On Problem of Conflict Interaction of Two Players in the Network Environment

In developing the network management systems often encountered a situation where there is a need to deal with malicious intrusion attempts aimed at obstructing the work. In this case, methods of management based on fluid models and a discrete controlled random walk model requires certain changes. In this work a generalization of the usual models of single server queue which can describe the attacking action and behaviour of the system of protection is presented. Formulation and analysis of the problem are proposed. There are conditions found under which the game can be finished. Introduction Areas where one can apply network models are very different – information networks, telecommunications, gas transportation and energy systems, distributed production processes. Information network applications are especially important. Today networks are related to almost all sides of human activity. As a result, security and reliability of information flows directly affect the quality of service, efficiency and overall economic development of entire industries. Networks complexity and interconnections are growing constantly. Today most of organizations depend on reliable working of the information networks. On the other hand, the vulnerability of networks is also increasing every year. This is due mainly to the fact that more potential attackers have access to resources with networks growing. Nowdays, network is a complex (often nonlinear) system with significant unknown disturbance. Our influence possibilities are constrained by some parameters called control parameters. An important point of control theory is its flexible approach to modeling. We typically consider a linear, deterministic model. In the work [4] said an idea that the control system should be simplest model that capture essential feature of the system to be controlled. Let us define network terminology. The network here consists of a finite set of nodes. Each node contains a set of buffers. These buffers can hold finite amount of packets. One or more servers process packets at a given buffer. A general stochastic model defined in the work [4]. Let us make a short summary. Define the vector valued queue-length process Q that evolves on N R . The vector valued cumulative allocation process u N R Z   . The ith component of ) (t Z , denoted ) (t Zi , is equal to the cumulative time that the activity i has run up to time t. The evolution of the queue-length process is described by the vector equation,