Stochastic Systems最新文献

{"title":"Generalized Sequential Stochastic Assignment Problem","authors":"A. Khatibi, S. Jacobson","doi":"10.1287/stsy.2018.0017","DOIUrl":"https://doi.org/10.1287/stsy.2018.0017","url":null,"abstract":"The sequential stochastic assignment problem (SSAP) assigns sequentially arriving tasks with stochastic parameters (coming from a known distribution) to workers with fixed success rates so as to ma...","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/stsy.2018.0017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42994114","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}

{"title":"Transform Methods for Heavy-Traffic Analysis","authors":"Daniela Hurtado-Lange, S. T. Maguluri","doi":"10.1287/stsy.2019.0056","DOIUrl":"https://doi.org/10.1287/stsy.2019.0056","url":null,"abstract":"The drift method was recently developed to study queuing systems in steady state. It was used successfully to obtain bounds on the moments of the scaled queue lengths that are asymptotically tight in heavy traffic and in a wide variety of systems, including generalized switches, input-queued switches, bandwidth-sharing networks, and so on. In this paper, we develop the use of transform techniques for heavy-traffic analysis, with a special focus on the use of moment-generating functions. This approach simplifies the proofs of the drift method and provides a new perspective on the drift method. We present a general framework and then use the moment-generating function method to obtain the stationary distribution of scaled queue lengths in heavy traffic in queuing systems that satisfy the complete resource pooling condition. In particular, we study load balancing systems and generalized switches under general settings.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/stsy.2019.0056","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49211379","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}

{"title":"Delay-Based Service Differentiation with Many Servers and Time-Varying Arrival Rates","authors":"Xu Sun, W. Whitt","doi":"10.1287/STSY.2018.0015","DOIUrl":"https://doi.org/10.1287/STSY.2018.0015","url":null,"abstract":"We study the problem of staffing (specifying a time-varying number of servers) and scheduling (assigning newly idle servers to a waiting customer from one of K classes) in the many-server V model w...","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/STSY.2018.0015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44902461","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}

{"title":"Optimal Control of Markov-Modulated Multiclass Many-Server Queues","authors":"A. Arapostathis, Anirban Das, G. Pang, Yi Zheng","doi":"10.1287/stsy.2019.0029","DOIUrl":"https://doi.org/10.1287/stsy.2019.0029","url":null,"abstract":"We study multiclass many-server queues for which the arrival, service, and abandonment rates are all modulated by a common finite-state Markov process. We assume that the system operates in the “av...","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/stsy.2019.0029","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43880844","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}

{"title":"Nonparametric Estimation of Service Time Characteristics in Infinite-Server Queues with Nonstationary Poisson Input","authors":"A. Goldenshluger, D. Koops","doi":"10.1287/STSY.2018.0026","DOIUrl":"https://doi.org/10.1287/STSY.2018.0026","url":null,"abstract":"This paper provides a mathematical framework for estimation of the service time distribution and the expected service time of an infinite-server queueing system with a nonhomogeneous Poisson arrival process, in the case of partial information, where only the number of busy servers are observed over time. The problem is reduced to a statistical deconvolution problem, which is solved by using Laplace transform techniques and kernels for regularization. Upper bounds on the mean squared error of the proposed estimators are derived. Some concrete simulation experiments are performed to illustrate how the method can be applied and to provide some insight in the practical performance.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/STSY.2018.0026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41291834","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}

{"title":"Heavy-Traffic Limit of theGI/GI/1 Stationary Departure Process and Its Variance Function","authors":"W. Whitt, Wei You","doi":"10.1287/STSY.2018.0011","DOIUrl":"https://doi.org/10.1287/STSY.2018.0011","url":null,"abstract":"Heavy-traffic limits are established for the stationary departure process from a GI/GI/1 queue and its variance function. The limit process is a function of the Brownian motion limits of the arrival and service processes plus the stationary reflected Brownian motion (RBM) limit of the queue-length process. An explicit expression is given for the variance function, which depends only on the first two moments of the interarrival times and service times plus the previously determined correlation function of canonical (drift −1, diffusion coefficient 1) RBM. The limit for the variance function here is used to show that the approximation for the index of dispersion for counts of the departure process used in our new robust queueing network analyzer is asymptotically correct in the heavy-traffic limit.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/STSY.2018.0011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42913971","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}

{"title":"An Analysis of a Large-Scale Machine Repair Model","authors":"P. Momcilovic, A. Motaei","doi":"10.1287/STSY.2018.0010","DOIUrl":"https://doi.org/10.1287/STSY.2018.0010","url":null,"abstract":"A machine repair model under general operating/repair distributions is considered in the Quality-and-Efficiency Driven asymptotic (QED) regime: both the number of machines and the number of repairm...","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/STSY.2018.0010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43912666","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}

{"title":"Smoothed Variable Sample-Size Accelerated Proximal Methods for Nonsmooth Stochastic Convex Programs","authors":"A. Jalilzadeh, U. Shanbhag, J. Blanchet, P. Glynn","doi":"10.1287/stsy.2022.0095","DOIUrl":"https://doi.org/10.1287/stsy.2022.0095","url":null,"abstract":"We consider the unconstrained minimization of the function F, where F = f + g, f is an expectation-valued nonsmooth convex or strongly convex function, and g is a closed, convex, and proper function. (I) Strongly convex f. When f is -strongly convex in x, traditional stochastic subgradient schemes (SSG) often display poor behavior, arising in part from noisy subgradients and diminishing steplengths. Instead, we apply a variable sample-size accelerated proximal scheme (VS-APM) on F, the Moreau envelope of F; we term such a scheme as (mVS-APM) and in contrast with (SSG) schemes, (mVS-APM) utilizes constant steplengths and increasingly exact gradients. We consider two settings. (a) Bounded domains. In this setting, (mVS-APM) displays linear convergence in inexact gradient steps, each of which requires utilizing an inner (prox-SSG) scheme. Specically, (mVS-APM) achieves an optimal oracle complexity in prox-SSG steps of [Formula: see text] with an iteration complexity of [Formula: see text] in inexact (outer) gradients of F to achieve an -accurate solution in mean-squared error, computed via an increasing number of inner (stochastic) subgradient steps; (b) Unbounded domains. In this regime, under an assumption of state-dependent bounds on subgradients, an unaccelerated variant (mVS-APM) is linearly convergent where increasingly exact gradients ∇xF(x) are approximated with increasing accuracy via (SSG) schemes. Notably, (mVS-APM) also displays an optimal oracle complexity of [Formula: see text]; (II) Convex f. When f is merely convex but smoothable, by suitable choices of the smoothing, steplength, and batch-size sequences, smoothed (VS-APM) (or sVS-APM) achieves an optimal oracle complexity of [Formula: see text] to obtain an -optimal solution. Our results can be specialized to two important cases: (a) Smooth f. Since smoothing is no longer required, we observe that (VS-APM) admits the optimal rate and oracle complexity, matching prior ndings; (b) Deterministic nonsmooth f. In the nonsmooth deterministic regime, (sVS-APM) reduces to a smoothed accelerated proximal method (s-APM) that is both asymptotically convergent and optimal in that it displays a complexity of [Formula: see text], matching the bound provided by Nesterov in 2005 for producing -optimal solutions. Finally, (sVS-APM) and (VS-APM) produce sequences that converge almost surely to a solution of the original problem.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44435698","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}

{"title":"Optimal Liquidity-Based Trading Tactics","authors":"Charles-Albert Lehalle, Othmane Mounjid, M. Rosenbaum","doi":"10.1287/stsy.2021.0078","DOIUrl":"https://doi.org/10.1287/stsy.2021.0078","url":null,"abstract":"We consider an agent who needs to buy (or sell) a relatively small amount of assets over some fixed short time interval. We work at the highest frequency meaning that we wish to find the optimal tactic to execute our quantity using limit orders, market orders, and cancellations. To solve the agent’s control problem, we build an order book model and optimize an expected utility function based on our price impact. We derive the equations satisfied by the optimal strategy and solve them numerically. Moreover, we show that our optimal tactic enables us to outperform significantly naive execution strategies.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42851891","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}

{"title":"Exact Asymptotics for a Multitimescale Model with Applications in Modeling Overdispersed Customer Streams","authors":"M. Heemskerk, M. Mandjes","doi":"10.1287/STSY.2019.0032","DOIUrl":"https://doi.org/10.1287/STSY.2019.0032","url":null,"abstract":"In this paper we study the probability $xi_n(u):={mathbb P}left(C_ngeqslant u n right)$, with $C_n:=A(psi_n B(varphi_n))$ for Levy processes $A(cdot)$ and $B(cdot)$, and $varphi_n$ and $psi_n$ non-negative sequences such that $varphi_n psi_n =n$ and $varphi_ntoinfty$ as $ntoinfty$. Two timescale regimes are distinguished: a `fast' regime in which $varphi_n$ is superlinear and a `slow' regime in which $varphi_n$ is sublinear. We provide the exact asymptotics of $xi_n(u)$ (as $ntoinfty$) for both regimes, relying on change-of-measure arguments in combination with Edgeworth-type estimates. The asymptotics have an unconventional form: the exponent contains the commonly observed linear term, but may also contain sublinear terms (the number of which depends on the precise form of $varphi_n$ and $psi_n$). To showcase the power of our results we include two examples, covering both the case where $C_n$ is lattice and non-lattice. Finally we present numerical experiments that demonstrate the importance of taking into account the doubly stochastic nature of $C_n$ in a practical application related to customer streams in service systems; they show that the asymptotic results obtained yield highly accurate approximations, also in scenarios in which there is no pronounced timescale separation.","PeriodicalId":36337,"journal":{"name":"Stochastic Systems","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2018-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1287/STSY.2019.0032","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42456816","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}