degree structure of the resulting graph and show that a forward component of linear size arises if the edge density is chosen sufficiently large in relation to the “young-age preference” that tunes how quickly old transactions become unattractive. Funding: The research of C. Mönch is supported by the Deutsche Forschungsgemeinschaft [Grant 443916008].","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135703140","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: 0

Optimal Server Assignment in Queues with Flexible Servers and Abandonments 具有灵活服务器和放弃的队列中的最优服务器分配

Stochastic Systems Pub Date : 2023-04-13 DOI: 10.1287/stsy.2023.0109

S. Andradóttir, H. Ayhan

引用次数: 1

Asymptotically Optimal Inventory Control for Assemble-to-Order Systems 装配订货系统的渐近最优库存控制

Stochastic Systems Pub Date : 2023-03-01 DOI: 10.1287/stsy.2022.0099

Martin I. Reiman, Haohua Wan, Qiong Wang

{"title":"Asymptotically Optimal Inventory Control for Assemble-to-Order Systems","authors":"Martin I. Reiman, Haohua Wan, Qiong Wang","doi":"10.1287/stsy.2022.0099","DOIUrl":"https://doi.org/10.1287/stsy.2022.0099","url":null,"abstract":"We consider assemble-to-order (ATO) inventory systems with a general bill of materials and general deterministic lead times. Unsatisfied demands are always backlogged. We apply a four-step asymptotic framework to develop inventory policies for minimizing the long-run average expected total inventory cost. Our approach features a multistage stochastic program (SP) to establish a lower bound on the inventory cost and determine parameter values for inventory control. Our replenishment policy deviates from the conventional constant base stock policies to accommodate nonidentical lead times. Our component allocation policy differentiates demands based on backlog costs, bill of materials, and component availabilities. We prove that our policy is asymptotically optimal on the diffusion scale, that is, as the longest lead time grows, the percentage difference between the average cost under our policy and its lower bound converges to zero. In developing these results, we formulate a broad stochastic tracking model and prove general convergence results from which the asymptotic optimality of our policy follows as specialized corollaries. Funding: This study is based on work supported by the National Science Foundation [Grant CMMI-1363314].","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"173 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136132076","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: 0

Managing Queues with Reentrant Customers in Support of Hybrid Healthcare 与重新进入的客户一起管理队列以支持混合医疗保健

Stochastic Systems Pub Date : 2023-01-31 DOI: 10.1287/stsy.2022.0105

Noa Zychlinski

{"title":"Managing Queues with Reentrant Customers in Support of Hybrid Healthcare","authors":"Noa Zychlinski","doi":"10.1287/stsy.2022.0105","DOIUrl":"https://doi.org/10.1287/stsy.2022.0105","url":null,"abstract":"The COVID-19 pandemic has profoundly boosted the use of hybrid healthcare settings, which orchestrate face-to-face services together with virtual ones. The advantages of virtual healthcare services are clear: they are less costly and less disruptive for patients who can receive the service in the comfort of their home and reduce patients’ exposure to illnesses prevalent in healthcare facilities. Nevertheless, there is evidence that patients are likely to require a supplementary in-person service upon completion of their virtual service. Motivated by such settings, we study a multiservice queueing system with face-to-face, virtual, and supplementary service channels. The service operator needs to allocate service capacity among the three classes and decide how to prioritize the patients when a service provider becomes available. The strong dependency between virtual and supplementary visits makes the problem challenging. Based on a fluid relaxation, we develop an index-based policy, the [Formula: see text] rule (or the [Formula: see text] rule in short), which, in addition to the holding cost, service time, abandonment rate, and service reward, also carefully balances the return probability and associated penalty. The theoretical results along with numerical experiments demonstrate the effectiveness of the proposed policy and the importance of capacity coordination when managing hybrid service settings. Our work provides insights on the trade-off between convenience and the value of care when offering virtual healthcare services. Funding: The author was supported in part by an Israel Science Foundation [Grant 277/21] and the Israel National Institute for Health Policy Research [Grant 2021/160/R].","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41584737","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

Convergence Rates of Epsilon-Greedy Global Optimization Under Radial Basis Function Interpolation 径向基函数插值下Epsilon-Greedy全局优化的收敛速度

Stochastic Systems Pub Date : 2022-08-02 DOI: 10.1287/stsy.2022.0096

Jialin Li, I. Ryzhov

引用次数: 4