Perturbation Analysis and Optimization of Multiclass Multiobjective Stochastic Flow Models

Stochastic Flow Models (SFMs) are stochastic hybrid systems that abstract the dynamics of many complex discrete event systems and provide the basis for their control and optimization. SFMs have been used to date to study systems with a single user class or some multiclass settings in which performance metrics are not class-dependent. In this paper, we develop a SFM framework for multiple classes and class-dependent performance objectives, where competing classes employ threshold control policies and service is provided on a First Come First Serve (FCFS) basis. In this framework, we analyze new phenomena that result from the interaction of the different classes and give rise to a new class of “induced” events that capture delays in the SFM dynamics. We derive Infinitesimal Perturbation Analysis (IPA) estimators for derivatives of various class-dependent objectives, and use them as the basis for on-line optimization algorithms that apply to the underlying discrete event system (not the SFM). This allows us to contrast system-centric and user-centric objectives, thus putting the resource contention problem in a game framework. The unbiasedness of IPA estimators is established and numerical results are provided to illustrate the effectiveness of our method for the case where there are no constraints on the controllable thresholds and to demonstrate the gap between the results of system-centric optimization and user-centric optimization.     

Infinitesimal Perturbation Analysis and Optimization for Make-to-Stock Manufacturing Systems Based on Stochastic Fluid Models

In this paper we study Make-To-Stock manufacturing systems and seek on-line algorithms for determining optimal or near optimal buffer capacities (hedging points) that balance inventory against stockout costs. Using a zStochastic Fluid Model (SFM), we derive sample derivatives (sensitivities) which, under very weak structural assumptions on the defining demand and service processes, are shown to be unbiased estimators of the sensitivities of a cost function with respect to these capacities. When evaluated based on the sample path of discrete-part systems, we show that these estimators are greatly simplified. Thus, they can be easily implemented and evaluated on line. Though the implementation on discrete-part systems does not necessarily preserve the unbiasedness property, simulation results show that stochastic approximation algorithms that use such estimates do converge to optimal or near optimal hedging points. Supported in part by the National Science Foundation under Grants EEC-0088073 and DMI-0330171, by AFOSR under contract F49620-01-0056, and by ARO under grant DAAD19-01-0610.     

Perturbation Analysis of Multiclass Stochastic Fluid Models

We use a stochastic fluid model (SFM) to capture the operation of finite-capacity queueing systems with multiple customer classes. We derive gradient estimators for class-dependent loss and workload related performance metrics with respect to any one of several threshold parameters used for buffer control. These estimators are shown to be unbiased and directly observable from a sample path without any knowledge of underlying stochastic characteristics of the traffic processes. This renders them computable in on-line environments and easily implementable in settings such as communication networks.     

Using Augmented Infinitesimal Perturbation Analysis for Capacity Planning in Intree ATM Networks

Augmented Infinitesimal Perturbation Analysis is used to determine asymptotically unbiased and strong consistent gradient estimates for use in the capacity planning of intree ATM networks. These gradients are used to determine the locally optimal minimum average network delay by applying a steepest descent algorithm with projection and an Armijo line search to solve the capacity assignment (CA) problem. The network capacities are governed by a linear cost constraint. It is assumed that input regulators (e.g., leaky bucket regulators) are used at the source of each virtual circuit. All virtual circuit external arrivals are modeled as independent Poisson processes. Regenerative simulation is used to determine gradient estimates.     

Approximation Errors of Perturbation Methods in Solving a Class of Dynamic Stochastic General Equilibrium Models

We establish the standard procedures in solving a class of dynamic stochastic general equilibrium models with a second-order approximation to the policy function. The innovation is that the means of exogenous shocks vary with the variances. The numerical results show that second-order perturbation methods generate large approximation errors regarding to the responses of policy functions to shocks.     

一类随机摄动系统的鲁棒控制与仿真

在内模控制(IMC)结构下对一类随机摄动系统的鲁棒控制及其仿真研究作了探讨.首先针对一类随机模型误差的描述定义了一个实际敏感度和标称敏感度之间的加权敏感度误差,然后应用谱分解的方法调整标称控制器来最小化加权敏感度误差在整个频段上的方差,为一类随机摄动系统提供了一种鲁棒控制器设计方法,可使系统期望的标称性能对模型误差具有良好的鲁棒性.最后根据随机摄动系统的特点进行仿真研究,进一步说明了所得控制方法的有效性.     

Workload Models for Stochastic Networks: Value Functions and Performance Evaluation

This paper concerns control and performance evaluation for stochastic network models. Structural properties of value functions are developed for controlled Brownian motion (CBM) and deterministic (fluid) workload-models, leading to the following conclusions: Outside of a null-set of network parameters, the following hold. The fluid value-function is a smooth function of the initial state. Under further minor conditions, the fluid value-function satisfies the derivative boundary conditions that are required to ensure it is in the domain of the extended generator for the CBM model. Exponential ergodicity of the CBM model is demonstrated as one consequence. The fluid value-function provides a shadow function for use in simulation variance reduction for the stochastic model. The resulting simulator satisfies an exact large deviation principle, while a standard simulation algorithm does not satisfy any such bound. The fluid value-function provides upper and lower bounds on performance for the CBM model. This follows from an extension of recent linear programming approaches to performance evaluation.     

Stochastic Fragments: A Framework for the Exact Reduction of the Stochastic Semantics of Rule-Based Models

In this paper, we propose an abstract interpretation-based framework for reducing the state space of stochastic semantics for protein-protein interaction networks. Our approach consists in quotienting the state space of networks. Yet interestingly, we do not apply the widely-used strong lumpability criterion which imposes that two equivalent states behave similarly with respect to the quotient, but a weak version of it. More precisely, our framework detects and proves some invariants about the dynamics of the system: indeed the quotient of the state space is such that the probability of being in a given state knowing that this state is in a given equivalence class, is an invariant of the semantics. Then we introduce an individual-based stochastic semantics (where each agent is identified by a unique identifier) for the programs of a rule-based language (namely Kappa) and we use our abstraction framework for deriving a sound population-based semantics and a sound fragments-based semantics, which give the distribution of the traces respectively for the number of instances of molecular species and for the number of instances of partially defined molecular species. These partially defined species are chosen automatically thanks to a dependency analysis which is also described in the paper.     

Validating Simulation Models: A General Framework and Four Applied Examples

This paper provides a framework for discussing the empirical validation of simulation models of market phenomena, in particular of agent-based computational economics models. Such validation is difficult, perhaps because of their complexity; moreover, simulations can prove existence, but not in general necessity. The paper highlights the Energy Modeling Forum’s benchmarking studies as an exemplar for simulators. A market of competing coffee brands is used to discuss the purposes and practices of simulation, including explanation. The paper discusses measures of complexity, and derives the functional complexity of an implementation of Schelling’s segregation model. Finally, the paper discusses how courts might be convinced to trust simulation results, especially in merger policy.      

Stochastic Models and Adaptive Algorithms for Energy Balance in Sensor Networks

We consider the important problem of energy balanced data propagation in wireless sensor networks and we extend and generalize previous works by allowing adaptive energy assignment. We consider the data gathering problem where data are generated by the sensors and must be routed toward a unique sink. Sensors route data by either sending the data directly to the sink or in a multi-hop fashion by delivering the data to a neighbouring sensor. Direct and neighbouring transmissions require different levels of energy consumption. Basically, the protocols balance the energy consumption among the sensors by computing the adequate ratios of direct and neighbouring transmissions. An abstract model of energy dissipation as a random walk is proposed, along with rigorous performance analysis techniques. Two efficient distributed algorithms are presented and analyzed, by both rigorous means and simulation. The first one is easy to implement and fast to execute. The protocol assumes that sensors know a-priori the rate of data they generate. The sink collects and processes all these information in order to compute the relevant value of the protocol parameter. This value is transmitted to the sensors which individually compute their optimal ratios of direct and neighbouring transmissions. The second protocol avoids the necessary a-priori knowledge of the data rate generated by sensors by inferring the relevant information from the observation of the data paths. Furthermore, this algorithm is based on stochastic estimation methods and is adaptive to environmental changes.     

变时滞随机忆阻器神经网络的同步控制

在实现实际的复杂人工神经网络模型以及大规模集成电路时,随机噪声是不可避免的.因此,随机忆阻器神经网络具有重要的现实研究意义.针对变时滞随机忆阻器神经网络的同步控制问题,基于非光滑分析以及集值映射、随机微分包含的理论,利用Lyapunov函数和基本不等式的方法,设计了一个线性反馈控制器.通过恰当选择控制器增益,实现了随机忆阻器神经网络驱动系统与相应的响应系统之间的指数同步,所得到的结果保守性更小.最后,给出数值例子验证了理论结果的有效性.     

Optimal Control and Stochastic Simulation of Large Nonlinear Models with Rational Expectations

This paper presents a computationally fesible procedure for the optimalcontrol and stochastic simulation of large nonlinear models with rationalexpectations under the assumption of certainty equivalence.     

Robust Control of Uncertain Stochastic Recurrent Neural Networks with Time-varying Delay

In this paper, robust control of uncertain stochastic recurrent neural networks with time-varying delay is considered. A novel control method is given by using the Lyapunov functional method and linear matrix inequality (LMI) approach. Several delay-independent and delay-dependent sufficient conditions are then further derived to ensure the global asymptotical stability in mean square for the uncertain stochastic recurrent neural networks, and the estimation gains can also be obtained. Numerical examples are constructed to verify the theoretical analysis in this paper.     

Stochastic Control of Linear and Nonlinear Econometric Models: Some Computational Aspects

This paper considers the optimal control of small econometric models applying the OPTCON algorithm. OPTCON determines approximate numerical solutions to optimum control problems for nonlinear stochastic systems. These optimum control problems consist in minimizing a quadratic objective function for linear and nonlinear econometric models with additive and multiplicative (parameter) uncertainties. The algorithm was programmed in C# and in MATLAB and allows for stochastic control with open-loop and passive learning (open-loop feedback) information patterns. Here we compare the results of applying the OPTCON2 version of the algorithm to two macroeconomic models for Slovenia, the nonlinear model SLOVNL and the linear model SLOVL. The results for both models are similar, with open-loop feedback controls giving better results on average and less outliers than open-loop controls. The number of outliers is higher in the nonlinear case and especially under high parameter uncertainty.     

A Framework for Stochastic System Modelling and Analysis: Work in Progress

Stochastic Graph Transformation combines the benefits of graphical modelling with stochastic analysis techniques. In this paper we report on our framework Sma for Stochastic Modelling and Analysis, and SGT, a tool which uses the framework for Stochastic Graph Transformation.     

极大代数上的随机线性系统与DEDS的扰动分析

本文给出了串行生产线的极大代数上的随机线性状态方程,证明了扰动分析适用于这类DEDS系统,并给出了其扰动分析的计算方法,该法是较为简单的.     

一种简易的无模型控制算法--改进的同时扰动随机逼近控制

同时扰动随机逼近控制算法是一种特别适合于应用在工况变化大、非线性强的工业过程的无模型控制算法。但该算法采用了神经网络作为函数逼近器，使得在工程上的实现过于复杂，文章对此作出改进，使其大大简化，更适合于在工程上应用。     

Intra-layer Synchronization in Duplex Networks with Time-Varying Delays and Stochastic Perturbations Under Impulsive Control

Neural Processing Letters - This paper concerns the intra-layer synchronization in duplex networks with stochastic perturbations under impulsive control. In this paper, we proposed a dynamical...     

Set Stabilization of Large-Scale Stochastic Boolean Networks: A Distributed Control Strategy

<正>Dear Editor,This letter deals with the set stabilization of stochastic Boolean control networks(SBCNs) by the pinning control strategy, which is to realize the full control for systems by imposing control inputs on a fraction of agents.