Vacations in GI X/M Y/1 systems and Riemann boundary value problems

We consider systems of GI/M/1 type with bulk arrivals, bulk service and exponential server vacations. The generating functions of the steady-state probabilities of the embedded Markov chain are found in terms of Riemann boundary value problems, a necessary and sufficient condition of ergodicity is proved. Explicit formulas are obtained for the case where the generating function of the arrival group size is rational. Resonance between the vacation rate and the system is studied. Complete formulas are given for the cases of single and geometric arrivals. This revised version was published online in June 2006 with corrections to the Cover Date.     

Stationary Distributions of GI/M/c Queue with PH Type Vacations

We study a GI/M/c type queueing system with vacations in which all servers take vacations together when the system becomes empty. These servers keep taking synchronous vacations until they find waiting customers in the system at a vacation completion instant.The vacation time is a phase-type (PH) distributed random variable. Using embedded Markov chain modeling and the matrix geometric solution methods, we obtain explicit expressions for the stationary probability distributions of the queue length at arrivals and the waiting time. To compare the vacation model with the classical GI/M/c queue without vacations, we prove conditional stochastic decomposition properties for the queue length and the waiting time when all servers are busy. Our model is a generalization of several previous studies.     

Discrete-time GI/Geo/1 queue with multiple working vacations

Consider the discrete time GI/Geo/1 queue with working vacations under EAS and LAS schemes. The server takes the original work at the lower rate rather than completely stopping during the vacation period. Using the matrix-geometric solution method, we obtain the steady-state distribution of the number of customers in the system and present the stochastic decomposition property of the queue length. Furthermore, we find and verify the closed property of conditional probability for negative binomial distributions. Using such property, we obtain the specific expression for the steady-state distribution of the waiting time and explain its two conditional stochastic decomposition structures. Finally, two special models are presented.      

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

The FDTD simulation for the performance of dispersive cloak devices

In this paper, we defined the scattering energy intensity based on the Poynting vector to quantitatively study the cloak effect of electromagnetic waves in the time domain. The influences of the effective working frequency bands of four kinds of electromagnetic cloak materials, incidence angle of electromagnetic waves and the number of approximately cloak layers on the cloak effect are studied. To the best of our knowledge, this is the first time to use the time domain method to quantitatively study the effective working frequency band and the scattering energy intensity of cloak materials.     

The Surface Analysis Working Group at the Consultative Committee for Amount of Substance,Metrology in Chemistry and Biology: A successful initiative by Martin Seah

Dr Martin Seah, NPL, was the initiator, founder, and first chairman of the Surface Analysis Working Group (SAWG) at the Consultative Committee for Amount of Substance, Metrology in Chemistry and Biology (CCQM) at the Bureau International des Poids et Mesures (BIPM), the international organization established by the Metre Convention. This tribute letter summarizes his achievements during his chairmanship and his long-running impact on the successful work of the group after his retirement.     

Remarkably improved cycling stability of 3D porous Cu–Sn anode for lithium-ion full cells by adjusting working voltage range

Numerous studies confirm that three dimensional porous Cu–Sn (3DP Cu–Sn) anode possesses good application prospect in light of its desirable electrochemical performance on lithium ion half cells, but there are a few related systematic researches on lithium ion full cells until now, which is indispensable before its commercialization. Herein, the effects of galvanostatic charge-discharge voltage range on the cycling stability of 3DP Cu–Sn anode for lithium ion full cells are investigated systematically. The results show that the suitable charge-discharge voltage range plays a key role in improving the reversible capacity and cycling stability of the 3DP Cu–Sn||LiCoO₂ full cell, which is closely related to maintaining the electrode structure stable by controlling the amount of Li⁺ extracted and inserted. Especially, in the voltage range of 1.2–3.9 ​V, the full cell exhibits remarkably improved electrochemical properties with the high initial reversible capacity of 2.71 ​mAh cm⁻² and 71.95% capacity retention upon 80 cycles. We believe that this work can provide a significant reference for the practical application of porous Sn-based anodes.     

稀有气体卤化物准分子激光器工作气体实时补给技术

为延长稀有气体卤化物准分子激光器工作气体使用寿命,在原有供气设备基础上增加了工作气体实时补给技术.该技术采用FPGA控制系统将逐步提高放电电压、补充卤素气体和更换部分混合气体等操作有效组合起来.随着激光脉冲能量的下降,逐步提高放电电压;当放电电压达到最大值时,开始补充卤素气体,并恢复放电电压;当补充卤素气体效果不明显时,更换部分混合工作气体.将该技术应用于医用型ArF准分子激光器中进行实验研究,结果表明:在没有使用工作气体实时补给技术的情况下,激光器累计工作14.38 h后,输出单脉冲激光能量下降了17.2％;采用工作气体实时补给技术后,激光器输出能量下降速率明显降低,累计工作14.38 h,其单脉冲能量下降率能控制在3％范围内.因此,采用该技术可延长激光器工作气体的使用寿命、提高输出激光能量稳定性、减少停机次数并降低运行成本.     

Oxygen vacancy O-terminated surface: The most exposed surface of hexagonal WO3 (001) surface

It is known that exposed surface determines material’s performance. WO₃ is widely used in gas sensing and its working surface is proposed to control its sensitivity. However, the working surface, or most exposed surface with detailed surface structure remain unclear. In this paper, DFT calculation confirmed that oxygen vacancy O-terminated surface is the most exposed hexagonal WO₃ (001) surface, judging from competitive adsorption of CO and O₂, working surface determination for CO sensing and comparison of oxygen vacancy formation energies on different h-WO₃ (001) surfaces. It is found that DFT can be a useful alternate for exposed surface determination. Our results provide new perspectives and performance explanations for material research.     

Optimal strategy policy in batch arrival queue with server breakdowns and multiple vacations

This paper considers a like-queue production system in which server vacations and breakdowns are possible. The decision-maker can turn a single server on at any arrival epoch or off at any service completion. We model the system by an M^[x]/M/1 queueing system with N policy. The server can be turned off and takes a vacation with exponential random length whenever the system is empty. If the number of units waiting in the system at any vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N units in the system, he immediately starts to serve the waiting units. It is assumed that the server breaks down according to a Poisson process and the repair time has an exponential distribution. We derive the distribution of the system size through the probability generating function. We further study the steady-state behavior of the system size distribution at random (stationary) point of time as well as the queue size distribution at departure point of time. Other system characteristics are obtained by means of the grand process and the renewal process. Finally, the expected cost per unit time is considered to determine the optimal operating policy at a minimum cost. The sensitivity analysis is also presented through numerical experiments.