基于改进的GM(1,1)-Markov链组合模型广东省单位GDP能耗预测

本文以灰色系统理论的GM(1,1)模型和随机过程理论的Markov链模型为基础构建了一个动态GM(1,1)-Markov链组合预测模型。该模型同时利用了GM(1,1)模型对序列趋势因素良好的拟合能力和Markov链模型对残差序列信息的提取能力。为进一步提高该模型的预测精度,用泰勒(Taylor)近似方法和新信息优先的思想对该模型进行了改进。最后,以1991-2014年广东省单位GDP能耗数据实证了该模型的预测效果。     

Modelling and decision support in physiology and medicine: a methodological framework with lllustration

This paper presents a methodological framework for modelling that has found wide application in the complex domains of physiology and medicine. The processes of model validation are centrally embedded within this framework. The parallelism between modelling per se and the development of model-based decision support systems is then considered, showing that it is possible to devise a unified methodological framework which encompasses the requirements both of model validation and decision support system evaluation. The applicability of the framework is demonstrated in the validation of a mathematical model of blood glucose dynamics; and in the development and evaluation of decision support systems such as those which are aimed at addressing the problem of advising the insulin-dependent diabetic patient on the adjustment of insulin dosage     

Bifurcations in a human migration model of Scheurle-Seydel type-II: Rotating waves

This paper treats the conditions for the existence of rotating wave solutions of a system modelling the behavior of students in graduate programs at neighbouring universities near each other which is a modified form of the model proposed by Scheurle and Seydel. We assume that both types of individuals are continuously distributed throughout a bounded two-dimension spatial domain of two types (circle and annulus), across whose boundaries there is no migration, and which simultaneously undergo simple (Fickian) diffusion. We will show that at a critical value of a system-parameter bifurcation takes place: a rotating wave solution arises.     

Exploring the model development process in discrete-event simulation: insights from six expert modellers

This paper explores the model development process in discrete-event simulation (DES) by reporting on an empirical study that follows six expert modellers while building simulation models. DES is a widely used modelling approach, however little is known about the modelling processes and methodology adopted by modellers in practice. Verbal Protocol Analysis is used to collect data, where the participants are asked to speak aloud while modelling. The results show that the expert modellers spend a significant amount of time on model coding, verification and validation, and data inputs. The modellers iterate often between modelling activities. Patterns of modelling behaviour are identified, suggesting that the modellers adopt distinct modelling styles. This study is useful in that it provides an empirical view of existing DES modelling practice, which in turn can inform existing research and simulation practice as well as teaching of DES modelling to novices.     

Model development in discrete-event simulation and system dynamics: An empirical study of expert modellers

An empirical study comparing the model development process followed by experts in discrete-event simulation (DES) and system dynamics (SD) modelling is undertaken. verbal protocol analysis (VPA) is used to study the modelling process followed by ten expert modellers (5 SD and 5 DES). Participants are asked to build simulation models based on a case study and to think aloud while modelling. The generated verbal protocols are divided into seven modelling topics: problem structuring, conceptual modelling, data inputs, model coding, verification & validation, results & experimentation and implementation and then analyzed. Our results suggest that all modellers switch between modelling topics, however DES modellers follow a more linear progression. DES modellers focus significantly more on model coding and verification & validation, whereas SD modellers on conceptual modelling. Observations are made revealing some interesting differences in the way the two groups of modellers tackle the case. This paper contributes towards the comparison of DES and SD.     

Relevance assumed: a case study of balanced scorecard development using system dynamics

The balanced scorecard (BSC) has become a popular concept for performance measurement. It focuses attention of management on only a few performance measures and bridges different functional areas as it includes both financial and non-financial measures. However, doubts frequently arise regarding the quality of the BSCs developed as well as the quality of the process in which this development takes place. This article describes a case study in which system dynamics (SD) modelling and simulation was used to overcome both kinds of problems. In a two-stage modelling process (qualitative causal loop diagramming followed by quantitative simulation), a BSC was developed for management of one organizational unit of a leading Dutch insurer. This research illustrates how, through their involvement in this development process, management came to understand that seemingly contradictory goals such as customer satisfaction, employee satisfaction and employee productivity were, in fact, better seen as mutually reinforcing. Also, analysis of the SD model showed how, contrary to ex ante management intuition, performance would first have to drop further before significant improvements could be realized. Finally, the quantitative modelling process also helped to evaluate several improvement initiatives that were under consideration at the time, proving some of them to have unclear benefits, others to be very promising indeed.     

Random collision model for random genetic drift and stochastic difference equation

Summary At first we introduce a simple stochastic difference equation, to simulate random sampling drift in population genetics, which is naturally obtained from a random collision model. Next, we introduce a random collision model to simulate overdominance model in population genetics. We assume in a time interval °t, a random collision of four particles, which represents overdominant selection, takes place at a certain probability, where a particle corresponds to a gene. We assume that mutation takes place by some rate and assume that every new mutation is different from extant alleles. We estimate mean heterozygosity by our simulation method and compare it with the result obtained by using a stochastic difference equation for overdominance model. The Institute of Statistical Mathematics     

Model legitimisation in operational research

This paper suggests that model validation and model legitimisation are two overlapping but nevertheless distinct activities, and that it takes more than being valid for an OR model to be organizationally acceptable: it has to be legitimate. The paper forwards the idea that the implementation of a model is necessarily part of a change process and hence has impact on the organization. It discusses how organizational contract and legitimacy are related to one another, and how, in a change process, a model can be used in different modes by different stakeholders. Concrete suggestions for model legitimisation are proposed. The paper concludes by linking model legitimisation and model validation.     

Chartwell Books: A Case Study in Mathematical Modelling

A case is described that has been used successfully many times as a vehicle for teaching mathematical modelling. The case has been closely derived from a consultancy assignment with Chartwell Books. The place of mathematical modelling within decision-support systems is examined, and this is followed by an outline of one such mathematical modelling methodology. The problem situation facing the managing director of Chartwell Books concerning the modelling of labour and material costs is described. A detailed application of the mathematical modelling methodology is worked through, finishing with a discussion of the value of the case for student teaching and of the problems that students have encountered when tackling the Chartwell case. Possible extensions to the basic methodology, such as validation and the human-computer interface, are also briefly considered.     

Discrete-event modelling of an urban transportation system

The modelling of an urban transportation system is addressed. The transportation network is modelled as an oriented graph in which nodes represent single-mode or intermodal stations, integrating different transportation services. Its characteristics make it suitable to model the network as a Discrete Event System. In introducing the model proposed, attention is paid to the definition of all its components, but particular care is necessary for the identification of the probability distributions of the stochastic variables. The validation procedure performed to check the reliability of the model is described in detail. Some numerical results about a case study are presented and discussed.     

On Markovian approximations for virtual-build-to-order systems

The Virtual Build-to-Order (VBTO) approach strives to allow a producer to fulfil customers with the specific product variants they seek more efficiently than a conventional order fulfilment system. It does so by opening the planning pipeline. Here the feasibility of modelling the VBTO system as a Markov process is investigated. Two system configurations are considered—a random pipeline feed policy that assumes only knowledge of the overall demand pattern and an informed policy that ensures a mix of different variants in the system. First-order Markov models, which assume stationarity requirements are satisfied, are developed for small VBTO systems. The model for the informed feed policy has excellent agreement with simulation results and confirms the superiority of this policy over the random policy. The model for the random policy is more accurate at high variety than at low variety levels. Accuracy is improved with a second-order Markov model. Although impractical for modelling large scale VBTO systems for either configuration, the Markov approach is valuable in providing insights, theoretical foundations and validation for simulation models. It aids the interpretation of observations from simulations of large scale systems and explains the mechanism by which an unrepresentative stock mix develops over time for the random policy.     

A practical exercise in simulation model validation

The validation of continuous system simulation models is a matter of great practical importance. Unfortunately, however, it often receives very little attention in university-level courses on modelling and simulation. The paper considers some possible reasons for the lack of emphasis given to model validation issues in education and describes an exercise which has been designed to introduce students to some practical aspects of internal verification and external validation of nonlinear dynamic models. The work involves a laboratory-scale system based on two inter-connected tanks of liquid and also demonstrates some important limitations of a widely-used nonlinear model. Features which make the chosen system particularly suitable for this teaching application include the relatively simple physical nature of the system and the fact that all the key variables of the model are accessible for measurement. Students are exposed to a range of practical issues, such as the selection of the sampling rate for data collection and the design of experiments to provide data sets appropriate for external validation purposes. Dealing successfully with such questions and carrying out validation tests exposes students to concepts of model credibility and the whole process of model development and application. They are also challenged in terms of their practical abilities to use computer simulation techniques and in their understanding of the mathematical model and the physics of the real system. It is argued that an exercise of this type can have very important educational benefits.     

On a formalisation of the process of quantitative model building

The paper proposes a formalisation of the process of quantitative model building. One of the main structural ideas is a partition of this process into an abstraction and relaxation part. Clearly this partition not only separates different approximation procedures but also facilitates the difficult task of model validation. The modelling process is described as a sequence of abstraction and relaxation steps governed by a meta-process of various multi-person multi-criterion decisions.     

Multiple Timescales, Mixed Mode Oscillations and Canards in Models of Intracellular Calcium Dynamics

A range of representative models of intracellular calcium dynamics are surveyed, with the aim of determining which model characteristics are qualitatively unchanged by changes to details of the model components. Techniques from geometric singular perturbation theory are used to investigate the role of separation of timescales in determining model dynamics, with particular emphasis on identifying parameter regimes in which mixed mode oscillations are present as a result of the separation of timescales. We find that the number of distinct timescales and the number of variables evolving on each timescale varies between models and depends on both the model assumptions and on the parameter regime of interest within the model, but in all cases, the presence of canards and associated mixed mode oscillations provides a mechanism by which the models can robustly exhibit complex oscillations, with the frequency of oscillation depending sensitively on parameter values. We find that analysis of the number and nature of the distinct timescales in a model allows us to make useful predictions about the dynamics associated with the model, and that this may give us more information about the model dynamics than a classification according to the modelling assumptions made about different cellular mechanisms in deriving the models.     

Analysis of the vibrations due to thermal deflection of the drum in the coiling process

The modelling of the coiling process involves a mechanical model of the dynamic system that consists of the rotating coiling drum and the axially and transversally moving strip. Due to the coiling a change of mass in the system takes place. For such a variable mass system a control volume concept has to be introduced in order to get the equations of motion of the dynamic system with variable parameters. A Runge Kutta time integration algorithm is applied to compute the solution. It is assumed that the outer radius of the coiling drum increases linear with the rotation angle. The bending deflection of the shaft results from an inhomogeneous temperature distribution within the coiled material on the coiling drum. Two different boundary conditions of the moving strip have been considered and it is demonstrated that the thermal deflection of the drum has a high influence upon the fluctuation of the strip force. For a given geometry and strip speed we obtain a critical thermal deflection where the minimum strip tension force is zero. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling pedestrian dynamics into a metro station by thermostatted kinetic theory methods

This paper deals with the modelling of pedestrian dynamics at the entry of a metro station by means of the thermostatted kinetic theory framework. Specifically, the model depicts the time evolution of the pedestrian dynamics at the turnstiles under no panic conditions. The modelling of the microscopic interactions is based on the stochastic game theory and reflects the decision dynamics of the turnstiles pursued by pedestrians. A qualitative analysis is addressed to the equilibrium solutions by means of the classical stability theory of perturbations. Numerical simulations aim at showing the emerging behaviours captured by the model. In particular the model validation is obtained by performing a sensitivity analysis on the parameters and on the initial conditions. Further refinements and research perspective, including the modelling under panic conditions, are discussed in the last section of the paper.     

The Paucity of Model Validation in Operational Research Projects

Validation as a concept is not well defined in the methodology of model building, although it is generally considered to be an important part of the modelling process. This paper considers the amount and type of validation carried out in a series of projects, and establishes contrasts between the expected and observed modes of validation.     

On the application of substochastic semigroup theory to fragmentation models with mass loss

A linear integro-differential equation modelling multiple fragmentation with inherent mass loss is investigated by means of substochastic semigroup theory. The existence of a semigroup is established and, under natural conditions on certain coefficients, the generator of this semigroup is identified. This yields, in particular, a validation of the formal mass-loss rate equation for the model.     

A fuzzy goal programming method with imprecise goal hierarchy

Two most widely used approaches to treating goals of different importance in goal programming (GP) are: (1) weighted GP, where importance of goals is modelled using weights, and (2) preemptive priority GP, where a goal hierarchy is specified implying infinite trade-offs among goals placed in different levels of importance. These approaches may be too restrictive in modelling of real life decision making problems. In this paper, a novel fuzzy goal programming method is proposed, where the hierarchical levels of the goals are imprecisely defined. The imprecise importance relations among the goals are modelled using fuzzy relations. An additive achievement function is defined, which takes into consideration both achievement degrees of the goals and degrees of satisfaction of the fuzzy importance relations. Examples are given to illustrate the proposed method.