THE M/M/c QUEUE WITH （e,d） SETUP TIME

The authors present a new queueing model with （e, d） setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.     

The recursive solution of queue length for <Emphasis Type="Italic">Geo/G</Emphasis>/1 queue with <Emphasis Type="Italic">N</Emphasis>-policy

This paper considers a discrete-time queue with N-policy and LAS-DA(late arrival system with delayed access) discipline.By using renewal process theory and probability decomposition techniques,the authors derive the recursive expressions of the queue-length distributions at epochs n~-,n~+,and n.Furthermore,the authors obtain the stochastic decomposition of the queue length and the relations between the equilibrium distributions of the queue length at different epochs(n~-,n~+,n and departure epoch D_n).     

ON APPROXIMATION BY REPRODUCING KERNEL SPACES IN WEIGHTED L^p SPACES

In this paper, we investigate the order of approximation by reproducing kernel spaces on （-1, 1） in weighted L^p spaces. We first restate the translation network from the view of reproducing kernel spaces and then construct a sequence of approximating operators with the help of Jacobi orthogonal polynomials, with which we establish a kind of Jackson inequality to describe the error estimate. Finally, The results are used to discuss an approximation problem arising from learning theory.     

A perishable inventory system with service facilities, <Emphasis Type="Italic">MAP</Emphasis> arrivals and <Emphasis Type="Italic">PH</Emphasis> — Service times

We consider a continuous review perishable （s,S） inventory system with a service facility consisting of a waiting hall of finite capacity and a single server. We assume two types of customers, ordinary and negative, arrive according to a Markovian Arrival Process （MAP）. An ordinary customer joins the queue and a negative customer instead of joining the queue removes one ordinary customer from the queue. The removal rule adopted in this paper is RCE （removal of a customer from the end）. The individual customer＇s unit demand is satisfied after a random time of service which is assumed to have a phase-type distribution. The life time of each item and the lead time of the reorders have been assumed to be independent exponential distributions. The joint probability distribution of the number of customers in the system and the inventory level is obtained for the steady state case. Various stationary system performance measures are computed and the total expected cost rate is calculated. The results are illustrated numerically.     

MINIMAX PROGRAMMING UNDER GENERALIZED （p, r）-INVEXITY

Minimax programming problems involving generalized （p, r）-invex functions are consid- ered. Parametric sufficient optimality conditions and duality results are established under the aforesaid assumptions on the objective and constraint functions.     

Randomized policy of a poisson input queue with <Emphasis Type="Italic">J</Emphasis> vacations

This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations.After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation.If the number of arrivals does not reach N by the end of the J~(th) vacation,the server remains idle in the system until the number of arrivals in the queue re...     

ON CHARACTERIZATIONS OF D-η-PROPERLY PREQUASI-INVEX FUNCTION

Recently, various concepts of D-η-properly prequasi-invex functions were introduced and characterizations of D-η-properly prequasi-invex functions were presented under a certain set of conditions. In this paper, we show that the same results can be obtained under weaker assumptions.     

<Emphasis Type="Italic">Geom/G</Emphasis><Subscript>1</Subscript>, <Emphasis Type="Italic">G</Emphasis><Subscript>2</Subscript>/1/1 repairable Erlang loss system with catastrophe and second optional service

This paper studies a single server discrete-time Erlang loss system with Bernoulli arrival process and no waiting space. The server in the system is assumed to provide two different types of services, namely essential and optional services, to the customer. During the operation of the system, the arrival of the catastrophe will break the system down and simultaneously induce customer to leave the system immediately. Using a new type discrete supplementary variable technique, the authors obtain some performance characteristics of the queueing system, including the steady-state availability and failure frequency of the system, the steady-state probabilities for the server being idle, busy, breakdown and the loss probability of the system etc. Finally, by the numerical examples, the authors study the influence of the system parameters on several performance measures.     

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.     

ELIMINATION IN WEYI ALGEBRA AND q-IDENTITIES

In this paper, the following are introduced briefly： the basic concept of q-proper-hypergeometric; an algorithmic proof theory for q-proper-hypergeometric identities; and elimination in the non- commutative Weyl algebra. We give an algorithm for proving the single-variable q-proper-hypergeometric identities that is based on Zeilberger＇s approach and the elimination in Weyl algebra. Finally, we test several examples that have been proven by D. Zeilberger and H. Will using the WZ-pair method and Gosper algorithm.     

Generalized <Emphasis Type="Italic">p</Emphasis>-values for testing regression coefficients in partially linear models

The one-sided and two-sided hypotheses about the parametric component in partially linear model are considered in this paper. Generalized p-values are proposed based on fiducial method for testing the two hypotheses at the presence of nonparametric nuisance parameter. Note that the nonparametric component can be approximated by a linear combination of some known functions, thus, the partially linear model can be approximated by a linear model. Thereby, generalized p-values for a linear model are studied first, and then the results are extended to the situation of partially linear model. Small sample frequency properties are analyzed theoretically. Meanwhile, simulations are conducted to assess the finite sample performance of the tests based on the proposed p-values.     

A new <Emphasis Type="Italic">ɛ</Emphasis>-generalized projection method of strongly sub-feasible directions for inequality constrained optimization

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the ɛ-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new ɛ-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.     

ROBUST H∞ CONTROL FOR UNCERTAIN NONLINEAR SYSTEMS

This paper studies the robust H∞ disturbance attenuation with internal stability for uncertain nonlinear control systems. By adding one power integrator technique, this paper designs a explicit smooth robust dynamic feedback law while rejecting the disturbance to any specified degree of accuracy. Further, the example and simulation results show the effectiveness of the proposed schemes.     

IMPROVED ROBUST H-INFINITY ESTIMATION FOR UNCERTAIN CONTINUOUS-TIME SYSTEMS

The design of full-order robust estimators is investigated for continuous-time polytopic uncertain systems. The main purpose is to obtain a stable linear estimator such that the estimation error system remains robustly stable with a prescribed H∞ attenuation level. Firstly, a simple alternative proof is given for an improved LMI representation of H∞ performance proposed recently. Based on the performance criterion which keeps the Lyapunov matrix out of the product of the system dynamic matrices, a sufficient condition for the existence of the robust estimator is provided in terms of linear matrix inequalities. It is shown that the proposed design strategy allows the use of parameterdependent Lyapunov functions and hence it is less conservative than the earlier results. A numerical example is employed to illustrate the feasibility and advantage of the proposed design.     

Reflection-in-and-on-Action in Participatory Action Research: Toward Assessment <Emphasis Type="Italic">for </Emphasis>Learning

This article is about the use of oral assessment for learning and was based on a reflection-in-and-on-action approach within a participatory action research framework. The purpose of this paper was to argue for the incorporation of oral assessment in tertiary science as a fair, reliable and valid approach to assessment. This study found that the interactive nature of the oral assessments led to improved learning of content for learners from their peers and assessors. Assessors too learnt about their students as individuals, their study habits and critiqued their teaching from the oral assessments. They also learned from their co-assessors. Valuable lessons were learned for collaborative team teaching and assessing for the benefit of assessors and learners alike. This study also found that action research afforded the assessors a new way of doing things empowering them to conduct research in their own classrooms, with their colleagues and their learners.     

<Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> disturbance attenuation for a class of time-delay Hamiltonian systems

This paper considers the problem of L ₂-disturbance attenuation for a class of time-delay port-controlled Hamiltonian systems. A γ-dissipative inequality is established by using a proper control law and a storage function. Then based on the Razumikhin stability theorem, a sufficient condition is proposed for the asymptotically stability of the closed-loop system. Finally, the authors investigate the case that there are time-invariant uncertainties belonging to some convex bounded polytypic domain and an L ₂ disturbance attenuation control law is proposed. Study of illustrative example with simulation shows that the presented method in this paper works very well in the disturbance attenuation of time-delay Hamiltonian systems.     

OPTIMAL BIRTH CONTROL FOR AN AGE-DEPENDENT COMPETITION SYSTEM OF N SPECIES

In this paper, we investigate optimal policies for an age-dependent n-dimensional competition system, which is controlled by fertility. By using Dubovitskii-Milyutin＇s general theory, the maximum principles are obtained for the problems with free terminal states, infinite horizon, and target sets, respectively.     

Properties of storage functions and applications to nonlinear stochastic <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> control

This paper discusses the properties of the storage functions for a class of nonlinear stochastic systems. Some necessary and sufficient conditions for a function to be a storage function are derived. As applications, the finite and infinite horizon nonlinear stochastic H _∞ controls for systems with state, control, and external disturbance dependent noise are investigated, which generalize the previous results.     

RELIABILITY OF LINEAR （n,f, k） SYSTEMS WITH WEIGHTED COMPONENTS

The (n, f, k): F(G) system consists of n components and the system fails (works) if and only if there are at least f failed (working) components or at least k consecutive failed (working) components. These system models can be used in electronic equipment, automatic payment systems in banks, and furnace systems. In this paper we introduce and study the (n, f, k):F and (n, f, k): G systems consisting of weighted components. Recursive equations are presented for reliability evaluation of these new models. We also provide some conditions on the weights to represent weighted-(n, f, k) systems as usual (n, f, k) systems.     

GENERALIZED p-VALUES AND GENERALIZED CONFIDENCE INTERVALS FOR VARIANCE COMPONENTS IN GENERAL RANDOM EFFECT MODEL WITH BALANCED DATA

Various random models with balanced data that are relevant for analyzing practical test data are described, along with several hypothesis testing and interval estimation problems concerning variance components. In this paper, we mainly consider these problems in general random effect model with balanced data. Exact tests and confidence intervals for a single variance component corresponding to random effect are developed by using generalized p-values and generalized confidence intervals. The resulting procedures are easy to compute and are applicable to small samples. Exact tests and confidence intervals are also established for comparing the random-effects variance components and the sum of random-effects variance components in two independent general random effect models with balanced data. Furthermore, we investigate the statistical properties of the resulting tests. Finally, some simulation results on the type Ⅰ error probability and power of the proposed test are reported. The simulation results indicate that exact test is extremely satisfactory for controlling type Ⅰ error probability.