A framework for building spreadsheet based decision models

Spreadsheet based decision modelling is widely used in business today. The functionality provided within the current integrated packages allows users to develop very complex business models. Unfortunately, most spreadsheet users do not follow any particular methodology when building spreadsheet based models. This in turn leads to many wasted hours of debugging and re-programming and often produces models that look more complex than they need to be and are also tedious to extend or modify. This paper presents an example of the type of framework that can be used when developing spreadsheet based business models. The framework encourages the efficient development of more effective models that are easy to use and easy to modify.     

On geometric dynamics of rigid multi-body systems

Standard methods to model multibody systems are aimed at systems with configuration spaces isomorphic to ℝⁿ . This limitation leads to singularities and other artifacts in case the configuration space has a different topology, for example in the case of ball joints or a free-floating mechanism. This paper discusses an extension of classical methods to allow for a very general class of joints, including all joints with a Lie group structure. The model equations are derived using the Boltzmann-Hamel equations and have very similar structure and complexity as obtained using classical methods, but they do not suffer from singularities. Furthermore, the equations are explicit differential equations that can be directly implemented in simulation software. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation and Analysis of a New Mobility Model for Mobile Communication Networks

The traffic generation models, which describe how the clients use the network services, as well as the mobility models, which describe how clients move within the service area covered by the network, are essential tools for QoS analysis in these environments. In this paper we present the simulation of a new mobility model implemented for the analysis of QoS parameters of a mobile network, such as channel occupation time, handoff and new call blocking probabilities.     

Quantitative and qualitative indices for the plant layout evaluation problem

In the past two decades, the researchers used to develop simulation models or mathematical programming models to estimate the performance measures of a production system which may or may not include the considerations of layout design, rather than develop indices specifically for evaluating a layout alternative. These models usually ask for very detailed information. Most of them involve oversimplifying assumptions and request overwhelming computational efforts such that they cannot be manipulated with ease in practice. The limitations and deficiencies of previous indices and performance measures include: parameters hard to obtain; inappropriate detailed data requirement; much effort to obtain little accuracy improvement; data available after operations start; no generic approach and no clear validation provided. To overcome these deficiencies, the generic approaches for developing quantitative and qualitative indices are provided and new indices for the flow criterion group and environment criterion group are presented. The parameters of each index are easier to obtain and do not require much effort on data collection. The validations of each quantitative index with examples are also provided. The generic approaches also allow the users to revise the indices according to the specific case considered.     

Two-stage queueing network models for quality control and testing

We study sojourn times in a two-node open queueing network with a processor sharing node and a delay node, with Poisson arrivals at the PS node. Motivated by quality control and blood testing applications, we consider a feedback mechanism in which customers may either leave the system after service at the PS node or move to the delay node; from the delay node, they always return to the PS node for new quality controls or blood tests. We propose various approximations for the distribution of the total sojourn time in the network; each of these approximations yields the exact mean sojourn time, and very accurate results for the variance. The best of the three approximations is used to tackle an optimization problem that is mainly inspired by a blood testing application.     

The Endogenous Analysis of Flows,with Applications to Migrations,Social Mobility and Opinion Shifts

For exponential random graph models, under quite general conditions, it is proved that induced subgraphs on node sets disconnected from the other nodes still have distributions from an exponential random graph model. This can help in the theoretical interpretation of such models. An application is that for saturated snowball samples from a potentially larger graph which is a realization of an exponential random graph model, it is possible to do the analysis of the observed snowball sample within the framework of exponential random graph models without any knowledge of the larger graph.     

Bayesian modeling of forestry data with R using optimization and simulation tools

Data generated in forestry biometrics are not normal in statistical sense as they rarely follow the normal regression model. Hence, there is a need to develop models and methods in forest biometric applications for non-normal models. Due to generality of Bayesian methods it can be implemented in the situations when Gaussian regression models do not fit the data. Data on diameter at breast height (dbh), which is a very important characteristic in forestry has been fitted to Weibull and gamma models in Bayesian paradigm and comparisons have also been made with its classical counterpart. It may be noted that MCMC simulation tools are used in this study. An attempt has been made to apply Bayesian simulation tools using \textbf{R} software.     

Embedding optimization in computational science workflows

Workflows support the automation of scientific processes, providing mechanisms that underpin modern computational science. They facilitate access to remote instruments, databases and parallel and distributed computers. Importantly, they allow software pipelines that perform multiple complex simulations (leveraging distributed platforms), with one simulation driving another. Such an environment is ideal for computational science experiments that require the evaluation of a range of different scenarios “in silico” in an attempt to find ones that optimize a particular outcome. However, in general, existing workflow tools do not incorporate optimization algorithms, and thus whilst users can specify simulation pipelines, they need to invoke the workflow as a stand-alone computation within an external optimization tool. Moreover, many existing workflow engines do not leverage parallel and distributed computers, making them unsuitable for executing computational science simulations. To solve this problem, we have developed a methodology for integrating optimization algorithms directly into workflows. We implement a range of generic actors for an existing workflow system called Kepler, and discuss how they can be combined in flexible ways to support various different design strategies. We illustrate the system by applying it to an existing bio-engineering design problem running on a Grid of distributed clusters.     

A nonlinear HIV/AIDS model with contact tracing

A nonlinear mathematical model is proposed and analyzed to study the effect of contact tracing on reducing the spread of HIV/AIDS in a homogeneous population with constant immigration of susceptibles. In modeling the dynamics, the population is divided into four subclasses of HIV negatives but susceptibles, HIV positives or infectives that do not know they are infected, HIV positives that know they are infected and that of AIDS patients. Susceptibles are assumed to become infected via sexual contacts with (both types of) infectives and all infectives move with constant rates to develop AIDS. The model is analyzed using the stability theory of differential equations and numerical simulation. The model analysis shows that contact tracing may be of immense help in reducing the spread of AIDS epidemic in a population. It is also found that the endemicity of infection is reduced when infectives after becoming aware of their infection do not take part in sexual interaction.     

A Markov Renewal Based Model for Wireless Networks

We propose a queueing network model which can be used for the integration of the mobility and teletraffic aspects that are characteristic of wireless networks. In the general case, the model is an open network of infinite server queues where customers arrive according to a non-homogeneous Poisson process. The movement of a customer in the network is described by a Markov renewal process. Moreover, customers have attributes, such as a teletraffic state, that are driven by continuous time Markov chains and, therefore, change as they move through the network. We investigate the transient and limit number of customers in disjoint sets of nodes and attributes. These turn out to be independent Poisson random variables. We also calculate the covariances of the number of customers in two sets of nodes and attributes at different time epochs. Moreover, we conclude that the arrival process per attribute to a node is the sum of independent Poisson cluster processes and derive its univariate probability generating function. In addition, the arrival process to an outside node of the network is a non-homogeneous Poisson process. We illustrate the applications of the queueing network model and the results derived in a particular wireless network.     

Distributed caching over heterogeneous mobile networks

Sharing content over a mobile network through opportunistic contacts has recently received considerable attention. In proposed scenarios, users store content they download in a local cache and share it with other users they meet, e.g., via Bluetooth or WiFi. The storage capacity of mobile devices is typically limited; therefore, identifying which content a user should store in her cache is a fundamental problem in the operation of any such content distribution system. In this work we propose Psephos, a novel mechanism for determining the caching policy of each mobile user. Psephos is fully distributed: users compute their own policies individually, in the absence of a central authority. Moreover, it is designed for a heterogeneous environment, in which demand for content, access to resources, and mobility characteristics may vary across different users. Most importantly, the caching policies computed by our mechanism are optimal: we show that Psephos maximizes the system’s social welfare. To the best of our knowledge, our work is the first to address caching with heterogeneity in a fully distributed manner.     

Hysteresis and Stick-Slip Motion of Phase Boundaries in Dynamic Models of Phase Transitions

Summary. We investigate hysteretic behavior in two dynamic models for solid-solid phase transitions. An elastic bar with a nonconvex double-well elastic energy density is subjected to time-dependent displacement boundary conditions. Both models include inertia and a viscous stress term that provides energy dissipation. The first model involves a strain-gradient term that models interfacial energy. In the second model this term is omitted. Numerical simulations combined with analytical results predict hysteretic behavior in the overall end-load versus end-displacement diagram for both models. The hysteresis is largely due to metastability and nucleation; it persists even for very slow loading when viscous dissipation is quite small. In the model with interfacial energy, phase interfaces move smoothly. When this term is omitted, hysteresis is much more pronounced. In addition, phase boundaries move in an irregular, stick-slip fashion. The corresponding load-elongation curve exhibits serrations, in qualitative agreement with certain experimental observations in shape-memory alloys. Received August 4, 1998; revised December 11, 1998     

A note on the eternal dominating set problem

We consider the “all guards move” model for the eternal dominating set problem. A set of guards form a dominating set on a graph and at the beginning of each round, a vertex not in the dominating set is attacked. To defend against the attack, the guards move (each guard either passes or moves to a neighboring vertex) to form a dominating set that includes the attacked vertex. The minimum number of guards required to defend against any sequence of attacks is the “eternal domination number” of the graph. In 2005, it was conjectured [Goddard et al. (J. Combin. Math. Combin. Comput. 52:169–180, 2005)] there would be no advantage to allow multiple guards to occupy the same vertex during a round. We show this is, in fact, false. We also describe algorithms to determine the eternal domination number for both models for eternal domination and examine the related combinatorial game, which makes use of the reduced canonical form of games.     

金融中的Levy模型及其仿真

近20年来,金融中Levy模型与蒙特卡洛仿真技术日益受到重视. 在连续时间过程的金融建模中带跳跃的Levy模型相比于连续轨道的布朗运动模型能很好地刻画市场的跳跃,更好地拟合金融数据的统计特征,更准确地对衍生品定价. 但是,相较于经典的Black-Scholes模型,用Levy模型对衍生品定价以及求解对冲策略的计算复杂度大大增加. 蒙特卡洛仿真成为Levy模型计算中最重要的方法之一. 首先详细地介绍了Levy模型引入的背景,并引出仿真方法在其中重要的应用价值. 最后,简要地给出了Levy过程仿真及其梯度估计的基本方法.     

Classification Trees With Bivariate Linear Discriminant Node Models

This article introduces a classification tree algorithm that can simultaneously reduce tree size, improve class prediction, and enhance data visualization. We accomplish this by fitting a bivariate linear discriminant model to the data in each node. Standard algorithms can produce fairly large tree structures because they employ a very simple node model, wherein the entire partition associated with a node is assigned to one class. We reduce the size of our trees by letting the discriminant models share part of the data complexity. Being themselves classifiers, the discriminant models can also help to improve prediction accuracy. Finally, because the discriminant models use only two predictor variables at a time, their effects are easily visualized by means of two-dimensional plots. Our algorithm does not simply fit discriminant models to the terminal nodes of a pruned tree, as this does not reduce the size of the tree. Instead, discriminant modeling is carried out in all phases of tree growth and the misclassification costs of the node models are explicitly used to prune the tree. Our algorithm is also distinct from the “linear combination split” algorithms that partition the data space with arbitrarily oriented hyperplanes. We use axis-orthogonal splits to preserve the interpretability of the tree structures. An extensive empirical study with real datasets shows that, in general, our algorithm has better prediction power than many other tree or nontree algorithms.     

Continuous polling models and application to ferry assisted WLAN

In this paper we focus on a class of polling systems encountered while modeling the ferry based wireless local area network (FWLAN). A moving ferry, while walking in a predetermined cyclic path, communicates with the static nodes (or users) of the network via a wireless link. The ferry is assumed to stop and communicate with a node that has a packet to send or to receive, when it is closest to that node. The location distribution of the node to which or from which a packet arrives is assumed to have a support of positive Lebesgue measure. These features imply that polling models with finite number of queues cannot be used to model the system. We study in this paper the continuous polling systems with service disciplines that model the use of the FWLAN (and that are more complex than the classical exhaustive or gated services). Our approach is based on discretization of the continuous polling model. We propose a special way of discretizing the continuous system such that: (1)?the known Pseudo conservation laws can be applied to obtain the stationary expected workload of the discrete systems; (2)?the limit, of these ??discretized' expected workloads, equals the stationary expected workload of the continuous system. Our results rely heavily on fixed point analysis of infinite dimensional operators.     

Searching for targets who want to be found

The paper reports some simulation results for models of the types of search that might be conducted by a rescue helicopter when looking for a walker who is lost in the desert and wants to be found. The walker has a smaller speed than the helicopter, but the walker can detect the helicopter at a greater distance than the helicopter can detect the walker. Possible search strategies include those in which the helicopter flies in a decreasing spiral or sweeps back and forth across a region. The walker may remain stationary, move randomly or walk towards the helicopter when he hears it. Simulation work suggests the types of strategies that may do best.     

Continuity for the asymptotic shape in the frog model with random initial configurations

We consider the so-called frog model with random initial configurations, which is described by the following evolution mechanism of simple random walks on the multidimensional cubic lattice: Some particles are randomly assigned to any site of the multidimensional cubic lattice. Initially, only particles at the origin are active and they independently perform simple random walks. The other particles are sleeping and do not move at first. When sleeping particles are hit by an active particle, they become active and start doing independent simple random walks. An interest of this model is how initial configurations affect the asymptotic shape of the set of all sites visited by active particles up to a certain time. Thus, in this paper, we prove continuity for the asymptotic shape in the law of the initial configuration.