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.

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.

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.

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.

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.

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.

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.

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.

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.

Self-absorption effects of laser-induced breakdown spectroscopy under different gases and gas pressures

The self-absorption effect is one of the main factors affecting the quantitative analysis accuracy of laser-induced breakdown spectroscopy.In this paper,the self-absorption effects of laserinduced 7050 Al alloy plasma under different pressures in air,Ar,and N2have been studied.Compared with air and N2,Ar significantly enhances the spectral signal.Furthermore,the spectral self-absorption coefficient is calculated to quantify the degree of self-absorption,and the influences of gas species and gas pressure on self-absorption are analyzed.In addition,it is found that the spectral intensity fluctuates with the change of pressure of three gases.It can also be seen that the fluctuation of spectral intensity with pressure is eliminated after correcting,which indicates that the self-absorption leads to the fluctuation of spectral intensity under different pressures.The analysis shows that the evolution of optical thin spectral lines with pressure in different gases is mainly determined by the gas properties and the competition between plasma confinement and Rayleigh–Taylor instability.

A data selection method for matrix effects and uncertainty reduction for laser-induced breakdown spectroscopy

Severe matrix effects and high signal uncertainty are two key bottlenecks for the quantitative performance and wide applications of laser-induced breakdown spectroscopy(LIBS).Based on the understanding that the superposition of both matrix effects and signal uncertainty directly affects plasma parameters and further influences spectral intensity and LIBS quantification performance,a data selection method based on plasma temperature matching(DSPTM)was proposed to reduce both matrix effects and signal uncertainty.By selecting spectra with smaller plasma temperature differences for all samples,the proposed method was able to build up the quantification model to rely more on spectra with smaller matrix effects and signal uncertainty,therefore improving final quantification performance.When applied to quantitative analysis of the zinc content in brass alloys,it was found that both accuracy and precision were improved using either a univariate model or multiple linear regression(MLR).More specifically,for the univariate model,the root-mean-square error of prediction(RMSEP),the determination coefficients(R^(2))and relative standard derivation(RSD)were improved from 3.30%,0.864 and 18.8%to 1.06%,0.986 and 13.5%,respectively;while for MLR,RMSEP,R^(2)and RSD were improved from 3.22%,0.871 and 26.2%to 1.07%,0.986 and 17.4%,respectively.These results prove that DSPTM can be used as an effective method to reduce matrix effects and improve repeatability by selecting reliable data.

Estimation of Lightning-Generated NO_(x) in the Mainland of China Based on Cloud-to-Ground Lightning Location Data

Lightning-generated nitrogen oxides(LNO_(x))have a major influence on the atmosphere and global climate change.Therefore,it is of great importance to obtain a more accurate estimation of LNO_(x).The aim of this study is to provide a reference for the accurate estimation of the total LNO_(x) in the mainland of China based on cloud-to-ground lightning(CG)location data from 2014 to 2018.The energy of each CG flash was based on the number of return strokes per CG flash,the peak current of each return stroke,and the assumed CG breakdown voltage.The energy of intracloud lightning(IC)was based on the estimated frequencies of IC and the assumed energy of each IC flash.Combining the energy of lightning and the number of nitric oxide(NO)molecules produced by unit energy(ρno),the total LNO_(x) production in the mainland of China was determined.The LNO_(x) in the mainland of China estimated in this study is in the range(0.157-0.321)×10^(9) kg per year[Tg(N)yr-1],which is on the high end of other scholars’works.Negative cloud-to-ground lightning(NCG)flashes produce the most moles of NO_(x),while positive cloud-to-ground lightning(PCG)flashes produce the least total moles of NO_(x).The breakdown voltage of PCG is greater than that of IC or NCG,while the latter has a greater output of LNO_(x).

The influence of pore characteristics on rock fragmentation mechanism by high-voltage electric pulse

High-voltage electric pulse(HVEP)is an innovative low-energy and high-efficiency technique.However,the underlying physics of the electrical breakdown within the rock,and the coupling mechanism between the various physical fields involved in HVEP still need to be further understood.In this study,we establish a 2D numerical model of multi-physical field coupling of the electrical breakdown of porous rock with randomly distributed pores to investigate the effect of pore characteristics(porosity,pore media composition)on the partial electrical breakdown of rock(i.e.the generation of a plasma channel inside the rock).Our findings indicate that the generation of a plasma channel is directionally selective and extends in the direction of a weak electrical breakdown intensity.As the porosity of the rock increases,so does the intensity of the electric field in the‘electrical damage’region—the greater the porosity,the greater the effectiveness of rock-breaking.As the fraction of pore fluid(S_(water)/S_(air))gradually declines,the generation time of the plasma channel decreases,and the efficacy of rock-breaking by HVEP increases.In addition,in this study,we conducted an indoor experiment utilizing an electric pulse drill to break down the rock in order to recreate the growth mode of the plasma channel in the rock.Moreover,the experimental results are consistent with the simulation results.In addition,the development of this type of partial electrical breakdown is confirmed to be related to electrode polarity and pore characteristics via the experiment of the symmetrical needle-needle electrode arrangement,which further demonstrates the mechanism of partial electrical breakdown.This research is significant for comprehending the process of electric impulse rock-breaking and gives theoretical guidance and technological support for advancing electric impulse drilling technology.

The response of zooplankton abundance in saline meromictic Lake Shira to a change in circulation regime

The long-term data(1996-2021)on the summer abundances of the dominant zooplankton species(copepod Arctodiaptomus salinus(Daday,1885),rotifers Brachionus plicatilis(Müller,1786)and Hexarthra sp.)in saline Lake Shira were used to analyze the response of zooplankton to air temperature and a change in the circulation regime of the lake:breakdown and reestablishment of meromixis.All groups of zooplankton responded to prolonged summer elevated temperatures by increasing their abundance.During the breakdown of the stable stratification of Lake Shira(2015-2016),zooplankton abundance increased on average by a factor of two and amounted to 9×10^(5)inds./m^(2)in the water column for copepods.That increase coincided with similar responses of other components of the lake’s mixolimnion ecosystem,whose biomasses increased approximately two-fold during that period.After the reestablishment of the meromixis,the abundance of zooplankton decreased to previous values.Thus,the abundance of zooplankton is largely determined by weather(the effect of temperature)and ecological factors(mixing regime).

Fault locating for traveling-wave accelerators based on transmission line theory

Radio-frequency(RF)breakdown analysis and location are critical for successful development of high-gradient traveling-wave(TW)accelerators,especially those expected to generate high-intensity,high-power beams.Compared with commonly used schemes involving dedicated devices or complicated techniques,a convenient approach for breakdown locating based on transmission line(TL)theory offers advantages in the typical constant-gradient TW-accelerating structure.To deliver such an approach,an equivalent TL model has been constructed to equate the TW-accelerating structure based on the fun-damental theory of the TL transient response in the time domain.An equivalence relationship between the TW-accelerating structure and the TL model has been established via analytical derivations associated with grid charts and verified by TL circuit simulations.Furthermore,to validate the proposed fault-locating method in practical applications,an elaborate analysis via such a method has been conducted for the recoverable RF-breakdown phenomena observed at an existing prototype of a TW-accelerating-structure-based beam injector constructed at the Huazhong University of Science and Technology.In addition,further considerations and discussion for extending the applications of the proposed method have been given.This breakdown-locating approach involving the transient response in the framework of TL theory can be a conceivable supple-ment to existing methods,facilitating solution to construction problems at an affordable cost.