具有两类失效模式的D-策略M/G/1可修排队系统分析

研究具有两类失效模式的D策略M/G/1可修排队系统,其中第一类失效是服务台在服务顾客期间发生的失效,第二类失效是服务台在空闲期间发生的失效,且两类失效模式的失效率不同.使用全概率分解技术和利用拉普拉斯变换与母函数等工具,从任意初始状态出发,讨论了系统队长的瞬时分布和稳态分布,获得了系统稳态队长分布的递推表达式与稳态队长的随机分解结果.进一步,在建立费用模型的基础上,通过数值计算实例讨论了使得系统在长期单位时间内达到最小值的最优控制策略D^*,并在同一组参数取值下与服务台不发生故障时的最优控制策略进行了比较.     

Two-parameter heavy-traffic limits for infinite-server queues with dependent service times

This paper is a sequel to our 2010 paper in this journal in which we established heavy-traffic limits for two-parameter processes in infinite-server queues with an arrival process that satisfies an FCLT and i.i.d. service times with a general distribution. The arrival process can have a time-varying arrival rate. In particular, an FWLLN and an FCLT were established for the two-parameter process describing the number of customers in the system at time t that have been so for a duration y. The present paper extends the previous results to cover the case in which the successive service times are weakly dependent. The deterministic fluid limit obtained from the new FWLLN is unaffected by the dependence, whereas the Gaussian process limit (random field) obtained from the FCLT has a term resulting from the dependence. Explicit expressions are derived for the time-dependent means, variances, and covariances for the common case in which the limit process for the arrival process is a (possibly time scaled) Brownian motion.     

N-控制策略且温储备失效M/G/1可修排队的可靠性指标

本文研究N-门限值进入控制策略且温储备失效M/G/1可修排队系统, 其中系统在处于温储备失效的状态下最多容许N(1)个顾客进入系统。 运用全概率分解技术和拉普拉斯变换工具, 对服务台第一次失效前的寿命概率分布、不可用度、(0,t]时间内的平均失效次数以及处于温储备失效而等待修理的概率等可靠性指标进行了讨论, 并给出了其稳态结果表达式。 最后, 通过数值实例分析了服务台因温储备故障的稳态不可用度和稳态故障频度随一些参数的变化情况。     

区域二级应急救援系统多救援点协同策略研究

主要研究在需求不确定的救援环境下,由一个区域救援总站和多个地方救援点组成的二级应急救援系统多种救援物资协同共享问题.各地方救援点对救援物资的需求为随机模糊变量,当某一地方救援点救援物资不足时,可以通过不同的协同方式进行应急补库,所有应急补库方式均考虑了地方救援点的优先级.据此建立了在一定服务满足率条件下以救援时间最短为目标函数的模型,结合随机模糊变量模拟和PSO、PSO-SA算法对模型进行了求解.最后对各种协同方式进行了对比并分析了相关变量的敏感性.结果表明:允许完全转运的协同共享方式能有效地缩短救援时间.     

Sojourn and waiting times in a single-server system with state-dependent mean service rate

A birth-death queueing system with asingle server, first-come first-served discipline, Poisson arrivals and state-dependent mean service rate is considered. The problem of determining the equilibrium densities of the sojourn and waiting times is formulated, in general. The particular case in which the mean service rate has one of two values, depending on whether or not the number of customers in the system exceeds a prescribed threshold, is then investigated. A generating function is derived for the Laplace transforms of the densities of the sojourn and waiting times, leading to explicit expressions for these quantities. Explicit expressions for the second moments of the sojourn and waiting times are also obtained.     

The variational calculus and approximation in policy space for Markovian decision processes

The functional equations of Markovian decision processes yield the state values (and gain rate in the undiscounted case). Variational expressions are exhibited here for these state values (and gain rate); these expressions are stationary when evaluated at the correct values. When guesses for the values (and gain rate) are inserted into these variational expressions, a superior guess is usually obtained. Repetition of this procedure is shown to be equivalent to the method of successive approximations in policy space. Two other unusual features of this procedure are these: when the linear equations determining the Lagrange multipliers are non-singular, the variational expressions for the state variables are precisely one Newton-Raphson iteration; when applied to a linear objective function and piecewise-linear constraints, which arises for the functional equations of Markovian decision processes, the variational test quantity is piecewise constant, i.e., its first variation and higher variations all vanish. The latter explains its good performance (one-step convergence) if good estimates are available.     

考虑交叉网络外部性的网约车平台市场定价研究

随着移动互联网的发展,具有双边市场特征的以网约车平台为载体的多种新型出行方式相继出现,但同时也带来了新的交通管理问题。基于双边市场理论,考虑了交叉网络外部性,从用户、司机均为单归属以及用户多归属、司机单归属两个方面研究了网约车平台的市场定价问题。同时,引入了时间敏感系数和司机提成比例表征网约车行业特征。最终得到了网约车平台对用户和司机的定价结构公式、用户和司机规模及平台收益。研究显示平台定价及收益与交叉网络外部性及时间敏感系数的关系与用户归属结构相关;平台定价及收益与差异化程度正相关,且在用户多归属情况下提高差异化程度会导致多归属方用户规模降低;在双边均为单归属情况下,提高司机提成比例会降低平台对出行用户的定价且增加对司机方的定价,最终导致平台均衡收益降低;但多归属下平台对司机的定价与司机提成比例的关系还与双边交叉网络外部性的相对大小有关。     

Delays to Aircraft Serviced by the Glide-Path

This paper considers some of the statistical service, flow and delay problems which arriving aircraft encounter in the glide-path of an airport runway. Mathematical expressions for service time distributions and delays are formulated in terms of the probability distributions of spacings between discharges of the glide-path. In this paper the author also considers some numerical solutions of the average glide-path separation as a function of \(\overline{w}\), the average delay to arriving aircraft, x₀, a minimum glide-path separation and λ the average Poisson flow rate of landing aircraft.     

Rare event asymptotics for a random walk in the quarter plane

This paper presents a novel technique for deriving asymptotic expressions for the occurrence of rare events for a random walk in the quarter plane. In particular, we study a tandem queue with Poisson arrivals, exponential service times and coupled processors. The service rate for one queue is only a fraction of the global service rate when the other queue is non-empty; when one queue is empty, the other queue has full service rate. The bivariate generating function of the queue lengths gives rise to a functional equation. In order to derive asymptotic expressions for large queue lengths, we combine the kernel method for functional equations with boundary value problems and singularity analysis.     

A model of imperfect preventive maintenance with dependent failure modes

Consider a system subject to two modes of failures: maintainable and non-maintainable. A failure rate function is related to each failure mode. Whenever the system fails, a minimal repair is performed. Preventive maintenances are performed at integer multiples of a fixed period. The system is replaced when a fixed number of preventive maintenances have been completed. The preventive maintenance is imperfect because it reduces the failure rate of the maintainable failures but does not affect the failure rate of the non-maintainable failures. The two failure modes are dependent in the following way: after each preventive maintenance, the failure rate of the maintainable failures depends on the total of non-maintainable failures since the installation of the system. The problem is to determine an optimal length between successive preventive maintenances and the optimal number of preventive maintenances before the system replacement that minimize the expected cost rate. Optimal preventive maintenance schedules are obtained for non-decreasing failure rates and numerical examples for power law models are given.     

计算机代数应用中的一个半逆序算法*

为了克服计算机代数应用中出现的"中间表达式爆炸"的困难,本文提出一种半逆序算法,将中间表达式在运算过程中以符号形式冻结起来,到求解的最后阶段予以解冻,从而避免了因存贮空间不足而导致的溢出.文中简述了该算法在非线性振动、冷却塔动力优化和非线性水波问题中的应用,证实了算法的有效性.     

Asymptotic Analysis of Free-Edge and Free-Corner Effects in Laminate Structures

Stress fields in the vicinity of free edges and corners of composite laminates exhibit singular characteristics and may lead to premature interlaminar failure modes like delamination fracture. It is of practical interest to investigate the nature of the arising free-edge and free-corner stress singularities - i.e. the singularity orders and modes - closely. The present investigations are performed using the Boundary Finite Element Method (BFEM) which in essence is a fundamental-solution-less boundary element method employing standard finite element formulations. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of Alternating-Priority Queueing Models with (Cross) Correlated Switchover Times

This paper analyzes a single server queueing system in which service is alternated between two queues and the server requires a (finite) switchover time to switch from one queue to the other. The distinction from classical results is that the sequence of switchover times from each of the queues need not be i.i.d. nor independent from each other; each sequence is merely required to form a stationary ergodic sequence. With the help of stochastic recursive equations explicit expressions are derived for a number of performance measures, most notably for the average delay of a customer and the average queue lengths under different service disciplines. With these expressions a comparison is made between the service disciplines and the influence of correlation is studied. Finally, through a number of examples it is shown that the correlation can significantly increase the mean delay and the average queue lengths indicating that the correlation between switchover times should not be ignored. This has important implications for communication systems in which a common communication channel is shared amongst various users and where the time between consecutive data transfers is correlated (for example in ad-hoc networks). In addition to this a number of notational mistakes in well-known existing literature are pointed out. AMS subject classification: 68M20, 60J85 A shorter version of this work has been published in the proceedings of IEEE Infocom 2005. This work was partly sponsored by the EURONGI network of excellence.     

Perturbation analysis of theGI/GI/1 queue

We examine a family ofGI/GI/1 queueing processes generated by a parametric family of service time distributions,F(x,), and we show that under suitable conditions the corresponding customer stationary expectation of the system time is twice continuously differentiable with respect to. Expressions for the derivatives are given which are suitable for single run derivative estimation. These results are extended to parameters of the interarrival time distribution and expressions for the corresponding second derivatives (as well as partial second derivatives involving both interarrivai and service time parameters) are also obtained. Finally, we present perturbation analysis algorithms based on these expressions along with simulation results demonstrating their performance.     

On testing of parameters in modulated power law process

The modulated power law process (MPLP) is often used to model failure data from repairable system, when both renewal type behaviour and time trends are present. The MPLP allows for the failure rate of a system to be affected by the failure and repair. Since the MLEs of the estimates do not have closed form expressions, they have to be approximated, and hence deriving a test procedure will be difficult. Black and Rigdon (1996) have proposed asymptotic MLEs and asymptotic likelihood ratio tests for the parameters which also do not have closed form expressions and hence are not easy for application. In this paper, we derive a closed form expression for the test statistics which is simple and easy to apply for testing (i) H₀: β=1 versus H₁: β≠1 when κ is known and (ii) H₀: (β=1 and κ=1) versus H₁: (β≠1 or κ≠1). The simulation study for percentiles and powers are given. We also compare the performance of the test with that of Black and Rigdon's (1996) test. Some numerical examples are also provided to illustrate the testing procedures. Copyright © 2001 John Wiley & Sons, Ltd.     

基于溢出效应与平台服务的竞争网络平台的销售模式研究

网络平台竞争与发展成为平台运营理论与实践的关键问题,急需解决。本文应用博弈论研究存在溢出效应和网络平台竞争环境下平台服务内生的网络平台销售模式选择,即网络平台商是允许制造商在其网络平台上直销产品的平台销售模式,还是网络平台商先从制造商购买产品再销售给消费者的转销模式。主要研究竞争网络平台的三种结构模型:双转销模式、双平台销售模式和混合模式。研究结果显示:网络平台商的利润随正溢出效应增加而增加,随负溢出效应增加而减少。当网络平台服务敏感程度较高且网络平台竞争较为激烈时,两个网络平台商均选择平台销售模式,形成占优均衡;此时,网络平台商获得最高利润,而且网络零售价和网络平台服务水平最高。     

A Modal Analysis of Resonance during the Whole-Body Vibration

The mechanism of resonance of a damping system of multi‐degrees of freedom such as the human body and the dependence of resonance on system parameters, particularly on the damping level, are studied in terms of detailed mathematical solutions of both the whole‐body vibrations and the eigen modes for a simple model. It is revealed that resonance would only occur near the eigen frequencies of neutral modes for which the complex eigen frequencies of the corresponding damping modes for the given damping level of the system have not moved far from the starting point (damping‐free case) along the corresponding tracks in the plane of complex eigen frequency yet. The major resonance would occur near the eigen frequency of the neutral mode where the modulus of the characteristic function of the system has the strongest, i.e., the deepest and sharpest, local minimum. For the present model, this neutral mode is the lowest neutral mode. It is found that the resonance and eigen frequencies increase with the stiffness of muscles and decrease with the body mass, with the portion of wobbling mass in the upper body, and with the portion of upper body mass in the whole body. Both the modal analysis and the analysis of the whole‐body vibration show that the phase differences among different parts of the system are still small at the unique or the lowest resonance frequency and increase dramatically only when the frequency of the vibrating source goes beyond the resonance frequency. Thus, some effects of body vibrations, e.g., internal loads, may reach their maximum not at the resonance frequency, but at a frequency somewhat higher than the resonance frequency. This may account for the fact that the frequency ranges for abdominal pain and for lumbosacral pain caused by body vibrations are not exactly the same as the frequency range for major body resonance but shifted to somewhat higher frequency ranges. It is therefore suggested that the frequency used for strength training in terms of vibrating devices should be above 20 Hz in order to avoid not only the major resonance but also the maximal internal loads.     

Discrete time queues with delayed information

We study the behavior of a single-server discrete-time queue with batch arrivals, where the information on the queue length and possibly on service completions is delayed. Such a model describes situations arising in high speed telecommunication systems, where information arrives in messages, each comprising a variable number of fixed-length packets, and it takes one unit of time (a slot) to transmit a packet. Since it is not desirable to attempt service when the system may be empty, we study a model where we assume that service is attempted only if, given the information available to the server, it is certain that there are messages in the queue. We characterize the probability distribution of the number of messages in the queue under some general stationarity assumptions on the arrival process, when information on the queue size is delayedK slots, and derive explicit expressions of the PGF of the queue length for the case of i.i.d. batch arrivals and general independent service times. We further derive the PGF of the queue size when information onboth the queue length and service completion is delayedK=1 units of time. Finally, we extend the results to priority queues and show that when all messages are of unit length, thec rule remains optimal even in the case of delayed information.     

On the stability of retrial queues

We consider the following Type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If λ is the arrival rate (average number per time unit) of calls and μ is one over the expected service time in the facility, it is well known that μ > λ is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers. This revised version was published online in June 2006 with corrections to the Cover Date.