Convergence to Equilibrium States for Fluid Models of Many-server Queues with Abandonment

Fluid models have become an important tool for the study of many-server queues with general service and patience time distributions. The equilibrium state of a fluid model has been revealed by Whitt (2006) and shown to yield reasonable approximations to the steady state of the original stochastic systems. However, it remains an open question whether the solution to a fluid model converges to the equilibrium state and under what condition. We show in this paper that the convergence holds under a mild condition. Our method builds on the framework of measure-valued processes developed in Zhang (2013), which keeps track of the remaining patience and service times

Separation of timescales in a two-layered network

We investigate a computer network consisting of two layers occurring in, for example, application servers. The first layer incorporates the arrival of jobs at a network of multi-server nodes, which we model as a many-server Jackson network. At the second layer, active servers at these nodes act now as customers who are served by a common CPU. Our main result shows a separation of time scales in heavy traffic: the main source of randomness occurs at the (aggregate) CPU layer; the interactions between different types of nodes at the other layer is shown to converge to a fixed point at a faster time scale; this also yields a state-space collapse property. Apart from these fundamental insights, we also obtain an explicit approximation for the joint law of the number of jobs in the system, which is provably accurate for heavily loaded systems and performs numerically well for moderately loaded systems. The obtained results for the model under consideration can be applied to thread-pool dimensioning in application servers, while the technique seems applicable to other layered systems too.Comment: 8 pages, 2 figures, 1 table, ITC 24 (2012

Dual Instrumental Method for Confounded Kernelized Bandits

The contextual bandit problem is a theoretically justified framework with wide applications in various fields. While the previous study on this problem usually requires independence between noise and contexts, our work considers a more sensible setting where the noise becomes a latent confounder that affects both contexts and rewards. Such a confounded setting is more realistic and could expand to a broader range of applications. However, the unresolved confounder will cause a bias in reward function estimation and thus lead to a large regret. To deal with the challenges brought by the confounder, we apply the dual instrumental variable regression, which can correctly identify the true reward function. We prove the convergence rate of this method is near-optimal in two types of widely used reproducing kernel Hilbert spaces. Therefore, we can design computationally efficient and regret-optimal algorithms based on the theoretical guarantees for confounded bandit problems. The numerical results illustrate the efficacy of our proposed algorithms in the confounded bandit setting

Provably Efficient Learning in Partially Observable Contextual Bandit

In this paper, we investigate transfer learning in partially observable contextual bandits, where agents have limited knowledge from other agents and partial information about hidden confounders. We first convert the problem to identifying or partially identifying causal effects between actions and rewards through optimization problems. To solve these optimization problems, we discretize the original functional constraints of unknown distributions into linear constraints, and sample compatible causal models via sequentially solving linear programmings to obtain causal bounds with the consideration of estimation error. Our sampling algorithms provide desirable convergence results for suitable sampling distributions. We then show how causal bounds can be applied to improving classical bandit algorithms and affect the regrets with respect to the size of action sets and function spaces. Notably, in the task with function approximation which allows us to handle general context distributions, our method improves the order dependence on function space size compared with previous literatures. We formally prove that our causally enhanced algorithms outperform classical bandit algorithms and achieve orders of magnitude faster convergence rates. Finally, we perform simulations that demonstrate the efficiency of our strategy compared to the current state-of-the-art methods. This research has the potential to enhance the performance of contextual bandit agents in real-world applications where data is scarce and costly to obtain.Comment: 47 page

Stochastic Graph Bandit Learning with Side-Observations

In this paper, we investigate the stochastic contextual bandit with general function space and graph feedback. We propose an algorithm that addresses this problem by adapting to both the underlying graph structures and reward gaps. To the best of our knowledge, our algorithm is the first to provide a gap-dependent upper bound in this stochastic setting, bridging the research gap left by the work in [35]. In comparison to [31,33,35], our method offers improved regret upper bounds and does not require knowledge of graphical quantities. We conduct numerical experiments to demonstrate the computational efficiency and effectiveness of our approach in terms of regret upper bounds. These findings highlight the significance of our algorithm in advancing the field of stochastic contextual bandits with graph feedback, opening up avenues for practical applications in various domains.Comment: arXiv admin note: text overlap with arXiv:2010.03104 by other author

Study on Spatial Distribution of Soil Available Microelement in Qujing Tobacco Farming Area, China

AbstractDescriptive analysis characteristics and spatial variation characteristics of soil available microelements were studied based on SPSS and GIS Soil available microelements spatial distribution maps were created with ordinary Kriging method. The results indicate that, 7 available microelements in tobacco soil obey lognormal distribution, all the available microelements were intermediate variability; Anisotropic structure of available microelements of tobacco soil varies evidently, spatial variability of available B was mainly caused by random factors, and others’ spatial variability were caused by structural factors and random factors; Spatial distribution maps show that, available B was widely deficient in tobacco soil of Qujing farming area, ‘lower level’ and ‘low level’ taken 7.74% and 68.20%, respectively available Zn distribution was moderate, only 1.32% of the area lack of Zn, available Cu, available Fe and available Mn were extremely high in the whole extension, available Mo was deficient in part of the region with 28.38%, water soluble Cl was higher than critical value(30mgkg−1)in the most of Qujing farming area, which taken 38.86%

Thirty-six months recurrence after acute ischemic stroke among patients with comorbid type 2 diabetes: A nested case-control study

Background: Stroke patients have to face a high risk of recurrence, especially for those with comorbid T2DM, which usually lead to much more serious neurologic damage and an increased likelihood of death. This study aimed to explore determinants of stroke relapse among patients with comorbid T2DM. Materials and methods: We conducted this case-control study nested a prospective cohort of ischemic stroke (IS) with comorbid T2DM. During 36-month follow-up, the second stroke occurred in 84 diabetic IS patients who were allocated into the case group, while 613 patients without recurrence were the controls. We collected the demographic data, behaviors and habits, therapies, and family history at baseline, and measured the variables during follow-up. LASSO and Logistic regression analyses were carried out to develop a prediction model of stroke recurrence. The receiver operator characteristic (ROC) curve was employed to evaluate the performance of the prediction model. Results: Compared to participants without recurrence, the higher levels of pulse rate (78.29 ± 12.79 vs. 74.88 ± 10.93) and hypertension (72.6 vs. 61.2 %) were recorded at baseline. Moreover, a lower level of physical activity (77.4 vs. 90.4 %), as well as a higher proportion of hypoglycemic therapy (36.9 vs. 23.3 %) was also observed during 36-month follow-up. Multivariate logistic regression revealed that higher pulse rate at admission (OR = 1.027, 95 % CI = 1.005 – 1.049), lacking physical activity (OR = 2.838, 9 5 % CI = 1.418 – 5.620) and not receiving hypoglycemic therapy (OR = 1.697, 95 % CI = 1.013 – 2.843) during follow-up increased the risk of stroke recurrence. We developed a prediction model using baseline pulse rate, hypoglycemic therapy, and physical activity, which produced an area under ROC curve (AUC) of 0.689. Conclusion: Physical activity and hypoglycemic therapy play a protective role for IS patients with comorbid diabetes. In addition to targeted therapeutics, the improvement of daily-life habit contributes to slowing the progress of the IS