Mathematics for Engineers

The previous chapters have given prominence to the power and efficiency of the analytical approach to communication systems modeling and analysis. However, many realizations make use of such specific mechanisms that their analysis is beyond the scope of mathematical tools. In that case, simulation provides an efficient way to overcome the difficulty.
A simulation experiment aims at reproducing dynamic system behavior (customers, servers, message errors, component failures, filtering or coding algorithms, etc.) using a computer program, most often run on specific software tools. On this software model, observations are performed, which give the figures of interest, such as spectral density, error rate, detection rate, loss and delay probabilities, mean or variance, etc. Clearly, the goal is not to reproduce the microscopic level of detail in the original system exactly, but to take account of those peculiarities in the mechanisms responsible for the overall behavior. It takes a careful analysis of the system, and a good understanding of transmission, coding, filtering, routing, queueing, defense mechanisms, etc., to extract the strict set of details compatible with the degree of precision required and the budget set for the study, expressed both in terms of the time needed to elaborate and validate the model as well as the duration of each simulation run.
Actually, simulation happens to offer quite a powerful approach for the engineer: not only does it allow a quantitative analysis of complex systems to be made, but it provides a software prototype of the system under development, whose role...