闭排队网络当性能函数与参数相关时的性能灵敏度分析

借助于无穷小矩阵摄动方法, 讨论了一类Markov过程, 其稳态性能关于参数摄动的灵敏度分析问题. 然后研究了闭排队网络的稳态性能灵敏度分析问题, 并在参数相关性能函数的情况下, 给出了网络的几种稳态性能的灵敏度公式. 这些公式表明稳态性能灵敏度很容易通过网络势能进行计算.     

基于反馈优先服务策略的产品研发管理模型研究

为了研究产品开发排队系统的平稳分布和稳态性能,运用排队理论对产品开发过程进行建模和分析,在改进传统反馈服务笨略基础上,构建产品开发反馈优先排队模型;通过构建拟生灭过程求解反馈优先服务策略下排队系统稳态性能指标,并对传统反馈服务策略和反馈优先服务策略下的性能指标进行比较.结果表明,反馈优先的存在对产品开发任务的时延产生较大影响,通过算例对反馈优先服务策略下产品开发排队系统稳态性能指标进行验证,数值模拟表明产品开发排队系统中的反馈优先服务策略优于传统的反馈服务策略.     

分布式测量系统服务窗口动态调度算法研究

在网络制造环境下,分布式测量系统(Distributed Measurement System,DMS)的负载是动态变化的,需要根据负载情况对测量系统上的资源进行动态调度.针对基于CORBA和DMIS的分布式测量系统,根据多用户非抢占优先排队网络静态性能模型,提出基于无穷小摄动分析(Infinitesimal Perturbation Analysis,IPA)的分布式测量系统服务窗口动态调度算法.算法以DMS系统负载的在线变化为输入,动态调整排队网络系统服务台的窗口数量,从而实现测量用户对动态时间性能的要求.最后在一个制造工厂中进行的应用实验,证明了算法的有效性.     

鲁棒极点配置控制系统的一种设计方法

本文提出了系统特征系数灵敏度的概念,导出了特征系数灵敏度与特征值灵敏度闻的关 系.在此基础上,提出了一种以加权特征系数灵敏度为性能指标,结构化小参数摄动下的鲁 棒极点配置控制系统的设计方法.特征系数灵敏度计算简单,目标函数的极小化采用标准的 具有二次收敛性质的参数最优化方法.     

带有参数摄动的网络化控制系统非脆弱H_∞控制

针对带有时变传输时延的网络化系统中控制器参数存在随机摄动问题,设计了一种非脆弱H_∞控制器。利用Lyapunov稳定性理论和线性矩阵不等式方法,得到了非脆弱H_∞控制器存在的充分条件,通过求解线性矩阵不等式得到该控制器增益。所设计的控制器在容许的随机参数摄动和有界时变时延下,能保证闭环网络化控制系统的稳定性和预定的H_∞性能指标。仿真例子验证了方法的有效性。     

分布式测量系统服务窗口动态调度方法研究

在网络制造环境下, 动态时间性能是测量系统的重要指标. 针对基于 CORBA (Common object request broker architecture) 和尺寸测量接口标准 (Dimensional measurement interface standard, DMIS) 的分布式测量系统 (Distributed measurement system, DMS), 根据多用户非抢占优先排队网络静态性能模型, 提出基于无穷小摄动分析的样本轨道划分方法, 建立测量系统服务窗口的动态调度算法, 实现测量系统的时间性能调优. 通过在一个制造工厂中进行的应用实验, 证明了此方法的有效性.     

线性系统的鲁棒状态反馈控制器

本文基于线性系统的状态反馈特征结构配置结果和矩阵特征值灵敏度分析理论,提出了线性系统的一种鲁棒状态反馈控制器,它在满足闭环系统特性要求的前提下,使得闭环极点关于系统参数摄动具有最小的灵敏度.     

网络化非线性系统的非脆弱H∞控制

具有对数量化、网络诱导时延和数据包丢失的网络化Lipschitz非线性系统控制器,存在参数摄动问题。为此,设计一种加性非脆弱状态反馈H∞控制器。将数据量化和网络诱导时延对被控系统的影响,转化为系统的不确定参数,网络化控制系统建模为马尔可夫跳变系统。采用Lyapunov稳定性理论和线性矩阵不等式方法,给出网络化Lipschitz非线性系统的加性非脆弱状态反馈H∞控制器存在的充分条件,该非脆弱H∞控制器可通过解线性矩阵不等式求出。仿真结果表明,当控制器存在参数摄动时,与传统控制器相比,非脆弱控制器不仅能使被控系统稳定,而且满足设定的H∞性能指标。     

数据库连接池的数学建模与性能分析

为有效地配置数据库连接池中的系统参数,根据数据库连接池管理过程的工作原理,引入离散时间排队论的思想,建立多服务台损失制的Geom/Geom/c/c离散时间排队模型。采用嵌入马尔科夫链方法,分析系统稳态队长的转移概率矩阵及其满足的递推关系式。应用模型的理论分析结果,导出请求阻塞概率、系统平均连接数、系统利用率、系统吞吐量等系统性能指标的数学表达式。通过实验证明了数据库连接池性能指标与系统配置参数之间的依赖关系。     

基于微分方程对称的分布参数系统稳态控制

应用对称群理论中经典对称, 以无穷小生成元为分析工具, 考虑分布参数系统的控制问题已有研究, 在此基础上, 本文给出利用微分方程对称实现分布参数系统稳态控制的方法. 通过求解微分方程的对称, 借助其和无穷小生成元之间的关系, 研究给出符合控制目标稳态要求的分布参数系统边界控制条件. 针对两个例子,说明了利用微分方程对称实现分布参数系统稳态控制的过程, 设计了边界控制条件, 进行了仿真说明. 相较基于经典对称获得分布参数系统无穷小生成元的过程, 利用微分方程对称, 避免了空间延拓过程, 并可能获得与其不同的无穷小生成元形式.     

Sensitivity formulas of performance in two-server cyclic queueing networks with phase-type distributed service times

With the approach of the infinitesimal generator perturbation, sensitivities of the steady-state performance are studied in two-server cyclic queueing networks with phase-type distributed service times. Sensitivity formulas expressed by the potentials of the networks are given for parameter-dependent performance functions. An algorithm to compute the potentials and the performance derivatives of the networks is given, and a numerical example is provided.     

On-line sensitivity analysis of Markov chains

Discrete-event systems modeled as continuous-time Markov processes and characterized by some integer-valued parameter are considered. The problem addressed is that of estimating performance sensitivities with respect to this parameter by directly observing a single sample path of the system. The approach is based on transforming the nominal Markov chain into a reduced augmented chain, the stationary-state probabilities which can be easily combined to obtain stationary-state probability sensitivities with respect to the given parameter. Under certain conditions, the reduced augmented chain state transitions are observable with respect to the state transitions of the system itself, and no knowledge of the nominal Markov-chain state of the transition rates is required. Applications for some queueing systems are included. The approach incorporates estimation of unknown transition rates when needed and is extended to real-valued parameters     

IPA Derivatives for Make-to-Stock Production-Inventory Systems With Lost Sales

This note applies the stochastic fluid model (SFM) paradigm to a class of single-stage, single-product make-to-stock (MTS) production-inventory systems with stochastic demand and random production capacity, where the finished-goods inventory is controlled by a continuous-time base-stock policy and unsatisfied demand is lost. This note derives formulas for infinitesimal perturbation analysis (IPA) derivatives of the sample-path time averages of the inventory level and lost sales with respect to the base-stock level and a parameter of the production rate process. These formulas are comprehensive in that they are exhibited for any initial inventory state, and include right and left derivatives (when they differ). The formulas are obtained via sample path analysis under very mild regularity assumptions, and are inherently nonparametric in the sense that no specific probability law need be postulated. It is further shown that all IPA derivatives under study are unbiased and fast to compute, thereby providing the theoretical basis for online adaptive control of MTS production-inventory systems.     

Probability distribution in varying-structure queueing networks

The paper is devoted to the computation of stationary distributions of queueing systems in random media. Results obtained for considered models follow from a theorem proved in the paper. As an application of the theorem, we consider Jackson networks whose structure (the set of working nodes, service and input flow intensities, routing matrix, state set) and type (open/closed network) varies as the state of another network or of the environment changes. Product-form formulas for the computation of stationary distributions of the considered networks are obtained, and algorithms for the solution of auxiliary problems are developed.     

Strong consistency of infinitesimal perturbation analysis for tandem queueing networks

Strong consistency of infinitesimal perturbation analysis for the sojourn times in a class of tandem queueing networks is proved. Service times at the queues are correlated, and they are affine functions of the variable parameters. Differentiability of the average sojourn times is not assumed, but proved. The analysis is not based on assumptions of regenerative cycles of the networks but on stability and ergodicity of the queueing processes involved. The proof of strong consistency is based on a set of abstract conditions, described in terms of properties of the sample performance functions. These conditions are first shown to be sufficient for strong consistency, and then their validity for the networks in question is proved.Research supported in part by the NSF under grants Nos. ECS85-15449 and CDR-8803012, under ONR contract nos. N00014-90-K-1093 and N00014-89-J-1023, and under Army contract no. DAAL-03-83-K-0171. This author is now with the Department of Manufacturing Engineering, Boston University, Boston, MA 02215.     

A hybrid method for performance analysis of G/G/m queueing networks

Open queueing networks are useful for the performance analysis of numerous real systems. Since exact results exist only for a limited class of networks, decomposition methods have been extensively used for approximate analysis of general networks. This procedure is based on several approximation steps. Successive approximations made in this approach can lead to a considerable error in the output. In particular, there are no general accurate formulas for computing the mean waiting time and the inter-departure variance in general multiple-server queues. This causes the results from decomposition methods when applied to G/G/m queueing networks to be very approximative and to significantly deviate from actual performance values. We suggest substituting some approximate formulae by low-cost simulation estimates in order to obtain more accurate results when benefiting from the speed of an analytical method. Numerical experiments are presented to show that the proposed approach provides improved performance.     

The structure of robust disturbance rejection control

This paper deals with the problem of disturbance rejection under state feedback in linear multivariable control systems. This problem is ill posed under arbitrary state space parameter perturbations. However, it is shown that with respect to arbitrary perturbations of the plant transfer function coefficients, a robust solvability, condition, and possibly a robust synthesis, can be obtained. These results are significant because the class of arbitrary state space parameter variations is too rich for practical interest, whereas the class of arbitrary variations in transfer functions more closely represents the realistic problem of engineering concern.     

带启动时间和可修服务台的M/M/1/N工作休假排队系统

分析带有启动时间、服务台可故障的M/M/1/N单重工作休假排队系统.在该系统中,服务台在休假期间不是完全停止工作,而是处于低速服务状态.假定服务台允许出现故障且当出现故障时,服务台停止为顾客服务且立即进行修理.服务台的失效时间和修理时间均服从指数分布,且工作休假期和正规忙期具有不同的取值;同时,从关闭期到正规忙期有服从指数分布的启动时间.建立此工作休假排队系统的有限状态拟生灭过程(QBD),使用矩阵几何方法得到QBD的各稳态概率相互依赖的率阵,从而求得稳态概率向量.通过有限状态QBD的最小生成元和稳态概率向量得到系统的基本阵和协方差矩阵,求解出系统方差、系统稳态可用度、系统吞吐率、系统稳态队长、系统稳态故障频度等系统性能.数值分析体现了所提出方法的有效性和实用性,通过敏感性分析将各参数对系统性能的影响进行了初探,为此模型的实际应用提供了很好的理论依据.