Stochastic Systems最新文献_第5页

Estimating Customer Impatience in a Service System With Unobserved Balking 在没有观测到Balking的服务系统中估计客户的不耐烦

Stochastic Systems Pub Date : 2020-05-07 DOI: 10.1287/stsy.2022.0101

Yoshiaki Inoue, L. Ravner, M. Mandjes

{"title":"Estimating Customer Impatience in a Service System With Unobserved Balking","authors":"Yoshiaki Inoue, L. Ravner, M. Mandjes","doi":"10.1287/stsy.2022.0101","DOIUrl":"https://doi.org/10.1287/stsy.2022.0101","url":null,"abstract":"This paper studies a service system in which arriving customers are provided with information about the delay they will experience. Based on this information, they decide to wait for service or leave the system. Specifically, every customer has a patience threshold, and they balk if the observed delay is above the threshold. The main objective is to estimate the parameters of the customers’ patience-level distribution and the corresponding potential arrival rate, using knowledge of the actual queue-length process only. The main complication and distinguishing feature of our setup lies in the fact that customers who decide not to join are not observed, and remarkably, we manage to devise a procedure to estimate the underlying patience and arrival rate parameters. The model is a multiserver queue with a Poisson stream of customers, enabling evaluation of the corresponding likelihood function of the state-dependent effective arrival process. We establish strong consistency of the MLE and derive the asymptotic distribution of the estimation error. Several applications and extensions of the method are discussed. The performance is further assessed through a series of numerical experiments. By fitting parameters of hyperexponential and generalized hyperexponential distributions, our method provides a robust estimation framework for any continuous patience-level distribution. Funding: The research of Yoshiaki Inoue is supported in part by JSPS KAKENHI [Grant JP18K18007]. The research of Liron Ravner and Michael Mandjes is partly funded by NWO Gravitation Project Networks [Grant 024.002.003]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/stsy.2022.0101 .","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47612031","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: 2

Customer-Server Population Dynamics in Heavy Traffic 繁忙交通中的客户-服务器群体动态

Stochastic Systems Pub Date : 2020-03-10 DOI: 10.1287/stsy.2021.0079

R. Atar, Prasenjit Karmakar, David Lipshutz

{"title":"Customer-Server Population Dynamics in Heavy Traffic","authors":"R. Atar, Prasenjit Karmakar, David Lipshutz","doi":"10.1287/stsy.2021.0079","DOIUrl":"https://doi.org/10.1287/stsy.2021.0079","url":null,"abstract":"We study a many-server queueing model with server vacations, where the population size dynamics of servers and customers are coupled: a server may leave for vacation only when no customers await, and the capacity available to customers is directly affected by the number of servers on vacation. We focus on scaling regimes in which server dynamics and queue dynamics fluctuate at matching time scales so that their limiting dynamics are coupled. Specifically, we argue that interesting coupled dynamics occur in (a) the Halfin–Whitt regime, (b) the nondegenerate slowdown regime, and (c) the intermediate near Halfin–Whitt regime, whereas the dynamics asymptotically decouple in the other heavy-traffic regimes. We characterize the limiting dynamics, which are different for each scaling regime. We consider relevant respective performance measures for regimes (a) and (b)—namely, the probability of wait and the slowdown. Although closed-form formulas for these performance measures have been derived for models that do not accommodate server vacations, it is difficult to obtain closed-form formulas for these performance measures in the setting with server vacations. Instead, we propose formulas that approximate these performance measures and depend on the steady-state mean number of available servers and previously derived formulas for models without server vacations. We test the accuracy of these formulas numerically.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49249865","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

Perfect Sampling of Hawkes Processes and Queues with Hawkes Arrivals Hawkes过程和Hawkes到达排队的完全抽样

Stochastic Systems Pub Date : 2020-02-15 DOI: 10.1287/stsy.2021.0070

Xinyun Chen

引用次数: 8

Efficient Scenario Generation for Heavy-Tailed Chance Constrained Optimization 重尾机会约束优化的高效场景生成

Stochastic Systems Pub Date : 2020-02-06 DOI: 10.1287/stsy.2021.0021

J. Blanchet, Fan Zhang, B. Zwart

{"title":"Efficient Scenario Generation for Heavy-Tailed Chance Constrained Optimization","authors":"J. Blanchet, Fan Zhang, B. Zwart","doi":"10.1287/stsy.2021.0021","DOIUrl":"https://doi.org/10.1287/stsy.2021.0021","url":null,"abstract":"We consider a generic class of chance-constrained optimization problems with heavy-tailed (i.e., power-law type) risk factors. As the most popular generic method for solving chance constrained optimization, the scenario approach generates sampled optimization problem as a precise approximation with provable reliability, but the computational complexity becomes intractable when the risk tolerance parameter is small. To reduce the complexity, we sample the risk factors from a conditional distribution given that the risk factors are in an analytically tractable event that encompasses all the plausible events of constraints violation. Our approximation is proven to have optimal value within a constant factor to the optimal value of the original chance constraint problem with high probability, uniformly in the risk tolerance parameter. To the best of our knowledge, our result is the first uniform performance guarantee of this type. We additionally demonstrate the efficiency of our algorithm in the context of solvency in portfolio optimization and insurance networks. Funding: The research of B. Zwart is supported by the NWO (Dutch Research Council) [Grant 639.033.413]. The research of J. Blanchet is supported by the Air Force Office of Scientific Research [Award FA9550-20-1-0397], the National Science Foundation [Grants 1820942, 1838576, 1915967, and 2118199], Defense Advanced Research Projects Agency [Award N660011824028], and China Merchants Bank.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45968877","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

Anonymous Stochastic Routing 匿名随机路由

Stochastic Systems Pub Date : 2019-10-30 DOI: 10.1287/stsy.2021.0074

Mine Su Erturk, Kuang Xu

引用次数: 3

Introduction to the Applied Probability Society’s “Open Problems in Applied Probability” Session at the INFORMS Annual Meeting, Phoenix, Arizona, November 4–7, 2018 2018年11月4日至7日，在亚利桑那州凤凰城举行的INFORMS年会上，应用概率学会“应用概率中的开放问题”会议介绍

Stochastic Systems Pub Date : 2019-10-16 DOI: 10.1287/stsy.2019.0039

R. Atar, Harsha Honappa