This approach uses a set of scalar parameters to model the behavior of a parallel system. These parameters express the average behavior of the parallel system under specified conditions.
In [Culler et al. 1993] they addressed communication in modeling parallel systems with the LogP model. The name comes from the four parameters that are used to characterize a parallel system: L for latency, o for communication overhead, g for the average ``gap'' between consecutive communication operations, and P for the number of memory and processor modules. LogP considers communication costs and the number of processors involved in the computation, improving the accuracy of the predictions. Beyond predicting the performance of applications, this framework is useful for evaluating parallel systems over various paradigms, because its parameters are machine independent. The application framework is very restrictive however; LogP cannot be used to predict complicated behaviors like saturation of routings in networks.
The use of scalar parameters to characterize parallel systems simplifies significantly the modeling task, but these parameters can be difficult to obtain, which restricts the applicability of the model and causes inaccuracies. Even if the scalar parameters are not difficult to obtain, they represent simplified assumptions about the behavior of the system, leading to inaccuracies in the model. Also, note that the models produced are the result of the user's understanding and knowledge about the parallel system. Thus, these modeling techniques not only do not help in explaining the system behavior, but also require that the user translate his knowledge into model parameters.