Effects of Reneging, Server Breakdowns and Vacation on a Batch Arrival Single Server Queueing System with Three Fluctuating Modes of Service

This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.

ON THE BREAKDOWNS OF THE GALERKIN AND LEAST-SQUARES METHODS

The Galerkin and least-squares methods are two classes of the most popular Krylov subspace methOds for solving large linear systems of equations. Unfortunately, both the methods may suffer from serious breakdowns of the same type: In a breakdown situation the Galerkin method is unable to calculate an approximate solution, while the least-squares method, although does not really break down, is unsucessful in reducing the norm of its residual. In this paper we first establish a unified theorem which gives a relationship between breakdowns in the two methods. We further illustrate theoretically and experimentally that if the coefficient matrix of a lienar system is of high defectiveness with the associated eigenvalues less than 1, then the restarted Galerkin and least-squares methods will be in great risks of complete breakdowns. It appears that our findings may help to understand phenomena observed practically and to derive treatments for breakdowns of this type.

11.2 W/mm power density AlGaN/GaN high electron-mobility transistors on a GaN substrate

In this letter,high power density AlGaN/GaN high electron-mobility transistors(HEMTs)on a freestanding GaN substrate are reported.An asymmetricΓ-shaped 500-nm gate with a field plate of 650 nm is introduced to improve microwave power performance.The breakdown voltage(BV)is increased to more than 200 V for the fabricated device with gate-to-source and gate-to-drain distances of 1.08 and 2.92μm.A record continuous-wave power density of 11.2 W/mm@10 GHz is realized with a drain bias of 70 V.The maximum oscillation frequency(f_(max))and unity current gain cut-off frequency(f_(t))of the AlGaN/GaN HEMTs exceed 30 and 20 GHz,respectively.The results demonstrate the potential of AlGaN/GaN HEMTs on freestanding GaN substrates for microwave power applications.

Single machine stochastic JIT scheduling problem subject to machine breakdowns

In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.

Scheduling jobs on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties

This article addresses the problem of scheduling n jobs with a common due date on a machine subject to stochastic breakdowns to minimize absolute early-tardy penalties.We investigate the problem under the conditions that the uptimes follow an exponential distribution,and the objective measure in detail is to minimize the expected sum of the absolute deviations of completion times from the common due date.We proceed to study in two versions (the downtime follows an exponential distribution or is a constant entailed for the repeat model job),one of which is the so-called preempt- resume version,the other of which is the preempt-repeat version.Three terms of work have been done.(i)Formulations and Preliminaries.A few of necessary definitions,relations and basic facts are established.In particular,the conclusion that the expectation of the absolute deviation of the completion time about a job with deterministic processing time t from a due date is a semi-V-shape function in t has been proved.(ii) Properties of Optimal Solutions.A few characteristics of optimal solutions are established.Most importantly,the conclusion that optimal solutions possess semi-V- shape property has been proved.(iii) Algorithm.Some computing problems on searching for optimal solutions are discussed.

Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period

This paper deals with a discrete-time Geo/Geo/1 queueing system with working breakdowns in which customers arrive at the system in variable input rates according to the states of the server. The server may be subject to breakdowns at random when it is in operation. As soon as the server fails, a repair process immediately begins. During the repair period, the defective server still provides service for the waiting customers at a lower service rate rather than completely stopping service.We analyze the stability condition for the considered system. Using the probability generating function technique, we obtain the probability generating function of the steady-state queue size distribution.Also, various important performance measures are derived explicitly. Furthermore, some numerical results are provided to carry out the sensitivity analysis so as to illustrate the effect of different parameters on the system performance measures. Finally, an operating cost function is formulated to model a computer system and the parabolic method is employed to numerically find the optimum service rate in working breakdown period.

Review of the SiC LDMOS power device

Silicon carbide(SiC),as a third-generation semiconductor material,possesses exceptional material properties that significantly enhance the performance of power devices.The SiC lateral double-diffused metal–oxide–semiconductor(LDMOS)power devices have undergone continuous optimization,resulting in an increase in breakdown voltage(BV)and ultra-low specific on-resistance(Ron,sp).This paper has summarized the structural optimizations and experimental progress of SiC LDMOS power devices,including the trench-gate technology,reduced surface field(RESURF)technology,doping technology,junction termination techniques and so on.The paper is aimed at enhancing the understanding of the operational mechanisms and providing guidelines for the further development of SiC LDMOS power devices.

Accurate method based on data filtering for quantitative multi-element analysis of soils using CF-LIBS

To obtain more stable spectral data for accurate quantitative analysis of multi-element,especially for the large-area in-situ elements detection of soils, we propose a method for a multielement quantitative analysis of soils using calibration-free laser-induced breakdown spectroscopy(CF-LIBS) based on data filtering. In this study, we analyze a standard soil sample doped with two heavy metal elements, Cu and Cd, with a specific focus on the line of Cu I324.75 nm for filtering the experimental data of multiple sample sets. Pre-and post-data filtering,the relative standard deviation for Cu decreased from 30% to 10%, The limits of detection(LOD)values for Cu and Cd decreased by 5% and 4%, respectively. Through CF-LIBS, a quantitative analysis was conducted to determine the relative content of elements in soils. Using Cu as a reference, the concentration of Cd was accurately calculated. The results show that post-data filtering, the average relative error of the Cd decreases from 11% to 5%, indicating the effectiveness of data filtering in improving the accuracy of quantitative analysis. Moreover, the content of Si, Fe and other elements can be accurately calculated using this method. To further correct the calculation, the results for Cd was used to provide a more precise calculation. This approach is of great importance for the large-area in-situ heavy metals and trace elements detection in soil, as well as for rapid and accurate quantitative analysis.

Patterning single-layer materials by electrical breakdown using atomic force microscopy

The development of nanoelectronics and nanotechnologies has been boosted significantly by the emergence of 2D materials because of their atomic thickness and peculiar properties,and developing a universal,precise patterning technology for single-layer 2D materials is critical for assembling nanodevices.Demonstrated here is a nanomachining technique using electrical breakdown by an AFM tip to fabricate nanopores,nanostrips,and other nanostructures on demand.This can be achieved by voltage scanning or applying a constant voltage while moving the tip.By measuring the electrical current,the formation process on single-layer materials was shown quantitatively.The present results provide evidence of successful pattern fabrication on single-layer MoS2,boron nitride,and graphene,although further confirmation is still needed.The proposed method holds promise as a general nanomachining technology for the future.

Numerical Analysis of Perforation during Hydraulic Fracture Initiation Based on Continuous-Discontinuous Element Method

Perforation is a pivotal technique employed to establish main flow channels within the reservoir formation at the outset of hydraulic fracturing operations.Optimizing perforation designs is critical for augmenting the efficacy of hydraulic fracturing and boosting oil or gas production.In this study,we employ a hybrid finite-discrete element method,known as the continuous–discontinuous element method(CDEM),to simulate the initiation of post-perforation hydraulic fractures and to derive enhanced design parameters.The model incorporates the four most prevalent perforation geometries,as delineated in an engineering technical report.Real-world perforations deviate from the ideal cylindrical shape,exhibiting variable cross-sectional profiles that typically manifest as an initial constriction followed by an expansion,a feature consistent across all four perforation types.Our simulations take into account variations in perforation hole geometries,cross-sectional diameters,and perforation lengths.The findings show that perforations generated by the 39g DP3 HMX perforating bullet yield the lowest breakdown pressure,which inversely correlates with increases in sectional diameter and perforation length.Moreover,this study reveals the relationship between breakdown pressure and fracture degree,providing valuable insights for engineers and designers to refine perforation strategies.

Characteristics of laser-induced breakdown spectroscopy of liquid slag

Rapid online analysis of liquid slag is essential for optimizing the quality and energy efficiency of steel production. To investigate the key factors that affect the online measurement of refined slag using laser-induced breakdown spectroscopy(LIBS), this study examined the effects of slag composition and temperature on the intensity and stability of the LIBS spectra. The experimental temperature was controlled at three levels: 1350℃, 1400℃, and 1450℃. The results showed that slag composition and temperature significantly affected the intensity and stability of the LIBS spectra. Increasing the Fe content and temperature in the slag reduces its viscosity, resulting in an enhanced intensity and stability of the LIBS spectra. Additionally, 42 refined slag samples were quantitatively analyzed for Fe, Si, Ca, Mg, Al, and Mn at 1350℃, 1400℃, and 1450℃.The normalized full spectrum combined with partial least squares(PLS) quantification modeling was used, using the Ca Ⅱ 317.91 nm spectral line as an internal standard. The results show that using the internal standard normalization method can significantly reduce the influence of spectral fluctuations. Meanwhile, a temperature of 1450℃ has been found to yield superior results compared to both 1350℃ and 1400℃, and it is advantageous to conduct a quantitative analysis of the slag when it is in a “water-like” state with low viscosity.

Estimating the yield stress of soft materials via laser-induced breakdown spectroscopy

Taking three typical soft samples prepared respectively by loose packings of 77-,95-,and 109-μm copper grains as examples,we perform an experiment to investigate the energy-dependent laser-induced breakdown spectroscopy(LIBS)of soft materials.We discovered a reversal phenomenon in the trend of energy dependence of plasma emission intensity:increasing initially and then decreasing separated by a well-defined critical energy.The trend reversal is attributed to the laser-induced recoil pressure at the critical energy just matching the sample's yield strength.As a result,a one-to-one correspondence can be well established between the samples'yield stress and the critical energy that is easily obtainable from LIBS measurements.This allows us to propose an innovative method for estimating the yield stress of soft materials via LIBS with attractive advantages including in-situ remote detection,real-time data collection,and minimal destructive to sample.

Phase field model for electric-thermal coupled discharge breakdown of polyimide nanocomposites under high frequency electrical stress

In contrast to conventional transformers, power electronic transformers, as an integral component of new energy power system, are often subjected to high-frequency and transient electrical stresses, leading to heightened concerns regarding insulation failures. Meanwhile, the underlying mechanism behind discharge breakdown failure and nanofiller enhancement under high-frequency electrical stress remains unclear. An electric-thermal coupled discharge breakdown phase field model was constructed to study the evolution of the breakdown path in polyimide nanocomposite insulation subjected to high-frequency stress. The investigation focused on analyzing the effect of various factors, including frequency, temperature, and nanofiller shape, on the breakdown path of Polyimide(PI) composites. Additionally, it elucidated the enhancement mechanism of nano-modified composite insulation at the mesoscopic scale. The results indicated that with increasing frequency and temperature, the discharge breakdown path demonstrates accelerated development, accompanied by a gradual dominance of Joule heat energy. This enhancement is attributed to the dispersed electric field distribution and the hindering effect of the nanosheets. The research findings offer a theoretical foundation and methodological framework to inform the optimal design and performance management of new insulating materials utilized in high-frequency power equipment.

Estimating the grain size of microgranular material using laser-induced breakdown spectroscopy combined with machine learning algorithms

Recent work has validated a new method for estimating the grain size of microgranular materials in the range of tens to hundreds of micrometers using laser-induced breakdown spectroscopy(LIBS).In this situation,a piecewise univariate model must be constructed to estimate grain size due to the complex dependence of the plasma formation environment on grain size.In the present work,we tentatively construct a unified calibration model suitable for LIBS-based estimation of those grain sizes.Specifically,two unified multivariate calibration models are constructed based on back-propagation neural network(BPNN)algorithms using feature selection strategies with and without considering prior information.By detailed analysis of the performances of the two multivariate models,it was found that a unified calibration model can be successfully constructed based on BPNN algorithms for estimating the grain size in the range of tens to hundreds of micrometers.It was also found that the model constructed with a priorguided feature selection strategy had better prediction performance.This study has practical significance in developing the technology for material analysis using LIBS,especially when the LIBS signal exhibits a complex dependence on the material parameter to be estimated.

Analysis of metabolic characteristics of metabolic syndrome in elderly patients with gastric cancer by non-targeted metabolomics

BACKGROUND The relationship between metabolic syndrome(MetS)and gastric cancer(GC),which is a common metabolic disease,has attracted much attention.However,the specific metabolic characteristics of MetS in elderly patients with GC remain unclear.AIM To investigate the differentially abundant metabolites and metabolic pathways between preoperative frailty and MetS in elderly patients with GC based on nontargeted metabolomics techniques.METHODS In this study,125 patients with nonfrail nonmeal GC were selected as the control group,and 50 patients with GC in the frail group were selected as the frail group.Sixty-five patients with GC combined with MetS alone were included in the MetS group,and 50 patients with GC combined with MetS were included in the MetS group.Nontargeted metabolomics techniques were used to measure plasma metabolite levels by ultrahigh-performance liquid chromatography-mass spectrometry.Multivariate statistical analysis was performed by principal component analysis,orthogonal partial least squares,pattern recognition analysis,cluster analysis,and metabolic pathway annotation.RESULTS A total of 125 different metabolites,including amino acids,glycerophospholipids,sphingolipids,fatty acids,sugars,nucleosides and nucleotides,and acidic compounds,were identified via nontargeted metabolomics techniques.Compared with those in the control group,there were 41,32,and 52 different metabolites in the MetS group,the debilitated group,and the combined group,respectively.Lipid metabolites were significantly increased in the MetS group.In the weak group,amino acids and most glycerol phospholipid metabolites decreased significantly,and fatty acids and sphingosine increased significantly.The combined group was characterized by significantly increased levels of nucleotide metabolites and acidic compounds.The alanine,aspartic acid,and glutamate metabolic pathways were obviously enriched in the asthenic group,and the glycerol and phospholipid metabolic pathways were obviously enriched in the combined group.CONCLUSION Elderly GC patients with simple frailty,simple combined MetS,and frailty combined with MetS have different metabolic characteristics,among which amino acid and glycerophospholipid metabolite levels are significantly lower in frail elderly GC patients,and comprehensive supplementation of fat and protein should be considered.Many kinds of metabolites,such as amino acids,lipids,nucleotides,and acidic compounds,are abnormally abundant in patients with MetS combined with fthenia,which may be related to tumor-related metabolic disorders.

A theoretical study of the signal enhancement mechanism of coaxial DP-LIBS

In the field of dual-pulse laser-induced breakdown spectroscopy(DP-LIBS)research,the pursuit of methods for determining pulse intervals and other parameters quickly and conveniently in order to achieve optimal spectral signal enhancement is paramount.To aid researchers in identification of optimal signal enhancement conditions and more accurate interpretation of the underlying signal enhancement mechanisms,theoretical simulations of the spatiotemporal processes of coaxial DP-LIBS-induced plasma have been established in this work.Using a model based on laser ablation and two-dimensional axisymmetric fluid dynamics,plasma evolutions during aluminum–magnesium alloy laser ablation under single-pulse and coaxial dualpulse excitations have been simulated.The influences of factors,such as delay time,laser fluence,plasma temperature,and particle number density,on the DP-LIBS spectral signals are investigated.Under pulse intervals ranging from 50 to 1500 ns,the time evolutions of spectral line intensity,dual-pulse emission enhancement relative to the single-pulse results,laser irradiance,spatial distribution of plasma temperature and species number density,as well as laser irradiance shielded by plasma have been obtained.The study indicates that the main reason behind the radiation signal enhancement in coaxial DP-LIBS-induced plasma is attributed to the increased species number density and plasma temperature caused by the second laser,and it is inferred that the shielding effect of the plasma mainly occurs in the boundary layer of the stagnation point flow over the target surface.This research provides a theoretical basis for experimental research,parameter optimization,and signal enhancement tracing in DP-LIBS.

Incorporating empirical knowledge into data-driven variable selection for quantitative analysis of coal ash content by laser-induced breakdown spectroscopy

Laser-induced breakdown spectroscopy(LIBS)has become a widely used atomic spectroscopic technique for rapid coal analysis.However,the vast amount of spectral information in LIBS contains signal uncertainty,which can affect its quantification performance.In this work,we propose a hybrid variable selection method to improve the performance of LIBS quantification.Important variables are first identified using Pearson's correlation coefficient,mutual information,least absolute shrinkage and selection operator(LASSO)and random forest,and then filtered and combined with empirical variables related to fingerprint elements of coal ash content.Subsequently,these variables are fed into a partial least squares regression(PLSR).Additionally,in some models,certain variables unrelated to ash content are removed manually to study the impact of variable deselection on model performance.The proposed hybrid strategy was tested on three LIBS datasets for quantitative analysis of coal ash content and compared with the corresponding data-driven baseline method.It is significantly better than the variable selection only method based on empirical knowledge and in most cases outperforms the baseline method.The results showed that on all three datasets the hybrid strategy for variable selection combining empirical knowledge and data-driven algorithms achieved the lowest root mean square error of prediction(RMSEP)values of 1.605,3.478 and 1.647,respectively,which were significantly lower than those obtained from multiple linear regression using only 12 empirical variables,which are 1.959,3.718 and 2.181,respectively.The LASSO-PLSR model with empirical support and 20 selected variables exhibited a significantly improved performance after variable deselection,with RMSEP values dropping from 1.635,3.962 and 1.647 to 1.483,3.086 and 1.567,respectively.Such results demonstrate that using empirical knowledge as a support for datadriven variable selection can be a viable approach to improve the accuracy and reliability of LIBS quantification.

Integrated Experimental and Simulation Investigation of Breakdown Voltage Characteristics Across Electrode Configurations in SF_(6) Circuit Breakers

This study investigates the breakdown voltage characteristics in sulfur hexafluoride(SF6)circuit breakers,employing a novel approach that integrates both experimental investigations and finite element simulations.Utilizing a sphere-sphere electrode configuration,we meticulously measured the relationship between breakdown voltage and electrode gap distances ranging from 1 cm to 4.5 cm.Subsequent simulations,conducted using COMSOL Multiphysics,mirrored the experimental setup to validate the model’s accuracy through a comparison of the breakdown voltage-electrode gap distance curves.The simulation results not only aligned closely with the experimental data but also allowed the extraction of detailed electric field strength,electric potential contours,and electric current flow curves at the breakdown voltage for gap distances extending from 1 to 4.5 cm.Extending the analysis,the study explored the electric field and potential distribution at a constant voltage of 72.5 kV for gap distances between 1 to 10 cm,identifying the maximum electric field strength.A comprehensive comparison of five different electrode configurations(sphere-sphere,sphere-rod,sphere-plane,rod-plane,rod-rod)at 72.5 kV and a gap distance of 1.84 cm underscored the significant influence of electrode geometry on the breakdown process.Moreover,the research contrasts the breakdown voltage in SF6 with that in air,emphasizing SF6’s superior insulating properties.This investigation not only elucidates the intricate dynamics of electrical breakdown in SF6 circuit breakers but also contributes valuable insights into the optimal electrode configurations and the potential for alternative insulating gases,steering future advancements in high-voltage circuit breaker technology.

Production Control of a Manufacturing System with Random Machine Breakdowns

We consider a serial production system with machine breakdowns, where the machine at each station alternates between up and down states with exponential up and down time distributions. To obtain insight about the optimal production strategy, we focus on one production station. Its production process (output) and that of the previous station (input) are modeled by point processes with stochastic intensities. Our objectives is to control both input and output intensities such that expected discounted profit is maximized. We show that the optimal control policy is of a threshold type which is characterized by two threshold values.When each station in the serial system has reliable machines, the well known Kanban production strategy, which was first developed in Toyota Motor Co. of Japan, is usually used to control the production process at each station. Our result in this paper implies that, among other things, the traditional Kanban control rule has to be modified if the production environment is random.

The comparison of manganese spectral lines for self-absorption reduction in LIBS using laser-induced fluorescence

The detection of manganese(Mn)in steel by laser-induced breakdown spectroscopy(LIBS)provides essential information for steelmaking.However,self-absorption greatly disrupts the LIBS spectral lines of Mn with high content.In this study,to minimize self-absorption for Mn spectral lines in LIBS,laser-induced fluorescence(LIF)was applied.Compared with conventional LIBS,the self-absorption factors(α)of Mn I 403.08,403.31,and 403.45 nm lines were reduced by 90%,88%,and 88%,respectively;the root mean square errors of crossvalidation were decreased by 88%,85%,and 87%,respectively;the average relative errors were reduced by 93%,90%,and 91%,respectively;and average relative standard deviations were decreased by 29%,32%,and 33%,respectively.The LIBS-LIF was shown to successfully minimize the self-absorption effect and spectral intensity fluctuation and improve detection accuracy.