Formalization

The growing complexity of simulation models requires a formal system that helps in model specification. This is truer still when the different individuals working to build the model come from different areas, and especially if the model is evolutionary. An example would be a social model or an economic model with engineers, economists, sociologists, psychologists and other researchers working on it. This factor, detailed in Werner and Werner (1972), makes it necessary to establish a common mechanism to help in the definition of elements’ behavior. Nevertheless, due to the diversity of the various elements of the model (some of which could be considered submodels), some formalisms are easier to use than others. The relative speed of the different submodels can be a good indicator for determining what is best in each case.

Mechanisms to transform models between different formalisms can therefore be useful. They allow the use of different formalisms depending on the submodel and help integrate the specification of the entire model through the formalism transformation.

In his paper “DEVS as a common denominator for multi-formalism hybrid systems modeling” (Vangheluwe 2000) Hans L. M. Vangheluwe clearly expresses the need to establish mechanisms for working with models specified by different formalisms. He explains three of the main mechanisms for doing this:

1. Meta-formalism: A formalism that incorporates the different formalisms of the various submodels that make up the system.
2. Common formalism: A mechanism that converts all formalisms to a common formalism.
3. Co-simulation: Independent simulators that work together. 

The specification formalism must be easy and clear, so that people who are not used to working with formalisms can quickly understand the model. The formalism must also be powerful, so that the complexity of the model can be represented.

It is difficult to determine if one formalism is simpler than another, because everyone has a personal preference. This chapter therefore presents a theoretical connection between two of the most widely used specification formalisms: DEVS and SDL.

DEVS, developed by mathematician Bernard Zeigler in the 1970s, is one of the most powerful formalisms for the specification of discrete event systems (DES). It is based on systems theory, which makes it universal. Hence, all other formalisms can be represented through DEVS models (Zeigler and Vahie 1993). That is, models represented by a Petri net or by differential equations can be represented in a DEVS model. Hybrid models are more complicated, but can also be represented by DEVS.

In his paper “Structure, flow, change: toward a social systems simulation methodology” (Werner 2000), Ronald Werner proposed the creation of an environment to describe sociology models: “The modeling environment consists of three structural elements: (1) The social system states are symbolized by circles. (2) The social processes are symbolized by rectangles. (3) The direction of flow is symbolized by directional arrows.”

This work clearly expresses the need for a graphical representation of model structure. Werner's model representation environment has similarities with the SDL formalism, which leads us to believe that it could be a good graphical representation formalism for DEVS in the social sciences and, more generally, in evolutionary models.

References:

Werner, Roland; Werner, Joan T. 1972. A pragmatic approach to social systems modeling and simulation. Social Systems Simulation Group, San Diego State University.

Werner, Roland. 2000. Structure, flow, change: Towards a social systems simulation methodology. Social Systems Simulation Group. San Diego State University.

Zeigler, Bernard P.; Vahie, Sankait. 1993. DEVS formalism and methodology: unity of conception/diversity of application, in the proceedings of the 25th Winter Simulation Conference. pp. 573-579. 12-15 December 1993. Los Angeles, California, United States (accessed 17 January 2005).