Stochastic Systems最新文献_第8页

Heavy-Traffic Analysis of Sojourn Time Under the Foreground–Background Scheduling Policy 前台-后台调度策略下Sojourn时间的重流量分析

Stochastic Systems Pub Date : 2017-12-11 DOI: 10.1287/stsy.2019.0036

B. Kamphorst, B. Zwart

引用次数: 5

A Monte Carlo Method for Estimating Sensitivities of Reflected Diffusions in Convex Polyhedral Domains 凸多面体区域反射扩散灵敏度估计的蒙特卡罗方法

Stochastic Systems Pub Date : 2017-11-30 DOI: 10.1287/STSY.2019.0031

David Lipshutz, K. Ramanan

{"title":"A Monte Carlo Method for Estimating Sensitivities of Reflected Diffusions in Convex Polyhedral Domains","authors":"David Lipshutz, K. Ramanan","doi":"10.1287/STSY.2019.0031","DOIUrl":"https://doi.org/10.1287/STSY.2019.0031","url":null,"abstract":"In this work we develop an effective Monte Carlo method for estimating sensitivities, or gradients of expectations of sufficiently smooth functionals, of a reflected diffusion in a convex polyhedral domain with respect to its defining parameters --- namely, its initial condition, drift and diffusion coefficients, and directions of reflection. Our method, which falls into the class of infinitesimal perturbation analysis (IPA) methods, uses a probabilistic representation for such sensitivities as the expectation of a functional of the reflected diffusion and its associated derivative process. The latter process is the unique solution to a constrained linear stochastic differential equation with jumps whose coefficients, domain and directions of reflection are modulated by the reflected diffusion. We propose an asymptotically unbiased estimator for such sensitivities using an Euler approximation of the reflected diffusion and its associated derivative process. Proving that the Euler approximation converges is challenging because the derivative process jumps whenever the reflected diffusion hits the boundary (of the domain). A key step in the proof is establishing a continuity property of the related derivative map, which is of independent interest. We compare the performance of our IPA estimator to a standard likelihood ratio estimator (whenever the latter is applicable), and provide numerical evidence that the variance of the former is substantially smaller than that of the latter. We illustrate our method with an example of a rank-based interacting diffusion model of equity markets. Interestingly, we show that estimating certain sensitivities of the rank-based interacting diffusion model using our method for a reflected Brownian motion description of the model outperforms a finite difference method for a stochastic differential equation description of the model.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/STSY.2019.0031","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42896893","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

The Impact of a Network Split on Cascading Failure Processes 网络分裂对级联故障过程的影响

Stochastic Systems Pub Date : 2017-11-13 DOI: 10.1287/stsy.2019.0035

F. Sloothaak, S. Borst, B. Zwart

引用次数: 1

Stochastic Gradient Descent in Continuous Time: A Central Limit Theorem 连续时间随机梯度下降:一个中心极限定理

Stochastic Systems Pub Date : 2017-10-11 DOI: 10.1287/stsy.2019.0050

Justin A. Sirignano, K. Spiliopoulos

引用次数: 27

Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty 具有模型不确定性的大流量下多类排队控制问题的渐近分析

Stochastic Systems Pub Date : 2017-10-03 DOI: 10.1287/stsy.2019.0034

A. Cohen

引用次数: 8

Queues Driven by Hawkes Processes 由Hawkes进程驱动的队列

Stochastic Systems Pub Date : 2017-07-17 DOI: 10.2139/SSRN.3003376

A. Daw, Jamol Pender

{"title":"Queues Driven by Hawkes Processes","authors":"A. Daw, Jamol Pender","doi":"10.2139/SSRN.3003376","DOIUrl":"https://doi.org/10.2139/SSRN.3003376","url":null,"abstract":"Many stochastic systems have arrival processes that exhibit clustering behavior. In these systems, arriving entities influence additional arrivals to occur through self-excitation of the arrival process. In this paper, we analyze an infinite server queueing system in which the arrivals are driven by the self-exciting Hawkes process and where service follows a phase-type distribution or is deterministic. In the phase-type setting, we derive differential equations for the moments and a partial differential equation for the moment generating function; we also derive exact expressions for the transient and steady-state mean, variance, and covariances. Furthermore, we also derive exact expressions for the auto-covariance of the queue and provide an expression for the cumulant moment generating function in terms of a single ordinary differential equation. In the deterministic service setting, we provide exact expressions for the first and second moments and the queue auto-covariance. As motivation for our Hawkes queueing model, we demonstrate its usefulness through two novel applications. These applications are trending internet traffic and arrivals to nightclubs. In the web traffic setting, we investigate the impact of a click. In the nightclub or \"Club Queue\" setting, we design an optimal control problem for the rate to admit club-goers.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2017-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44494648","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: 69

Likelihood Ratio Gradient Estimation for Steady-State Parameters 稳态参数的似然比梯度估计

Stochastic Systems Pub Date : 2017-07-09 DOI: 10.1287/STSY.2018.0023

P. Glynn, Mariana Olvera-Cravioto

引用次数: 8

Big Jobs Arrive Early: From Critical Queues to Random Graphs 大任务提前到来：从关键队列到随机图

Stochastic Systems Pub Date : 2017-04-11 DOI: 10.1287/stsy.2019.0057

G. Bet, R. van der Hofstad, J. V. van Leeuwaarden

引用次数: 6

Universality of Power-of-d Load Balancing in Many-Server Systems 多服务器系统中功率负载均衡的通用性

Stochastic Systems Pub Date : 2016-12-02 DOI: 10.1287/stsy.2018.0016

Debankur Mukherjee, S. Borst, J. V. van Leeuwaarden, P. Whiting

引用次数: 78

Mean-Field Limits for Large-Scale Random-Access Networks 大规模随机接入网络的平均域限制

Stochastic Systems Pub Date : 2016-11-29 DOI: 10.1287/stsy.2021.0068

Fabio Cecchi, S. Borst, J. V. van Leeuwaarden, P. Whiting

{"title":"Mean-Field Limits for Large-Scale Random-Access Networks","authors":"Fabio Cecchi, S. Borst, J. V. van Leeuwaarden, P. Whiting","doi":"10.1287/stsy.2021.0068","DOIUrl":"https://doi.org/10.1287/stsy.2021.0068","url":null,"abstract":"We establish mean-field limits for large-scale random-access networks with buffer dynamics and arbitrary interference graphs. Although saturated buffer scenarios have been widely investigated and yield useful throughput estimates for persistent sessions, they fail to capture the fluctuations in buffer contents over time and provide no insight in the delay performance of flows with intermittent packet arrivals. Motivated by that issue, we explore in the present paper random-access networks with buffer dynamics, where flows with empty buffers refrain from competition for the medium. The occurrence of empty buffers thus results in a complex dynamic interaction between activity states and buffer contents, which severely complicates the performance analysis. Hence, we focus on a many-sources regime where the total number of nodes grows large, which not only offers mathematical tractability but is also highly relevant with the densification of wireless networks as the Internet of Things emerges. We exploit timescale separation properties to prove that the properly scaled buffer occupancy process converges to the solution of a deterministic initial value problem and establish the existence and uniqueness of the associated fixed point. This approach simplifies the performance analysis of networks with huge numbers of nodes to a low-dimensional fixed-point calculation. For the case of a complete interference graph, we demonstrate asymptotic stability, provide a simple closed form expression for the fixed point, and prove interchange of the mean-field and steady-state limits. This yields asymptotically exact approximations for key performance metrics, in particular the stationary buffer content and packet delay distributions.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2016-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"66531337","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: 3