Informatica

The result of simulation of an idealized thin wet film connecting fixed points in the Euclidean plane is a length-minimizing curve. Gradually increasing the exterior pressure we are able to achieve the film configuration near to the Steiner minimal tree. This film evolution may be an interesting tool for solving the Euclidean Steiner problem, but several dead-point situations may occur for a certain location of fixed points. A continuous evolution of the film is impossible by increasing the pressure in these situations. The investigation of dead-point situations gives the ways of overcoming the difficulties of dead-point situations and continuing the film evolution by temporarily decreasing pressure.

The Steiner problem asks for the shortest network that spans a given set of fixed points in the Euclidean plane. The problem is NP hard.

The paper deals with a simple model of the competition of two queuing systems, providing the same service. Each system may vary its service price and its service rate. The customers choose the system with less total service price, that depends on the waiting time and on the service price. The possibility for the existence of equilibrium is investigated. Simple cases are investigated analytically. It is shown that the Nash equilibrium exists in special cases only. A modification of the Stakelberg equilibrium is proposed as a model of competition with a prognosis. This prognosis helps form more stable prices and more stable strategies of competitors. The case of social economics is investigated, too. The dynamics of the competition of more realistic stochastic queuing systems is investigated by Monte Carlo simulation. The simulative analysis is realized by means of a rule-based simulation system.

The model of the HIV/AIDS infection spread is proposed and investigated. The paper deals with some specific features of the disease spread at the initial stage, i.e., when the infection extent is small enough. We propose a model characterizing any risk group by three differential equations. These equations describe the dynamics of active susceptible, active infected, and passive infected individuals. The evaluation of parameters from demographical and medical data is discussed. The package for the investigation of infection is presented, and possibilities to control the infection are shown. Two general directions of control may be distinguished: the HIV/AIDS blood tests and the publicity and availability of protective means. The investigations showed under what conditions the HIV/AIDS infection may be stopped.

The aggregate approach to the formal description, verification and simulation of computer network protocols is considered in the paper. With this approach, the offered design stages can be performed using a single mathematical scheme. The reachability analysis method and the program proof technique are viewed as methods for correctness analysis. The proposed approach for correctness analysis and model construction was used in creating the protocol analysis system PRANAS.