A Discrete-Time Single-Server Queueing System Under Multiple Vacations and Setup-Closedown Times

Abstract

This article concerns a Geo/G/1/∞ queueing system under multiple vacations and setup-closedown times. Specifically, the operation of the system is as follows. After each departure leaving an empty system, the server is deactivated during a closedown time. At the end of each closedown time, if at least a customer is present in the system, the server begins the service of the customers (is reactivated) without setup; however, if the system is completely empty, the server takes a vacation. At the end of each vacation, if there is at least a customer in the system, the server requires a startup time (is reactivated) before beginning the service of the customers; nevertheless, if there are not customers waiting in the system, the server takes another vacation. By applying the supplementary variable technique, the joint generating function of the server state and the system length together with the main performance measures are derived. We also study the length of the different busy periods of the server. The stationary distributions of the time spent waiting in the queue and in the system under the FCFS discipline are analysed too. Finally, a cost model with some numerical results is presented.     

Reliability analysis for the consecutive-k-out-of-n: F system with repairmen taking multiple vacations

Commonly studied models of the consecutive-k-out-of-n: F repairable systems in the existing literatures were considering the systems which had one repairman without vacation or infinite repairmen without vacations. In addition to those models, multiple repairmen without vacations are studied occasionally. However, technical personnel are very short in some fields. Some failed components cannot be repaired in time. This paper deals with the phenomenon of waiting for repair by supposing R repairmen with multiple vacations in the system. Using the pairs (i, |j|), the factor that the R repairmen taking multiple vacations was embedded into the classical C(k, n: F) system. Reliability indexes are presented. Finally, the Runge–Kutta method was used to a special case, and the experimental results demonstrate the necessity and validity of the new model.     

Optimization problems of replacement first or last in reliability theory

This paper takes up age and periodic replacement last models with working cycles, where the unit is replaced before failure at a total operating time T or at a random working cycle Y, whichever occurs last, which is called replacement last. Expected cost rates are formulated, and optimal replacement policies which minimize them are discussed analytically. Comparisons between such a replacement last and the conventional replacement first are made in detail. It is determined theoretically and numerically which policy is better than the other according to the ratios of replacement costs and how the mean time of working cycles affects the comparison results. It is also shown that the unit can be operating for a longer time and avoid unnecessary replacements when replacement last is done. For further studies, expected cost rates of modified models and their applications in a standard cumulative damage model with working cycles are obtained and computed numerically. Finally, case studies on replacement last and first in maintaining electronic systems of naval ships under battle and non-battle statuses are given.     

开放型办公室掩蔽语音环境下工作效率的客观评价方法

本文研究了开放型办公室中平稳噪声掩蔽语音环境下噪声可懂度的客观评价指标与工作效率之间的关系。文章通过对三种客观评价指标:Speech Transmission Index(STI),Perceptually Evaluation of Speech Quality(PESQ)和modified Normalized Covariance Method(mNCM)与专门设计的主观实验结果相对比,得到了该条件下客观评价指标与主观烦扰度和工作效率之间的关系。结果显示,客观评价指标与主观实验结果均具有较高的相关性,说明利用客观评价指标来预测、评估工作效率具有可行性。实验结果还初步揭示了噪声的语言可懂度和工作效率之间的变化规律:在噪声的语言可懂度的中间区域,工作效率变化显著;但噪声的语言可懂度高于一定值以后,工作效率趋于稳定。     

结霜工况风量对风冷热泵性能影响的研究

针对一台名义制冷量为50kW的风冷热泵冷热水机组,实验研究了迎面空气流量变化对机组结霜工况性能的影响。实验结果表明,结霜条件下,迎面空气流量降低促使机组工作性能大幅降低;迎面空气流量的变化对V型换热器表面霜层分布没有影响。空气流量的降低只是造成换热器表面结霜量的增多,适当提高风机转速具有抑制结霜、有效提高机组运行性能的作用;来流风速的不均匀分布对结霜以及霜层的分布有重要影响。     

绿松石成分的EDXRF方法研究

利用激光剥蚀电感耦合等离子体质谱仪(LA-ICP-MS)测试方法对来自湖北的26块表面相对干净、颜色均匀的绿松石样品进行定值,每个样品表面按照“田字格”的方式逐一测试9个点,用于评价绿松石成分的均匀性。数据结果显示,绿松石样品中Al,P,K,Cu,Fe,V,Cr和Zn的平均变异系数在5.4%以下,而CaO和SiO₂的平均变异系数分别为34.8%和16.2%,说明绿松石中Si和Ca元素存在明显的不均匀性。选取其中的21个样品作为参考标准样品,5个作为未知样品,采用能量色散型X射线荧光光谱仪(EDXRF)建立绿松石的工作曲线,用于测定绿松石的成分。研究结果显示主量元素Al,P和Cu工作曲线的相关系数在92.3%~94.3%之间,平均相对误差在4.6%~9.7%;微量元素Fe,Cr和Zn的相关系数达到0.990以上,K和V元素工作曲线的相关系数分别为0.939和0.972,这五种元素平均相对误差范围在7.2%~13.9%;而Si和Ca元素工作曲线的相关系数分别为0.958和0.866,且在5个未知样品中,Si和Ca元素的平均相对误差分别为348%和27.8%,这与绿松石中Si和Ca元素的含量低和不均匀性,以及仪器方法的检出限等影响因素有关。重复性实验显示Al,P,Cu,Fe和Zn元素的相对标准偏差(RSD)均在1%以内,精密度较高;V,Cr,K,Ca和Si元素的RSD在1.34%~10.17%之间。该研究为快速、准确、无损地定量测定绿松石中Al,P,Cu,Fe,Cr,Zn,V和K等元素的含量提供了一种新思路和新方法,可运用于实验室的绿松石检测鉴定。     

The relationship between noise and mode of delivery on recognition memory and working memory

The present research sought to investigate the effect of noise, comparable to that experienced in an aircraft cabin, on cognitive performance in terms of working memory and recognition memory. In addition, and since advancements in technology have long permitted the exchange of information via various media, the present research also sought to investigate the effect of in-cabin aircraft noise on the medium in which the target signal is delivered. Thirty-two participants (19 female), half non-native English speakers with an average age of 21.84 years (SD = 3.16), and all with normal hearing were asked to complete four different memory tasks under two different experimental factors. The first independent variable was noise, with two conditions: no noise versus wideband noise at 80 dBA. The second independent variable was mode of presentation, with two conditions: target signal presented aurally or visually. With the presentation of stimuli presented in a counterbalanced order, the results from a series of mixed repeated measures analyses revealed that working memory appears largely immune from the effects of wideband noise at 80 dBA. In contrast, recognition memory is most vulnerable to the effects of this noise. In terms of mode of delivery, presenting the target signal visually improves recall performance on the recognition memory task and two of the three working memory tasks (not the linguistics working memory task). Also noise had a greater effect on non-native English speakers on the recognition memory task. These results highlight the varying effect of noise on memory, and the benefits of considering alternate methods of presenting information in noisy settings, such as aviation.     

具有两阶段服务和服务台故障M/M/1/N多重休假排队系统

研究了具有两阶段服务和服务台故障的M/M/1/N多重休假排队系统.利用马尔可夫过程理论建立了系统稳态概率方程组,并利用分块矩阵解法,得到了稳态概率的矩阵解.然后由此得出了系统的平均队长、平均等待队长等性能指标.     

Application of the method of collective marks to someM/G/1 vacation models with exhaustive service

We use the Method of Collective Marks to analyze some time-dependent processes in theM/G/1 queue with single and multiple vacations. With the server state specified at a fixed timet>0, the Laplace transforms with respect tot of mixed transforms for the joint distribution of the number of departures by timet, the queue length, the virtual waiting time, the elapsed and remaining service/vacation times at timet are derived by means of probabilistic interpretations. The Laplace-Stieltjes transform of the virtual waiting time at timet is also given. Some well known results are special cases.This research was supported by the University of Amsterdam.     

Time-dependent analysis of M/G/1 vacation models with exhaustive service

We analyze the time-dependent process in severalM/G/1 vacation models, and explicitly obtain the Laplace transform (with respect to an arbitrary point in time) of the joint distribution of server state, queue size, and elapsed time in that state. Exhaustive-serviceM/G/1 systems with multiple vacations, single vacations, an exceptional service time for the first customer in each busy period, and a combination ofN-policy and setup times are considered. The decomposition property in the steady-state joint distribution of the queue size and the remaining service time is demonstrated.