Approximating M/G/1 Waiting Time Tail Probabilities

Abstract

We propose a new approximation formula for the waiting time tail probability of the M/G/1 queue with FIFO discipline and unlimited waiting space. The aim is to address the difficulty of obtaining good estimates when the tail probability has non-exponential asymptotics. We show that the waiting time tail probability can be expressed in terms of the waiting time tail probability of a notional M/G/1 queue with truncated service time distribution plus the tail probability of an extreme order statistic. The Cramér–Lundberg approximation is applied to approximate the tail probability of the notional queue. In essence, our technique extends the applicability of the Cramér–Lundberg approximation to cases where the standard Lundberg condition does not hold. We propose a simple moment-based technique for estimating the parameters of the approximation; numerical results demonstrate that our approximation can yield very good estimates over the whole range of the argument.     

用跳马步系列研究奇素数阶规则完美幻方的个数

本文先介绍跳马步系列的有关概念及性质，然后用跳马步系列研究奇素数阶规则完美幻 方的个数。     

福龙丸事件与美国对日政策的调整

1954年 ,日本渔船福龙丸第五的船员在比基尼海域遭受美国氢弹试验放射性物质的伤害 ,并导致一名船员死亡。日美两国围绕船只处理、受害者治疗、赔偿等问题进行交涉 ,引发了战后以来日美关系的第一次危机 ,日本国民掀起了反美、反吉田茂政权的风潮。美国政府重新审查对日政策 ,制定了NSC5516/1文件 ,确认了吉田茂提出的渐增军备的方针 ,该文件成为此后美国对日政策的纲领性文件     

Bathtub distributions: a review

Bathtub distributions are characterized by bathtub failure rate functions . These are possibly more realisitic models than the monotone failure rate models . A systematic account of such distributions is not available and this review aims to give such an account . We give some easily verifiable conditions to check the bathtub property of a distribution along with methods to construct such distributions . We also discuss some stochastic and reliablity mechanisms which lead to bathtub distributions. These include mixtures ( stochastic failure rate models ) , series system , stochastic differential equation models and so on. We also review inference on bathtub distributions. The paper concludes with a rather exhaustive list of bathtub distributions.     

试论监督制约机制

随着社会改革的深入发展，人们越来越深刻地认识到监督机制在社会主义市场经济体制运行过程中的重要作用。它不仅是完善体制，落实法制的重要中介环节，而且是从根源上制约腐败现象的根本举措。本文从两种不同的民主制约机制的视角分析论证体制、机制、法制的内在统一性和建构有中国特色的民主监督制约机制的必要性和重要性。     

航空装备教学方法及任职教育模式的研究与实践

揭示航空装备的内在联系,确立以功能作为航空装备认知主线的教学思想。构建了功能主线教学法和"1+X"任职教育模式,提升了航空装备创新教育水平。     

The effects of correlation among observations on the consistency property of sample variance

It is well known that even when the sample observations are correlated and not normal the sample variance, S² converges in probability to E(S²). But the required sample size for S² to be a consistent estimator of E(S²) is an open question. Some light is shed on this question in this paper. In particular the relation between the rate of convergence and the correlation property of the observations is explored. It is shown that the retardation to the rate of convergence is not appreciable if the correlation is moderate but it can be severe for extreme correlations.     

The effects of ROS in prostatic stromal cells under hypoxic environment

Abstract

Objective: The objective of this study is to explore the effects of reactive oxygen species (ROS) under hypoxic environment in prostatic stromal cells (PSC).

Methods and materials: To detect the expression of ROS in PSC and the tissues of benign prostatic hyperplasia (BPH) by flow cytometry; under hypoxic conditions, to observe the changes of cells growth and ROS in PSC; quantitative PCR was used to detect hypoxia inducible factor-1α (HIF-1α), androgen receptors (AR), vascular endothelial growth factor (VEGF), and interleukin-8 (IL-8) in PSC; After edaravone intervening, to examine the changes of cells growth, ROS, HIF-1α, AR, VEGF, and IL-8 under hypoxic conditions.

Results: The expression of ROS in tissues and cells which under hypoxic condition was significantly increased. 3% O₂ promoted the proliferation. The HIF-1α, AR, VEGF, and IL-8 were upregulated under 3% O₂. After edaravone intervening, ROS significantly decreased, HIF-1α and VEGF were downregulated, and cell proliferation declined.

Conclusions: Hypoxia stimulates the generation of ROS, and the ROS may play a key role in BPH.     

A Retrial Queue with a Constant Retrial Rate,Server Downs and Impatient Customers

ABSTRACT

In this paper, we consider a retrial queueing system consisting of a waiting line of infinite capacity in front of a single server subject to breakdowns. A customer upon arrival may join the queue (waiting line) or go to the retrial orbit (another queue) to retry for service after a random time. Only the customer at the head of the retrial orbit is allowed to retry for service. Upon retrial, the customer enters the service if the server is idle; otherwise, it may go back to the retrial orbit or leave the system (become impatient). All the interarrival times, service times, server up times, server down times and retrial times are exponential, and all the necessary independence conditions in these variables are assumed. For this system, we provide sufficient conditions under which, for any given number of customers in the orbit, the stationary probability of the number of customers in the waiting line decays geometrically. We also provide explicitly an expression for the decay parameter.