Queue size distribution of Geo/G/1 queue under the Min(<Emphasis Type="Italic">N,D</Emphasis>)-policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N,D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n ⁺. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n ^-, n and n ⁺ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

Schools as Communities: Purveyors of Democratic Values and the Cornerstones of a Public Philosophy

Establishing interdependency and community among people may be the solution to reestablishing or creating a tighter fabric of support for childrens' development, for building cultural democracy and a democratic state. This paper attempts to create a bridge between education and the construction of sustainable democratic communities in education, as a basis for building a public philosophy. Ultimately, sustainable democratic educational communities may address the concerns of today and tomorrow and build sustainable democratic communities in the larger global society.     

Reliability indices of discrete-time Geox/G/1 queueing system with unreliable service station and multiple adaptive delayed vacations

This paper considers the discrete-time Geo~x/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research.Following problems will be discussed:1) The probability that the server is in a "generalized busy period" at time n;2) The probability that the service station is in failure at time n,i.e.,the transient unavailability of the service station,and the steady state unavailability of the service station;3) The expected number of service station failures during the time interval(0,n],and the steady state failure frequency of the service station;4) The expected number of service station breakdowns in a server’s "generalized busy period".Finally,the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper.     

Beer's “organizational tensegrity” and the challenge of democratic management

Many systems scientists are keenly interested in the democratization of management, particularly in the development of better processes for democratic decision making. Stafford Beer's recent development of a consensus decision-making process based on “organizational tensegrity” is an exciting contribution in this area, which also has important implications for the design of democratic organizational structures. This paper describes some experimentation with these ideas (with assistance from Beer) in two work groups at Pacific Bell and explores the potential of Beer's process for democratic management.     

The structure of departure process and optimal control strategy <Emphasis Type="Italic">N</Emphasis>* for <Emphasis Type="Italic">Geo/G</Emphasis>/1 discrete-time queue with multiple server vacations and Min(<Emphasis Type="Italic">N,V</Emphasis>)-Policy

This paper considers the departure process and the optimal control strategy for a discretetime Geo/G/1 queueing model in which the system operates under the control of multiple server vacations and Min(N, V)-policy. Using the law of total probability decomposition, the renewal theory and the probability generating function technique, the transient and the steady-state probabilities that the server is busy at any epoch n⁺ are derived. The authors also obtain the explicit expression of the probability generating function for the expected number of departures occurring in the time interval (0⁺, n⁺] from any initial state. Meanwhile, the relationship among departure process, server’s state process and service renewal process in server busy period is found, which shows the special structure of departure process. Especially, some corresponding results of departure process for special discrete-time queues are directly gained by our results. Furthermore, the approximate expansion for calculating the expected number of departures is presented. In addition, some other important performance measures, including the expected length of server busy period, server’s actual vacation period and busy cycle period etc., are analyzed. Finally, some numerical results are provided to determine the optimum value N* for minimizing the system cost under a given cost structure.     

On the nonexistence of nontrivial small cycles of the µ function in 3x+1 conjecture

This paper studies the property of the recursive sequences in the 3x+ 1 conjecture.The authors introduce the concept ofμfunction,with which the 3x + 1 conjecture can be transformed into two other conjectures:one is eventually periodic conjecture of theμfunction and the other is periodic point conjecture.The authors prove that the 3x + 1 conjecture is equivalent to the two conjectures above.In 2007,J.L.Simons proved the non-existence of nontrivial 2-cycle for the T function.In this paper,the authors prove that theμfunction has no l-periodic points for 2≤l≤12.In 2005, J.L.Simons and B.M.M de Weger proved that there is no nontrivial 2-cycle for the T function for l≤68,and in this paper,the authors prove that there is no nontrivial l-cycle for theμfunction for 2≤l≤102.     

A discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times

The authors discuss a discrete-time Geo/G/1 retrial queue with J-vacation policy and general retrial times. As soon as the orbit is empty, the server takes a vacation. However, the server is allowed to take a maximum number J of vacations, if the system remains empty after the end of a vacation. If there is at least one customer in the orbit at the end of a vacation, the server begins to serve the new arrivals or the arriving customers from the orbit. For this model, the authors focus on the steady-state analysis for the considered queueing system. Firstly, the authors obtain the generating functions of the number of customers in the orbit and in the system. Then, the authors obtain the closed-form expressions of some performance measures of the system and also give a stochastic decomposition result for the system size. Besides, the relationship between this discrete-time model and the corresponding continuous-time model is also investigated. Finally, some numerical results are provided.     

发展心理学的非线性动力学分析

运用非线性动力学的观点来分析发展心理学。因为个体是一个开放的系统，它必须与外界有物质、能量和信息的交换，在一定条件下自行产生组织性。所以，个体发展不单是遗传和环境相互作用的结果，还要受其原有心理结构和主观能动性的巨大影响。因为个体发展是个不断重建平衡的过程，即由量变积累产生质变的过程，质变的飞跃是在远离平衡态时实现的，所以说个体发展是一个既有连续性又有间断性的过程。另外，我们不能把个体发展单纯地看成线性过程。     

Functional coefficient autoregressive conditional root model

This paper proposes an extended model based on ACR model:Functional coefficient autoregressive conditional root model（FCACR）.Under some assumptions,the authors show that the process is geometrically ergodic,stationary and all moments of the process exist.The authors use the polynomial spline function to approximate the functional coefficient,and show that the estimate is consistent with the rate of convergence O_p(h^v+1+n^-1/3).By simulation study,the authors discover the proposed method can approximate well the real model.Furthermore,the authors apply the model to real exchange rate data analysis.     

Empirical likelihood for longitudinal partially linear model with α-mixing errors

This paper considers large sample inference for the regression parameter in a partially linear regression model with longitudinal data and α-mixing errors. The authors introduce an estimated empirical likelihood for the regression parameter and show that its limiting distribution is a mixture of central chi-squared distributions. Also, the authors derive an adjusted empirical likelihood method which is shown to have a central chi-square limiting distribution. A simulation study is carried out to assess the performance of the empirical likelihood method.     

A proximal point algorithm for a system of generalized mixed variational inequalities

This paper introduces and considers a new system of generalized mixed variational inequalities in a Hilbert space,which includes many new and known systems of variational inequalities and generalized variational inequalities as special cases.By using the two concepts of 77-subdifferential andη-proximal mappings of a proper function,the authors try to demonstrate that the system of generalized mixed variational inequalities is equivalence with a fixed point problem.By applying the equivalence, a new and innovativeη-proximal point algorithm for finding approximate solutions of the system of generalized mixed variational inequalities will be suggested and analyzed.The authors also study the convergence analysis of the new iterative method under much weaker conditions.The results can be viewed as a refinement and improvement of the previously known results for variational inequalities.     

Distributed Consensus-Based <Emphasis Type="Italic">K</Emphasis>-Means Algorithm in Switching Multi-Agent Networks

This paper discusses a distributed design for clustering based on the K-means algorithm in a switching multi-agent network, for the case when data are decentralized stored and unavailable to all agents. The authors propose a consensus-based algorithm in distributed case, that is, the double-clock consensus-based K-means algorithm (DCKA). With mild connectivity conditions, the authors show convergence of DCKA to guarantee a distributed solution to the clustering problem, even though the network topology is time-varying. Moreover, the authors provide experimental results on various clustering datasets to illustrate the effectiveness of the fully distributed algorithm DCKA, whose performance may be better than that of the centralized K-means algorithm.     

Social learning with time-varying weights

This paper investigates a non-Bayesian social learning model, in which each individual updates her beliefs based on private signals as well as her neighbors＇ beliefs. The private signM is involved in the updating process through Bayes＇ rule, and the neighbors＇ beliefs are embodied in through a weighted average form, where the weights are time-varying. The authors prove that agents eventually have correct forecasts for upcoming signals, and all the beliefs of agents reach a consensus. In addition, if there exists no state that is observationally equivalent to the true state from the point of view of all agents, the authors show that the consensus belief of the whole group eventually reflects the true state.     

An on-line scheduling problem of parallel machines with common maintenance time

In this paper, the authors consider an on-line scheduling problem of m (m ≥ 3) identical machines with common maintenance time interval and nonresumable availability. For the case that the length of maintenance time interval is larger than the largest processing time of jobs, the authors prove that any on-line algorithm has not a constant competitive ratio. For the case that the length of maintenance time interval is less than or equal to the largest processing time of jobs, the authors prove a lower bound of 3 on the competitive ratio. The authors give an on-line algorithm with competitive ratio $4 - \tfrac{1} {m} $ . In particular, for the case of m = 3, the authors prove the competitive ratio of the on-line algorithm is $\tfrac{{10}} {3} $ .     

Global stability of endemic equilibrium point of basic virus infection model with application to HBV infection

In this paper, the authors first show that if R ₀ ≤ 1, the infection free steady state is globally attractive by using approaches different from those given by Min, et al.(2008). Then the authors prove that if R ₀ > 1, the endemic steady state is also globally attractive. Finally, based on a patient’s clinical HBV DNA data of anti-HBV infection with drug lamivudine, the authors establish an ABVIM. The numerical simulations of the ABVIM are good in agreement with the clinical data.     

The Stability of Schrdinger Equation with Boundary Control Matched Disturbance

This paper studies the stability of Schr¨odinger equation with boundary control matched disturbance. The time-varying gain extended state observer is utilized to estimate disturbance and state. Meanwhile, the authors get a continuous controller by the active disturbance rejection control strategy, which shows that the closed-loop system of Schr¨odinger equation is asymptotically stable.These results are illustrated by simulation examples.     

Queue Size Distribution of Geo/G/1 Queue Under the Min(N,D)-Policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D,whichever occurs first(Min(N,D)-policy).By using renewal process theory and total probability decomposition technique,the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state,and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n~+.Meanwhile,the authors obtain the explicit expressions of the additional queue length distribution.Furthermore,the important relations between the steady state queue length distributions at different time epochs n~-,n and n~+ are also reported.Finally,the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution,and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

信息产业发展规律与模式研究

国内外有关信息产业发展规律与模式的研究大多局限于定性分析与描述,相关的定量研究并不多见。本文在此作了有益的探讨,建立了信息产业的生长方程与生命方程,揭示了信息产业发展变化规律的动力学特性,提出了信息产业的三个互异发展模式,引申了信息产业发展的控制论思考。     

Some inverse optimization problems on network

In this paper, the authors consider some inverse problems on network, such as the inverse transport problems with gains (IGTP) and the inverse linear fractional minimum cost flow problem (IFFP). Firstly, the authors give the mathematics model of (IGTP) and an efficient method of solving it under l ₁ norm; Secondly, taking advantage of the optimality conditions, the authors consider the (IFFP) and give a simple method of solving it. Finally, an numerical example test is also developed.     

管理机制设计理论

管理机制是管理系统运行的机理, 管理者就是在管理机制的支持下使的被管理者向着一定的状态发展或运动的。长期以来, 构造管理机制的方法仅仅局限于直觉与经验。本文研究如何科学地建立管理机制。文章认为管理机制设计有四个步骤：1.倾向分析。即分析被管理者有哪些自发追求。2.回报分析, 即针对每一种倾向分析被管理者有哪些可以提供的回报。3.状态分析, 即对达到管理目标时被管理者的各种标志进行分析。4.构造“结”, 即把状态与回报相连接, 文章还进一步研究了构造“结”的技术问题, 如“结”的形式、强度、状态受力的平衡、“结”的串联与并联等等。