Fractional Brownian Heavy Traffic Approximations of Multiclass Feedforward Queueing Networks

We consider multiclass feedforward queueing networks under first in first out and priority service disciplines driven by long-range dependent arrival and service time processes. We show that in critical loading the normalized workload, queue length and sojourn time processes can converge to a multi-dimensional reflected fractional Brownian motion. This weak heavy traffic approximation is deduced from a deterministic pathwise approximation of the network behavior close to constant critical load in terms of the solution of a Skorokhod problem. Since we model the doubly infinite time interval, our results directly cover the stationary case.AMS subject classification: primary 90B15, secondary 60K25, 68M20     

A polling model with an autonomous server

This paper considers polling systems with an autonomous server that remains at a queue for an exponential amount of time before moving to a next queue incurring a generally distributed switch-over time. The server remains at a queue until the exponential visit time expires, also when the queue becomes empty. If the queue is not empty when the visit time expires, service is preempted upon server departure, and repeated when the server returns to the queue. The paper first presents a necessary and sufficient condition for stability, and subsequently analyzes the joint queue-length distribution via an embedded Markov chain approach. As the autonomous exponential visit times may seem to result in a system that closely resembles a system of independent queues, we explicitly investigate the approximation of our system via a system of independent vacation queues. This approximation is accurate for short visit times only.      

假期中顾客以概率θ进人的Geo/G/1(E,SV)排队系统的队长分布

考虑单重休假的Geo/G/1离散时间排队系统,其中在服务员休假期间到达的顾客以概率θ(0<θ≤1)进入系统.通过引入"服务员忙期"和使用全概率分解技术,从任意初始状态出发,研究了队长的瞬态和稳态性质,导出了在任意时刻n瞬态队长分布的z-变换的递推表达式和稳态队长分布的递推表达式,以及稳态队长的随机分解.最后,通过数值实例,讨论了稳态队长分布对系统参数的敏感性,并阐述了获得便于计算的稳态队长分布的表达式在系统容量设计中有重要的价值.     

Decomposability in queues with background states

A symmetric queue is known to have a nice property, the so-called insensitivity. In this paper, we generalize this for a single node queue with Poisson arrivals and background state, which changes at completion instants of lifetimes as well as at the arrival and departure instants. We study this problem by using the decomposability property of the joint stationary distribution of the queue length and supplementary variables, which implies the insensitivity. We formulate a Markov process representing the state of the queue as an RGSMP (reallocatable generalized semi-Markov process), and give necessary and sufficient conditions for the decomposability. We then establish general criteria to be sufficient for the queue to possess the property. Various symmetric-like queues with background states, including continuous time versions of moving server queues, are shown to have the decomposability.This author is partially supported by NEC C&C Laboratories.     

Circuit-switching networks with FIFO plus justifying blockout service on infinite graphs

A class of circuit-switching open queueing networks is discussed. The main result of the paper is that if extra message flows are not too intensive and the path distribution is mainly concentrated on the paths of (graph) distance 1 (nearest neighbour connections), then the network has a unique stationary working regime, no matter how large the configuration graph of the network is. Standard properties of this regime are established such as decay of correlation and continuity.     

M/G/1/N vacation model with varying E-limited service discipline

We define and analyze anM/G/1/N vacation model that uses a service discipline that we call theE-limited with limit variation discipline. According to this discipline, the server provides service until either the system is emptied (i.e. exhausted) or a randomly chosen limit ofl customers has been served. The server then goes on a vacation before returning to service the queue again. The queue length distribution and the Laplace-Stieltjes transforms of the waiting time, busy period and cycle time distributions are found. Further, an expression for the mean waiting time is developed. Several previously analyzed service disciplines, including Bernoulli scheduling, nonexhaustive service and limited service, are special cases of the general varying limit discipline that is analyzed in this paper.     

A mean-field limit for a class of queueing networks

A model of centralized symmetric message-switched networks is considered, where the messages having a common address must be served in the central node in the order which corresponds to their epochs of arrival to the network. The limitN is discussed, whereN is the branching number of the network graph. This procedure is inspired by an analogy with statistical mechanics (the mean-field approximation). The corresponding limit theorems are established and the limiting probability distribution for the network response time is obtained. Properties of this distribution are discussed in terms of an associated boundary problem.     

双曲约束下质点运动微分方程的建立与求解

以双曲约束为基本约束,建立质点在该约束情况下的运动微分方程;利用特殊函数的性质及椭圆积分,求出了这一问题的解析解,并对质点在一般平面约束情况下的运动情况作出了简明分析.     

促进化学教师专业发展的化学前沿资源例析

化学前沿资源的获取可以通过检索和阅读获得,结合近年来的文献实例探讨化学前沿对化学教师专业发展的特别意义：强化学科知识,促进学科视野与时俱进,彰显前沿研究的科学方法,有助于学科观念建构。将学科前沿资源应用于化学教学不限于教学情境创设、化学新题命制等,还有助于校本课程建设、实验创新设计和基于科学阅读的素养提升。     

高二学生认知结构、学科核心素养及学习困难的测量——以“卤代烃”为例

基于FLOWMAP测查高二学生"卤代烃"认知结构,并采用学科核心素养探究学生"卤代烃"学习困难。研究表明,学优生认知结构的优势体现在较高的认知"整合度"和准确率,学困生的劣势体现在较低的信息检索效率,学优生更善于运用描述及情境推理等信息处理策略建构知识。学生达到不同素养水平的学业要求差异较大。学习困难主要有不知道卤代烃的分类及物理性质,不明白或混淆发生取代反应与消去反应的特征、条件等,不知道卤代烃的用途。