Desired Characteristics of Boat Traffic Model

  Since the hypotheses mentioned in figure 1.5 are explicit about spatial and temporal aspects of boat traffic, it is crucial that the simulation used in this study reproduce these aspects. Temporally, it should produce output in the forms of schedules of boat traffic at various times. Spatially, it should be explicit enough to show areas of different kinds of boat traffic on a map.

When modeling processes or populations in space and time, one is faced with a number of choices of how to proceed with the conceptual formation. Importantly, one must consider whether one is modeling the individuals in their system as discrete individuals, or as a common continuous pool. Similarly, one must decide whether space and time will be modeled continuously, or segmented by discrete steps. Lindgren and Nordahl (1996) present a concise representation of the modeling implications of these choices which are reproduced in table 2.1. There is extensive literature published about the various paradigms, so a summary will not be attempted here. A brief description of the paradigms in the table is as follows:

 

 

2c 2cindividuals

2c 1cdiscrete 1ccontinuous

  |-|-| 22cmspace-time discrete CA CML

  |-|-| continuous Gas/Swarm PDE   -

Source: Lindgren and Nordahl (1996)

• If space, time, and your population are all to be modeled as continuous variables, then the system can be represented by a series of partial differential equations (PDE's). This has the advantage that your system can be represented in a fashion that can be solved analytically or with a minimum of computer coding. The disadvantage to this representation is that, since populations are modeled in the aggregate, much information can be lost about individuals' dynamics. Also, one would require some a priori information about the aggregate behaviors of the individuals being modeled to produce realistic results.
• If space and time are modeled in discrete units and steps, the resulting simulation becomes either a cellular automata (CA) or a Monte-Carlo lattice simulation, depending on whether cells are updated simultaneously. This method can produce astonishingly complex behavior from simple rule sets. While there are numerous examples of implementations of this technique for modeling one- and two-dimensional spatial processes (for a review see Weunsche and Lesser (1992)), simulations that add discrete individuals into the fray are relatively new (Minar et al., 1996).
• If one models the world in discrete time/space units, but wishes to model populations or properties of populations as continuous variables and couple them through diffusion, one ends up with a Coupled Map Lattice (CML). Again, this approach requires some knowledge about the aggregate dynamics of the population being studied.
• If one wishes to model the individuals as discrete entities and have them move around in a continuous space, one ends up with models similar to gas or swarm models. This form of simulation is still in its infancy due to the rather formidable problems of implementing it within a computer framework. One pioneering effort in implementation of this kind of simulation is described by Booth (1997).

The decision of whether to model a population by discrete individuals or by an aggregate whole depends largely on the resources that one has to dedicate to calculations of specific individuals, and how much one knows about the groups' aggregate behaviors. This is the basis of the debate of top-down vs. bottom-up approaches to modeling, and will be discussed further in this study.