The approximation analysis of the discrete-time Geo/Geo/1 system with additional optional service

This paper analyses a discrete-time Geo/Geo/1 queueing system, where all arriving customers demand the first essential service and some of them may further demand an additional optional service. The interarrival times, the service times of the essential service and the second optional service for arrivals are assumed to be random variables with Geometric distributions. Such a model has potential applications in computer or digital communication network systems. We model this system by the level-dependent and independent quasi-birth-death processes and develop efficient computation algorithms of the stationary distribution of the number of customers in the system using matrix analytic method. A cost model is derived to determine the optimal values of the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach.     

Asymptotic analysis and simple approximation of the loss probability of the GI/M/c/K queue

We consider the GI^X/M/c/K queues with partial rejection or total rejection, and find an asymptotic behavior of loss probability of the GI^X/M/c/K queue as K tends to infinity. The asymptotic loss probability is expressed only in terms of the roots of the characteristic equation and the boundary probabilities of the corresponding GI^X/M/c queue. Numerical examples show that the asymptotic loss probability is a quite accurate approximation for the loss probability of the GI^X/M/c/K queue even when the system capacity K is moderate.     

Tool maintenance optimization for multi-station machining systems with economic consideration of quality loss and obsolescence

Tools used in a machining process are vulnerable to frequent wear-outs and failures during their useful life. Maintenance is thus considered essential under such conditions. Additionally, it is widely recognized that the maintenance of manufacturing equipments and the quality of manufactured product are highly interrelated. However, few detailed study has been found in the literature dealing with the effects of maintenance policies on the operational performance of such a system, especially the long-term average cost. The need for a method to determine the optimal tool maintenance policy has become increasingly important. Since the multiple tools in a multi-station machining system generally have significant interactive impacts on the product quality loss, the optimal multi-component maintenance models for several policies are investigated to address the interdependence among these tools. Three distinctive multi-component maintenance policies, i.e., age replacement, block replacement, and block replacement with minimal repair, are identified and analyzed. The proposed approach focuses on these maintenance policies with consideration of both component catastrophic failures, and the interdependence of component degradations on the product quality loss as well as the obsolescence cost. The effects of various maintenance policies on the system performance are simulated, and they are used to determine the best policy for a given system. An illustrative example is used to demonstrate effectiveness and applicability of the proposed approach. The results presented a comparative analysis of specified maintenance policies with respect to the total maintenance cost with consideration of the product quality loss and the obsolescence cost.     

A matrix approach for the transient solution of an M/M/1/N queue with discouraged arrivals and reneging

This paper illustrates a computable matrix technique that can be used to derive explicit expressions for the transient state probabilities of a finite waiting space single-server queue, namely (M/M/1/N), having discouraged arrivals and reneging. The discipline is the classical first-come, first-served (FCFS). We obtain the transient solution of the system, with results in terms of the eigenvalues of a symmetric tridiagonal matrix. Finally, numerical calculations are given to illustrate the effectiveness of this technique and system behaviour.     

On boundary feedback stabilization of Timoshenko beam with rotor inertia at the tip

The feedback stabilization problem of a nonuniform Timoshenko beam system with rotor inertia at the tip of the beam is studied. First, as a special kind of linear boundary force feedback and moment control is applied to the beam‘ s tip, the strict mathematical treatment, a suitable state Hilbert space is chosen, and the well-poseness of the corresponding closed loop system is proved by using the semigroup theory of bounded linear operators. Then the energy corresponding to the closed loop system is shown to be exponentially stable. Finally, in the special case of umform beam, some sufficient and necessary conditions for the corresponding closed loop system to be asymptotically stable are derived.     

On the use of optimization models for portfolio selection: A review and some computational results

Portfolio theory deals with the question of how to allocate resources among several competing alternatives (stocks, bonds), many of which have an unknown outcome. In this paper we provide an overview of different portfolio models with emphasis on the corresponding optimization problems. For the classical Markowitz mean-variance model we present computational results, applying a dual algorithm for constrained optimization.     

An effective online teaching method: the combination of collaborative learning with initiation and self-regulation learning with feedback

In modern business environments, work and tasks have become more complex and require more interdisciplinary skills to complete, including collaborative and computing skills for website design. However, the computing education in Taiwan can hardly be recognised as effective in developing and transforming students into competitive employees. In this regard, the author adopted collaborative learning (CL) with initiation and self-regulated learning (SRL) with feedback to develop students' collaborative skills and regular learning habits and further contribute to practical computing skills for website design. This study comprised an experiment that included 279 second-year university students from five class sections, including four experimental groups (CISF group, n = 57; CIS group, n = 53; CI group, n = 68; C group, n = 68), and a control group (T group, n = 33). The results reveal that students who received the combined treatment of online CL with initiation and SRL with feedback attained the best grades for their computing skills for website design among the five groups. The author further discusses the implications for teachers, schools and educators who plan to design practical scenarios and online learning activities for their students.     

A necessary and sufficient condition for parameter insensitive disturbance-rejection problem with state feedback

In this paper a necessary and sufficient condition for a parameter insensitive disturbance-rejection problem with state feedback which was pointed out as an open problem by Bhattacharyya to be solvable is proved. A constructive algorithm of simultaneously (A,B)-invariant subspaces for a finite-number of linear systems and a relationship between simultaneously (A,B)-invariant subspaces and generalized (A,B)-invariant subspaces play an important role to prove the main result.     

A novel classification method: A hybrid approach based on extension of the UTADIS with polynomial and PSO-GA algorithm

In this study, a new multi-criteria classification technique for nominal and ordinal groups is developed by expanding the UTilites Additives DIScriminantes (UTADIS) method with a polynomial of degree T which is used as the utility function rather than using a piecewise linear function as an approximation of the utility function of each attribute. We called this method as PUTADIS. The objective is calculating the coefficients of the polynomial and the threshold limit of classes and weight of attributes such that it minimizes the number of misclassification error. Estimation of unknown parameters of the problem is calculated by using a hybrid algorithm which is a combination of particle swarm optimization algorithm (PSO) and Genetic Algorithm (GA). The results obtained by implementing the model on different datasets and comparing its performance with other previous methods show the high efficiency of the proposed method.