The concept of a multilevel, hierarchical structure cannot be defined by a short succinct statement. A glance through the cases presented in Chap. I can convince one that an all-embracing definition would amount to enumeration of possible alternatives. We therefore answer the question by pointing out some of the essential characteristics which every hierarchy has, in particular: vertical arrangement of subsystems which comprise the overall system, priority of action or right of intervention of the higher level subsystems, and dependence of the higher level subsystems upon actual performance of the lower levels.
Any hierarchy one considers contains a vertical arrangement of subsystems, in that the overall system is viewed as consisting of a family of interacting subsystems as shown in Fig. 2.1. By the term „system“ or „subsystem“ we simply mean a transformation of the input data into outputs; the transformation can be either dynamic evolving in actual time, an „on-line system“, or it can be a problem-solving procedure, in which case the decomposition is conceptual, in that each block represents an operation to be performed, not necessarily simultaneously, with the operations of other blocks, an „of-line system“. Examples of both types of system will be given later. Both inputs and outputs can be distributed to all levels, although most often the exchange with the environment is taken place on the lower (or lowest) level. When talking about vertical arrangement, we refer to higher and lower level units, with the obvious interpretation. Let us also indicate that the interaction between levels does not have to involve only the adjacent levels, as shown for simplicity in Fig. 2.1, although, to a degree, this depends on what one considers as subsystems on a given level.