Rayba S. Theory and mathematical models of the wireless sensor network with random access.

The dissertation is devoted to solving an important scientific problem of a theoretical principles and probabilistic models of Wireless Sensor Network (WSN) with random access and analysis of quality of transmission in these networks. The elaborated models, based on mathematical apparatus PASTA (Poisson Arrivals See Time Averages), were used for the practical implementation of the implemented solutions for monitoring hospital and botanical field experiment among others. Created probabilistic models of single-hop type network leads to better availability of WSN in many practical applications. The main feature of the developed models of random access networks is: one-way transmission (simplex) in information transmission from all nodes to the base station. All nodes use the same frequency channel at random points in time during the transmission of a single protocol. The other advantage is also a single- channel work of the base station. The nodes stay completely independent of each other, they do not communicate between each other, because instead of receiving systems they have broadcasting ones. Lack of receivers at nodes (№ duplex type communication) allows for a very large arrangement simplify and in the processing information range at the node (algorithms simplification). This solution also allows for very big savings of power supply for node (lack of power for receiver which is monitoring the network condition). Above features allow for low construction costs of nodes. Very short protocol possible to use in the network has several advantages, especially can reduce the energy consumption of node, but essentially is an extremely low collision probability of transmitted information packets by nodes. Low probability of collision qualifies the use of these models of the network in many practical applications. For the practical applications purposes there have been developed two protocols adapted to communication in proposed network models with random access. Models have been elaborated, with the same average time between transmissions. Equal average time between transmissions is the criterion of assignment nodes working as one group. Then elaborated were models with division into groups of nodes with different times between transmissions as a criterion for belonging to the same group. A special achievement in stochastic modeling of network access is developed network models with random network parameters, which is a particular innovation of this work. The selected network parameters such as: random number of nodes (situation well modeling networks with mobile nodes), random number of groups (situation well modeling networks when the conditions specifying belonging to particular groups are changing over time),random average time between transmissions in given group (situation well modeling networks using different sensors, with various physical quantities at the same time with different reading frequencies), random percentage participation of nodes in given group, allowing for significant improvement of the network transmission quality. Randomized network parameters in part or all, depending on the foreseen application allows for better organization of the radio space traffic by reducing the average number of packets transmitted per unit time. This allows for better matching of used model to implement a specific task. For each of these models, there was conducted an quality analysis of the transmission, obtaining formulas for the collision probability of signals in network in case of lack of division into group, with division into groups, in case of randomization particular parameters and the collision probability formula in which all parameters were randomized. The probability of collision is a parameter characterizing the transmission quality of information in the network. It is possible to improve the quality (decrease BER) by multiple repetition of the message (cyclic or randomized), which even in case of collision reduces its effects. The analysis shows that the elaborated network model with random access allows to maintain the quality of transmission at selected level of collision probability. In addition, based on elaborated models, simulation study was conducted to verify the theoretical formulas for the collision probability. Computer simulations of the network work confirmed a compatibility of obtained theoretical formulas for the collision probability with results from computer simulation. For implementation purposes created network models there have been developed communication protocols which allow to obtain a higher efficiency of WSN.