The multi-server retrial system with Bernoulli feedback and starting failures

In this paper, we present a detailed analysis of a multi-server retrial queue with Bernoulli feedback, where the servers are subject to starting failures. Upon completion of a service, a customer would decide either to leave the system with probability p or to join the retrial orbit again for another service with complementary probability 1?p. We analyse this queueing system as a quasi-birth–death process. Specifically, the equilibrium condition of the system is given for the existence of the steady-state analysis. Applying the matrix-geometric method, the formulae for computing the rate matrix and stationary probabilities are obtained. We further develop the matrix-form expressions for various system performance measures. A cost model is constructed to determine the optimal number of servers, the optimal mean service rate and the optimal mean repair rate subject to the stability condition. Finally, we give a practical example to illustrate the potential applicability of this model.     

Multi-server retrial queue with second optional service: algorithmic computation and optimisation

We consider an infinite-capacity M/M/c retrial queue with second optional service (SOS) channel. An arriving customer finds a free server would enter the service (namely, the first essential service, denoted by FES) immediately; otherwise, the customer enters into an orbit and starts generating requests for service in an exponentially distributed time interval until he finds a free server and begins receiving service. After the completion of FES, only some of them receive SOS. The retrial system is modelled by a quasi-birth-and-death process and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix-analytic approach. A cost model is derived to determine the optimal values of the number of servers and the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimisation approach as well as the effect of various parameters on system performance measures.     

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.     

Distributed output feedback MPC with randomly occurring actuator saturation and packet loss

In this paper, a distributed output feedback model predictive control (OFMPC) algorithm is presented for the polytopic uncertain system subject to randomly occurring actuator saturation and packet loss. Compared with the intensively applied state feedback control in MPC, the OFMPC is more feasible to the real world because the system states are often unmeasurable. With taking both actuator saturation and packet loss into account, the presented OFMPC algorithm is more practical. Moreover, by splitting the controller inputs into two independent parts, the presented dynamic output feedback control (DOFC) strategy provides more freedom to the controller design. With the global system decomposed into some subsystems, the computation complexity is reduced, thus the online designing time can be saved. By defining the estimation error function and forming an augmented system to handle the DOFC and by transforming the nonlinear feedback law into a convex hull of linear feedback laws, the distributed controllers are obtained by solving a linear matrix inequality (LMI) optimization problem. Finally, some simulation examples are employed to show the effectiveness of the techniques proposed in this paper. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysis of a multi-server queue with two priority classes and (M, N)-threshold service schedule I: non-preemptive priority

In this paper, we propose an ( M , N )-threshold non-preemptive priority service schedule for a queueing system consisting of two-parallel queues and a multi-server. The arrival process for each queue is Poisson, and the service times are exponentially distributed with different means. We derive the generating functions of the stationary joint queue-length distribution, and then obtain the mean queue length and the mean waiting time for each queue.     

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.     

Robust event‐triggered output feedback learning algorithm for voltage source inverters with unknown load and parameter variations

We consider the output feedback event‐triggered control of an off‐grid voltage source inverter (VSI) with unknown inductance‐capacitance (L ? C) filter dynamics and connected load in the presence of an input disturbance acting at the inverter. Due to uncertain dynamics and unmodeled parameters in the L ? C filter connected to the VSI, we use an adaptive observer to reconstruct the system's states by measuring only the voltage at the output. The control mechanism is constructed based on an impulsive actor/critic framework that approximates the cost, the event‐triggered controller, and the worst case disturbance and generates the desired AC output with the least energy dissipation. We provide rigorous stability proofs and illustrate the applicability of our results through a simulation example.     

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.     

Optimal velocity model with consideration of the lateral effect and its feedback control research

In this paper, a car-following model with the consideration of lateral effect is constructed. An improved control signal with considering more comprehensive information is introduced according to the feedback control theory. The stability conditions with control signal or not are derived. Numerical simulations are carried out to illustrate the advantage of the modified model with and without the control signal, and the results are consistent with the analytical ones.     

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.     

Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.     

Lookup table control method for vibration suppression of a flexible manipulator with optimization of the minimum settling time and energy consumption

Active vibration suppression of flexible manipulators is important in many engineering applications, such as robot manipulators and high‐speed flexible mechanisms. The demand for a short settling time and low energy consumption of vibration suppression requires consideration of optimal control. Under a wide range of operating conditions, however, the fixed optimal parameters determined for a control algorithm might not produce the best performance. Therefore, to enhance performance, this paper suggests a lookup table control method for a flexible manipulator. This method can tune itself to the optimal parameters on the basis of initial maximum responses to the controlled system. In this study, a multi‐objective genetic algorithm is used to search for optimal parameters with regard to positive position feedback to the control algorithm. In turn, with the optimal parameters, the multi‐objective functions of the settling time and energy consumption during the vibration control of a flexible manipulator can be minimized. The simulation and experimental results both indicate that the energy consumption can be reduced significantly if the settling time is slightly increased. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Learning faces with the BIAS model: On the importance of the sizes and locations of fixation regions

During perception of complex objects, the highest density of fixations occurs on the regions that are most salient. For example, when looking at a face, the regions that receive the largest density of fixations are the eyes, the nose, and the mouth. The fact that some regions within an object are more informative than other regions means that a learning system that can acquire this information from a teacher rather than from random fixations can learn faster and likewise recognize faster. An important question, from both the theoretical and practical points of view is: How important are the properties of the fixation regions for the learning system? In this work we consider one such system, the Bayesian integrate and shift (BIAS) model for learning object categories, and investigate its sensitivity to changes in the sizes and locations of fixation regions. We test the model using a face category and show that the learning algorithm is robust to large variations of the regions’ sizes and locations. Specifically, we show that the performance is inversely proportional to the sizes of the fixation regions and that the preferred locations are those that are closer to the center of the object.     

On the Control of Plants with Hysteresis: Overview and a Prandtl-Ishlinskii Hysteresis Based Control Approach

The development of control techniques to mitigate the effects of unknown hysteresis preceding with plants has recently re-attracted significant attention. In this paper, we first give a brief review of presently developed hysteresis models and hysteresis compensating control methods. Then, with the use of the Prandtl-Ishlinskii hysteresis model, we propose a robust adaptive control scheme. The novelty is that the model of hysteresis nonlinearities is firstly fused with the available control techniques without necessarily constructing a hysteresis inverse. The global stability of theadaptive system and tracking a desired trajectory to a certain precision are achieved. Simulations performed on a nonlinear system illustrate and clarify the approach.     

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.