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...
{"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}
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.
{"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}
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...
{"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}
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...
{"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}
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.
{"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}
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.
{"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}
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...
{"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}
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.
考虑函数F的无约束极小化问题，其中F = F + g, F是一个期望值非光滑凸函数或强凸函数，g是一个闭凸固有函数。(I)强凸f。当f在x中为-强凸时，传统的随机亚梯度方案(SSG)通常表现出较差的行为，部分原因是由于噪声的亚梯度和递减的步长。相反，我们在F (F的莫罗包络)上应用了变样本量加速近端方案(VS-APM);我们将这种方案称为(mVS-APM)，与(SSG)方案相比，(mVS-APM)利用恒定的步长和越来越精确的梯度。我们考虑两种情况。(a)有界域。在这种情况下，(mVS-APM)在不精确的梯度步骤中显示线性收敛，每个步骤都需要使用内部(prox-SSG)方案。具体来说，(mVS-APM)在[公式:见文]的prox-SSG步骤中实现了最优的oracle复杂度，在F的不精确(外部)梯度中实现了[公式:见文]的迭代复杂度，从而通过增加内部(随机)子梯度步骤的数量来实现均方误差的精确解;(b)无界域。在这种情况下，在子梯度上的状态依赖边界假设下，非加速变量(mVS-APM)是线性收敛的，其中越来越精确的梯度∇xF(x)通过(SSG)格式以越来越高的精度逼近。值得注意的是，(mVS-APM)也显示了最优的oracle复杂性[公式:见文本];(II)凸f。当f仅为凸但平滑时，通过对平滑序列、步长序列和批大小序列的适当选择，smooththed (VS-APM)(或sVS-APM)达到最优的oracle复杂度为[公式:见文]，从而得到一个-最优解。我们的结果可以专门用于两个重要的情况:(a)平滑f.由于不再需要平滑，我们观察到(VS-APM)承认最优速率和oracle复杂性，匹配先验结果;f.在非光滑确定性区域，(sVS-APM)简化为光滑加速近端方法(s-APM)，它是渐近收敛和最优的，因为它显示出[公式:见文]的复杂性，匹配Nesterov在2005年提供的产生-最优解的界。最后，(sVS-APM)和(VS-APM)产生的序列几乎肯定收敛于原问题的一个解。
{"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}
Charles-Albert Lehalle, Othmane Mounjid, M. Rosenbaum
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.
{"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}
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.
在本文中，我们研究Levy过程$A（cdot）$和$B（cdot）$的概率$xi_n（u）：=｛mathbb P｝left（C_ngeqslant u nright）$，其中$C_n:=A（pis_n B（varphi_n））$，以及$varphi-n$和$psi_n$非负序列，使得$varphi_npis_n=n$和$ varphi_ntoinfty$为$ntoinfty$。区分了两种时间尺度机制：$varphi_n$是超线性的“快”机制和$varphi_n$是次线性的“慢”机制。我们提供了两种制度的$xi_n（u）$（作为$ntoinfty$）的精确无症状性，依赖于测量变化参数和Edgeworth-型估计。渐近线具有非常规形式：指数包含常见的线性项，但也可能包含次线性项（次线性项的数量取决于$varphi_n$和$psi_n$的精确形式）。为了展示我们的结果的威力，我们包括了两个例子，涵盖了$C_n$是格和非格的情况。最后，我们给出了数值实验，证明了在服务系统中与客户流相关的实际应用中考虑$C_n$的双重随机性的重要性；他们表明，在没有明显的时间尺度分离的情况下，所获得的渐近结果产生了高度精确的近似。
{"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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：