Single-server queues with spatially distributed arrivals

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time.     

Relationships between characteristics in periodic Poisson queues

We study single server periodic queues in the day equilibrium conditions. The following characteristics of interest are considered at time of dayt: V^p(t)-the work load, L^p(t)-the number of customers and u^p(t)-the departure rate. We give relationships between E[V^p(t)], E[L^p(t)] and u^p(t). We also prove that E[V^p(t)] < and E[L^p(t)] < provided the second moment of the service time is finite.     

甲亚胺与姜黄素测定土壤有效硼方法的对比研究

土壤有效硼是决定土壤供硼能力的重要指标，目前中国多以沸水浸提土壤，并用姜黄素比色测硼值作为作物硼营养丰缺诊断指标．但在长期实践中，发现作物硼营养状况与热水溶性硼的相关性不稳定，同时测定值重现性不良。为提高作物硼营养诊断和预测的准确性，本研究通过０．０１ｍｏｌ／ＬＣａＣｌ２在２６０℃、３５ｍｉｎ浸提土壤条件下，用甲亚胺比色与沸水浸提，姜黄素比色法测定土壤有效硼的对比研究，证明甲亚胺法测定结果稳定，操作方法简便，适用于低硼土壤的大批量试样的自动分析。为甲亚胺测硼方法的推广应用，本研究已研制甲亚胺粉状试剂获得成功，与进口甲亚胺比较，性能完全一致。     

CROSS-LINKING OF AROMATIC POLY（THIOETHER）S

A novel cross-linking process using two high molecular weight aromatic poly(thioether)s,which were synthesized by the reactions of 4,4′-thiobisbenzenethiol with 4,4′-difluorobenzophenone and 4,4′-difluorodiphenylsulfone,respectively, and commercially available lower molecular weight poly(p-phenylene sulfide)was investigated.These reactions were carried out in bulk by the addition of silver tetrafluroborate andα,α′-dibromo-p-xylene at 190℃over a period of 45 min. Furthermore,the same procedure could be modified to cross-link compression-molded films of these three polymers.The thermal and solubility behaviors of these polymers before and after cross-linking reactions,are presented.     

Large deviation analysis of the single server queue

We establish the large deviation principle (LDP) for the virtual waiting time and queue length processes in the GI/GI/1 queue. The rate functions are found explicitly. As an application, we obtain the logarithmic asymptotics of the probabilities that the virtual waiting time and queue length exceed high levels at large times. Additional new results deal with the LDP for renewal processes and with the derivation of unconditional LDPs for conditional ones. Our approach applies in large deviations ideas and methods of weak convergence theory.This work was supported in part by AT&T Bell Labs.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Stationary queues with one autonomous server

Given a stationary stochastic continuous demand of service σ(θ_tω) dt with ∫ σ(ω)P(dω) < 1, we construct real stationary point processes $\text{(T}{}_{\mathrm{n}}\text{, n ∈}\text{Z}\text{)[T}{}_{\mathrm{n}}\text{< T}{}_{\mathrm{n}}\text{+1, lim}{}_{\mathrm{\pm \infty }}\text{T}{}_{\mathrm{n}}\text{= ±∞]}$ such that

for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [T_n, T_n+1[ the demand of service accumulated during the proceding intervals [T_n?1, T_n[ and take a rest of fixed duration D.     

基于AHP权重和灰色服务器负载预测的云计算On-line迁移策略

为了克服云计算环境下由于实时用户任务的不确定性到来和服务器性能差异而导致的云计算环境的负载不均衡问题,提出了一种AHP权重获取和灰度算法预测服务器负载的云计算on-line虚拟机迁移策略。首先,设计了基于AHP和灰色服务器预测的虚拟机on-line迁移模型,提出了采用AHP获取虚拟机各资源需求权重,然后,采用灰色模型预测下一时刻的服务器负载,采用此权值向量与各无需迁移的服务器的空闲资源向量进行加权得到加权和,将具有最小加权和的物理服务器作为迁移的目标宿主机。最后,定义了基于AHP权重和灰色服务器负载预测的云计算on-line迁移算法。在CloudSim环境下进行实验,结果表明文中的迁移策略使得云计算在响应用户任务时,具有任务失败次数少、SLA违约率低和迁移成功率高的优点,同时与其它方法相比,具有负载均衡程度高的优点,具有较强的可行性。     

Ab initio multi-reference configuration interaction of the low-lying states of the AsP molecule

Nine low-lying electronic states of the AsP molecule, including Σ , Ⅱ, and △ symmetries with singlet, triplet, and quintet spin multiplicities, are studied using multi-reference configuration interaction method.The potential energy curves and the spectroscopic constants of these nine states are determined, and compared with the experimental observed data as well as other theoretical works available at present.Three quintet states are reported for the first time.Furthermore, the analytical potential energy functions of these states are fitted using Murrell-Sorbie function and least square fitting method.