An Approach for Mathematical Modeling and Investigation of Computer Processes at a Macro Level

Abstract

In the digital age, the role of information technology and computer processes is growing. This requires refining the development of software by optimizing the communications between program components and seeking effective interaction in the implementation of processes. Complex module structures are usually developed, which require high compatibility between components and their proper functioning. The purpose of this article is to propose an approach for investigation of a set of connected computer processes executed on a macro level by using deterministic modelling. A formal technological procedure for conducting a deterministic investigation of the interaction between processes was developed. It allows for the transition from the object-original to an adequate mathematical model with its program realization. The core of the constructed procedure is the phases “mathematical formalization”, “mathematical description”, and “program realization”. The goal was to present an application of the procedure to investigate all possible realizations of connected processes, presented as nodes in a directed graph scheme of algorithms by determining the reachability. The program language APL2 was used as a tool for program description of the defined mathematical models, which were realized in the software system TryAPL2 for research automation. A preliminary mathematical formalization of interacting processes was made by presenting an example graph scheme and its transformation into an ordered structure. On the basis of the mathematical description, we developed two program models for automation of the transition to an ordered graph scheme and determination of all possible paths in it for activation of sequences of processes. The proposed models are part of a generalized environment for program investigation of the computer processing organization.

Mathematical Modelling and Study of Stochastic Parameters of Computer Data Processing

“…It was pointed out that the discrete graph theory could be applied as an initial description by drawing up a generalized graph scheme of algorithm (GSA), designed to load the processor as the main service node. This problem is discussed in [1], where the possibility of partial ordering over the set of tasks (which are characterized by absolute and relative priority) is considered. This allows us to define the so-called "complete algorithm", which can be described logically by the individual algorithms A i and the conditions for their activation at a specific input information flow.…”

“…To conduct experiments in the analytical study of the stochastic time parameters of computer processing, a program module (function ESTIMATES) was created in the language environment APL2. As an input argument, it uses the matrix of determined paths SA, which is obtained after the execution of another APL2-funcion named PATHS, presented in [1] (see Figure 3 for program code and a sample experiment). As stated in [1], this function is "for reachability evaluation and determining all paths in the investigated algorithmic structure with argument matrix L".…”

“…In the general case, computer processing is a set of procedures performed on data streams. The procedures are implemented on the basis of separate algorithms, the unification of which is considered a complete algorithm of computer processing, realized at the macro level [1]. This processing forms the workload of the system, which is assessed by determining the probabilistic characteristics for the employment of the individual components.…”

“…Confirmation of this is the discussion presented in [7] of the contribution of computer simulations to the design of a specific system (reactor) as a critical analysis of the possibility of integrating several tools into a common computational package. A procedure for model investigation in the development of computer systems and processes is presented in [1], emphasizing the need to choose an appropriate modelling method consistent with the goal.…”

“…The present work should be considered a continuation of the research done in [1], and aims to present an addition to the developed set of modules for mathematical modelling of computer processing. For this reason, the organization of the model investigation is made on the basis of the procedure presented in [1], performing consistently the phases provided in it: goal defining; preliminary formalization of the object of study; mathematical modelling; program realization; conducting experiments; results analysis. The main contributions of the article can be summarized as follows.…”