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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
Q1 Mathematics Pub Date : 2020-05-07 DOI: 10.1287/stsy.2022.0101
Yoshiaki Inoue, L. Ravner, M. Mandjes
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 .
本文研究了一种服务系统,在该系统中,为到达的客户提供有关他们将经历的延迟的信息。根据这些信息,他们决定等待服务或离开系统。具体来说,每个客户都有一个耐心阈值,如果观察到的延迟超过阈值,他们就会犹豫。主要目标是仅使用实际队列长度过程的知识来估计客户的耐心水平分布参数和相应的潜在到达率。我们设置的主要复杂性和显著特点在于,决定不加入的客户没有被观察到,值得注意的是,我们设法设计了一个程序来估计潜在的耐心和到达率参数。该模型是一个具有泊松客户流的多服务器队列,能够评估状态相关有效到达过程的相应似然函数。我们建立了MLE的强一致性,并导出了估计误差的渐近分布。讨论了该方法的几个应用和扩展。通过一系列数值实验进一步评估了性能。通过拟合超指数分布和广义超指数分布的参数,我们的方法为任何连续耐心水平分布提供了一个稳健的估计框架。资助:井上义明的研究得到了JSPS KAKENHI的部分支持[拨款JP18K18007]。Liron Ravner和Michael Mandjes的研究部分由NWO引力项目网络资助[拨款024.002.003]。补充材料:电子公司可在https://doi.org/10.1287/stsy.2022.0101。
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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
Q1 Mathematics Pub Date : 2020-03-10 DOI: 10.1287/stsy.2021.0079
R. Atar, Prasenjit Karmakar, David Lipshutz
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.
我们研究了一个有服务器休假的多服务器排队模型,其中服务器和客户的人口规模动态是耦合的:只有当没有客户等待时,服务器才能休假,而客户可用的容量直接受到休假服务器数量的影响。我们关注的是缩放机制,其中服务器动态和队列动态在匹配的时间尺度上波动,从而使它们的限制动态耦合。具体而言,我们认为有趣的耦合动力学发生在(a)Halfin–Whitt机制,(b)非退化减速机制,以及(c)Halfin-Whitt附近的中间机制中,而动力学在其他交通繁忙机制中渐近解耦。我们描述了极限动力学的特征,其对于每个标度制度是不同的。我们考虑了制度(a)和(b)各自的相关绩效指标,即等待和放缓的概率。尽管已经为不适应服务器休假的模型推导出了这些性能度量的闭式公式,但在服务器休假的环境中很难获得这些性能测量的闭式表达式。相反,我们提出了近似这些性能度量的公式,这些公式取决于可用服务器的稳态平均数量,以及之前推导的无服务器休假模型的公式。我们用数值方法检验了这些公式的准确性。
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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
Q1 Mathematics Pub Date : 2020-02-15 DOI: 10.1287/stsy.2021.0070
Xinyun Chen
In this paper we develop to our best knowledge the first perfect sampling algorithm for queues with Hawkes input (i.e., single-server queues with Hawkes arrivals and independent and identically distributed service times of general distribution). In addition to the stability condition, we also assume the excitation function of the Hawkes process has a light tail and the service time has finite moment-generating function in the neighborhood of the origin. In this procedure, we also propose a new perfect sampling algorithm for Hawkes processes with improved computational efficiency compared with the existing algorithm. Theoretical analysis and numerical tests on the algorithms’ correctness and efficiency are also included.
本文对具有Hawkes输入的队列(即具有Hawkes到达且服务时间为一般分布的独立且相同分布的单服务器队列)开发了我们所知的第一个完美采样算法。除稳定性条件外,我们还假设Hawkes过程的激励函数具有轻尾,服务时间在原点附近具有有限矩产生函数。在此过程中,我们还提出了一种新的Hawkes过程的完美采样算法,与现有算法相比,该算法的计算效率有所提高。对算法的正确性和有效性进行了理论分析和数值试验。
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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
Q1 Mathematics Pub Date : 2020-02-06 DOI: 10.1287/stsy.2021.0021
J. Blanchet, Fan Zhang, B. Zwart
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.
我们考虑一类具有重尾(即幂律型)风险因子的机会约束优化问题。作为求解机会约束优化问题最常用的通用方法,场景法生成的采样优化问题是一个精确的近似,具有可证明的可靠性,但当风险承受能力参数较小时,计算量变得难以处理。为了降低复杂性,我们从一个条件分布中采样风险因素,假设风险因素在一个分析可处理的事件中,该事件包含了违反约束的所有可能事件。证明了我们的逼近对原机会约束问题的高概率最优值有一个常数因子内的最优值,在风险容忍度参数上是一致的。据我们所知,我们的结果是这种类型的第一个统一的性能保证。我们还在投资组合优化和保险网络偿付能力的背景下证明了我们的算法的效率。资助:B. Zwart的研究得到了NWO(荷兰研究理事会)的支持[Grant 639.033.413]。J. Blanchet的研究得到了空军科研室[奖励FA9550-20-1-0397],国家科学基金[资助项目:1820942,1838576,1915967和2118199],国防高级研究计划局[资助项目:N660011824028]和招商银行的支持。
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引用次数: 0
Anonymous Stochastic Routing 匿名随机路由
Q1 Mathematics Pub Date : 2019-10-30 DOI: 10.1287/stsy.2021.0074
Mine Su Erturk, Kuang Xu
We propose and analyze a recipient-anonymous stochastic routing model to study a fundamental trade-off between anonymity and routing delay. An agent wants to quickly reach a goal vertex in a network through a sequence of routing actions, whereas an overseeing adversary observes the agent’s entire trajectory and tries to identify the agent’s goal among those vertices traversed. We are interested in understanding the probability that the adversary can correctly identify the agent’s goal (anonymity) as a function of the time it takes the agent to reach it (delay). A key feature of our model is the presence of intrinsic uncertainty in the environment, so that each of the agent’s intended steps is subject to random perturbation and thus may not materialize as planned. Using large-network asymptotics, our main results provide near-optimal characterization of the anonymity–delay trade-off under a number of network topologies. Our main technical contributions are centered on a new class of “noise-harnessing” routing strategies that adaptively combine intrinsic uncertainty from the environment with additional artificial randomization to achieve provably efficient obfuscation.
我们提出并分析了一个接收者匿名随机路由模型,以研究匿名和路由延迟之间的基本权衡。智能体希望通过一系列路由动作快速到达网络中的目标顶点,而监督对手则观察智能体的整个轨迹,并试图在这些经过的顶点中识别智能体的目标。我们感兴趣的是理解对手能够正确识别代理目标(匿名)的概率,作为代理达到目标所需时间(延迟)的函数。我们模型的一个关键特征是环境中存在固有的不确定性,因此智能体的每个预期步骤都受到随机扰动,因此可能不会按计划实现。利用大网络渐近性,我们的主要结果提供了许多网络拓扑下匿名-延迟权衡的近最优特征。我们的主要技术贡献集中在一类新的“噪声控制”路由策略上,该策略自适应地将来自环境的内在不确定性与额外的人工随机化相结合,以实现可证明的有效混淆。
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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
Q1 Mathematics Pub Date : 2019-10-16 DOI: 10.1287/stsy.2019.0039
R. Atar, Harsha Honappa
This Special Section of Stochastic Systems includes a number of open problems that were presented at a session organized by the Applied Probability Society during the INFORMS Annual Meeting held in...
随机系统的这一特别部分包括一些开放性问题,这些问题是在应用概率学会于。。。
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引用次数: 0
Open Problem—Adaptive Constant-Step Stochastic Approximation 开放问题-自适应常步随机逼近
Q1 Mathematics Pub Date : 2019-10-02 DOI: 10.1287/stsy.2019.0046
R. Pasupathy, Harsha Honnappa, S. R. Hunter
Suppose f:ℝd→ℝ is a smooth function that is bounded from below. The classic stochastic approximation (SA) recursion used to identify a stationary point of f is given byXk+1=Xk–ηkGk+1(Xk), k≥0,  (1)...
假设f:ℝd→ℝ 是一个从下面有界的光滑函数。用于识别f的平稳点的经典随机近似(SA)递归由Xk+1=Xk–ηkGk+1(Xk)给出, k≥0,  (1) 。。。
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引用次数: 1
Open Problem—Protocols for Resource-Sharing Networks with Locally Edge-Minimal Fluid Models 开放问题——具有局部边缘最小流体模型的资源共享网络协议
Q1 Mathematics Pub Date : 2019-09-19 DOI: 10.1287/stsy.2019.0044
Łukasz Kruk
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引用次数: 2
Open Problem—Load Balancing Using Delayed Information 打开使用延迟信息的问题-负载均衡
Q1 Mathematics Pub Date : 2019-09-19 DOI: 10.1287/stsy.2019.0045
David Lipshutz
Load-balancing algorithms are important for efficiently routing jobs in systems of parallel queues; however, there has been relatively little attention devoted to developing algorithms in the prese...
负载均衡算法对于并行队列系统中作业的高效路由至关重要。然而,目前很少有人关注开发算法。
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引用次数: 8
Open Problem—M/G/k/SRPT Under Medium Load 开放问题m /G/k/SRPT在中等负载下
Q1 Mathematics Pub Date : 2019-09-18 DOI: 10.1287/stsy.2019.0042
Isaac Grosof
The shortest remaining processing time (SRPT) scheduling policy has been deployed in many computer systems, such as web servers (Harchol-Balter et al. 2003), networks (Montazeri et al. 2018), datab...
最短剩余处理时间(SRPT)调度策略已被部署在许多计算机系统中,如web服务器(Harchol-Balter等人,2003)、网络(Montazeri等人,2018)、数据。。。
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引用次数: 1
期刊
Stochastic Systems
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