چارچوب شبیه سازی واحد و یکپارچه برای مدل های تصادفی فضایی

For spatial stochastic models, a lot of programs exist which deal with the simulation of specific models. But, combining them is not that easy and usually requires greater effort. This paper presents an object-oriented framework, i.e. a set of collaborating abstract and concrete classes, dealing with the simulation of such models. The selected fundamental models are only illustrating examples for the general concept. From the Java implementation of this framework, two code examples are shown, which could also be implemented similarly in any other object-oriented programming language. All interfaces and a lot of concrete classes can be implemented dimension-independent. The design and implementation problems arising in the context of static and dynamic plus sampling are specifically discussed.

Spatial stochastic–geometric models are random geometric structures, such as random configurations of points, overlapping (random) geometric objects at random locations, and random mosaics among others. They can be used to model global patterns and have proven useful in various fields, such as communication networks [1], materials science [15], medicine [9] and [10], physics [12], and astrophysics [13]. The combination of the existing simulation programs (cf. e.g. [15] and [16]) is not an easy task if possible at all. Furthermore, those implementations depend on the dimension of the simulated model. So, to simulate the model (for which a simulation program is given) in a higher dimension, at least changes are required, or a new program has to be developed. The framework for the simulation of spatial stochastic–geometric models presented in this paper gives a possible solution to these problems and provides an unified approach. There are several orthogonal models in the framework which can be arbitrarily combined. This leads to combinatorial complexity of possible applications. All models are designed as interfaces, which are dimension-independent. Therefore, the framework is basically independent of the dimension. Only for a part of the concrete classes it would be much more complicated to give a dimension-independent implementation. So, for such classes a separate implementation has to be provided for each dimension. The framework is implemented in Java [3]. It could, however, be implemented similarly in any object-oriented programming language. Two code examples of concrete models are presented, demonstrating the advantages of the framework design. All parts of the framework are explained using UML class diagrams [20]. The paper is organized as follows. Section 2 contains a brief description of fundamental spatial stochastic–geometric models considered as illustrating examples in the presented framework. Related work and common problems occurring during the combination of existing simulations are addressed in Section 3. The framework is described in Section 4, where sample implementations for two models are shown, followed by the summary and conclusions in Section 5.

The dimension-independent framework design for the simulation of spatial stochastic models presented in this paper––illustrated only with a few basic models for ease of understanding––gives a unified and simple way to generate samples of such models. Further models may be added without difficulties. For their implementation, the available classes and interfaces can be used, which makes this task easier. So, the framework helps to speed up the development of new simulation programs. In addition, the chosen design leads to better source code which is readable without great effort, as shown for the Boolean model and independently iterated tessellations. The basic problems, such as edge effects and plus sampling, arising when simulating spatial stochastic models have been treated in the present paper and possible solutions were given. Although, the framework has been implemented in Java, it can be implemented similarly in any other object-oriented programming language. The contributions of this paper are more general and not restricted to an implementation.