On the Strong Rates of Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables

A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.

Equivalent Conditions of Complete Convergence for Weighted Sums of Sequences of Extended Negatively Dependent Random Variables

By using Rosenthal type moment inequality for extended negatively de- pendent random variables, we establish the equivalent conditions of complete convergence for weighted sums of sequences of extended negatively dependent random variables under more general conditions. These results complement and improve the corresponding results obtained by Li et al. （Li D L, RAO M B, Jiang T F, Wang X C. Complete convergence and almost sure convergence of weighted sums of random variables. J. Theoret. Probab., 1995, 8： 49-76） and Liang （Liang H Y. Complete convergence for weighted sums of negatively associated random variables. Statist. Probab. Lett., 2000, 48： 317-325）.

Complete and Complete Moment Convergence for Weighted Sums of Widely Orthant Dependent Random Variables

In this paper, we establish a complete convergence result and a complete moment convergence result for weighted sums of widely orthant dependent random variables under mild conditions. As corollaries, the corresponding results for weighted sums of extended negatively orthant dependent random variables are also obtained, which generalize and improve the related known works in the literature.

Equivalent Conditions of Complete Convergence and Complete Moment Convergence for END Random Variables

In this paper,the complete convergence and the complete moment convergence for extended negatively dependent(END,in short) random variables without identical distribution are investigated.Under some suitable conditions,the equivalence between the moment of random variables and the complete convergence is established.In addition,the equivalence between the moment of random variables and the complete moment convergence is also proved.As applications,the Marcinkiewicz-Zygmund-type strong law of large numbers and the Baum-Katz-type result for END random variables are established.The results obtained in this paper extend the corresponding ones for independent random variables and some dependent random variables.

Strong Law of Large Numbers for Weighted Sums of Random Variables and Its Applications in EV Regression Models

This paper mainly studies the strong convergence properties for weighted sums of extended negatively dependent(END,for short)random variables.Some sufficient conditions to prove the strong law of large numbers for weighted sums of END random variables are provided.In particular,the authors obtain the weighted version of Kolmogorov type strong law of large numbers for END random variables as a product.The results that the authors obtained generalize the corresponding ones for independent random variables and some dependent random variables.As an application,the authors investigate the errors-in-variables(EV,for short)regression models and establish the strong consistency for the least square estimators.Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for illustration.

Exploring the impact of a coordinated variable speed limit control on congestion distribution in freeway

Over the past few decades, urban freeway congestion has been highly recognized as a serious and worsening traffic problem in the world. To relieve freeway congestion, several active traffic and demand management （ATDM） methods have been developed. Among them, variable speed limit （VSL） aims at regulating freeway mainline flow upstream to meet existing capacity and to harmonize vehicle speed. However, congestion may still be inevitable even with VSL implemented due to extremely high demand in actual practice. This study modified an existing VSL strategy by adding a new local constraint to suggest an achievable speed limit during the control period. As a queue is a product of the congestion phenomenon in freeway, the incentives of a queue build-up in the applied coordinated VSL control situation were analyzed. Considering a congestion occurrence （a queue build-up） characterized by a sudden and sharp speed drop, speed contours were utilized to demonstrate the congestion distribution over a whole freeway network in various sce- narios. Finally, congestion distributions found in both VSL control and non-VS control situations for various scenarios were investigated to explore the impact of the applied coordinated VSL control on the congestion distribution. An authentic stretch of V^hitemud Drive （I~~ID）, an urban freeway corridor in Edmonton, Alberta, Canada, was employed to implement this modified coordinated VSL control strategy; and a calibrated micro-simu- lation VISSIM model （model functions） was applied as the substitute of the real-world traffic system to test the above mentioned performance. The exploration task in this study can lay the groundwork for future research on how to improve the presented VSL control strategy for achieving the congestion mitigation effect on freeway.

Development and Testing of the GRAPES Regional Ensemble-3DVAR Hybrid Data Assimilation System

Based on the GRAPES（Global/Regional Assimilation and Prediction System） regional ensemble prediction system and 3DVAR（three-dimensional variational） data assimilation system,which are implemented operationally at the Numerical Weather Prediction Center of the China Meteorological Administration,an ensemble-based 3DVAR（En-3DVAR） hybrid data assimilation system for GRAPES-Meso（the regional mesoscale numerical prediction system of GRAPES） was developed by using the extended control variable technique to implement a hybrid background error covariance that combines the climatological covariance and ensemble-estimated covariance.Considering the problems of the ensemble-based data assimilation part of the system,including the reduction in the degree of geostrophic balance between variables,and the non-smooth analysis increment and its obviously smaller size compared with the 3DVAR data assimilation,corresponding measures were taken to optimize and ameliorate the system.Accordingly,a single pressure observation ensemble-based data assimilation experiment was conducted to ensure that the ensemble-based data assimilation part of the system is correct and reasonable.A number of localization-scale sensitivity tests of the ensemble-based data assimilation were also conducted to determine the most appropriate localization scale.Then,a number of hybrid data assimilation experiments were carried out.The results showed that it was most appropriate to set the weight factor of the ensemble-estimated covariance in the experiments to be 0.8.Compared with the 3DVAR data assimilation,the geopotential height forecast of the hybrid data assimilation experiments improved very little,but the wind forecast improved slightly at each forecast time,especially over 300 hPa.Overall,the hybrid data assimilation demonstrates some advantages over the3 DVAR data assimilation.