Introduction

A rather common misunderstanding about simulations is that they are not as sound as mathematical models. Computer simulations are, according to a popular view, characterised by an intermediate level of abstraction: they are more abstract than verbal descriptions but less abstract than ‘pure’ mathematics. This is nonsense. Simulations do consist of a well-defined (although not concise) set of functions, which relate inputs to outputs. These functions describe a fully recursive system and unambiguously define its macro dynamics. In this respect, AB models are no different from any other model: they are logical theorems saying that, given the environment and the rules described by the model, outputs necessarily follow from inputs. As in any other model, they provide sufficiency theorems: the environment and the rules are sufficient conditions to obtain the results, given the inputs. The resort to computer simulations is only an efficient way – given some conditions – to obtain the results.

In this chapter we offer a characterisation of AB models as recursive models. The chapter has a simple structure: Section 3.2 places AB modelling in the wider context of simulation models; Section 3.3 introduces the notation and the key concepts; finally, Section 3.4 concludes elaborating on what constitutes a proof in an AB setting.

Discrete-Event vs. Continuous Simulations and the Management of Time

Computer-based simulations face the problem of reproducing real-life phenomena, many of which are temporally continuous processes, using discrete microprocessors. The abstract representation of a continuous phenomenon in a simulation model requires that all events be presented in discrete terms. However, there are different ways of simulating a discrete system.

In Discrete Event Simulations (DES) entities are thought of as moving between different states as time passes. The entities enter the system and visit some of the states (not necessarily only once) before leaving the system. This can be contrasted with System Dynamics (SD), or continuous simulation modelling, a technique created during the mid-1950s by Jay Forrester at the Massachusetts Institute of Technology (Forrester, 1971), which characterises a system in terms of ordinary differential equations (ODEs). SD takes a slightly different approach to DES, focusing more on flows around networks than on the individual behaviour of entities. In SD, three main objects are considered: stocks, flows and delays. Stocks are basic stores of objects, as the number of unemployed workers.