A Statistical Analysis of the Effect of Capacity Limitation and Retry for Hierarchical Wireless Hybrid Networks

We investigate a hierarchical wireless hybrid network, implementing two different network paradigms: ad hoc and infrastructure-based systems, where mobile gateways, equipped with both cellular and infrastructure-less air interfaces, allow integration of the two separate paradigms. The paper reports results achieved through a mathematical analysis of the topology of wireless links, providing the distribution of the number of lowest-level nodes attached to the highest level. Nodes have a maximum capacity, and seek service at the upper level through a retry mechanism where the nodes are addressed according to a ranked list based on the level of received power. The mathematical analysis provides a means to allow access control, depending on the maximum number of radio resource units available at each node and the maximum number of retries at each level. Wireless nodes at different levels are uniformly distributed over the bi-dimensional plane with different densities; path loss and shadowing are included with different propagation parameters, different air interfaces are used, and different hard capacities characterise the nodes at the different levels. With respect to other papers recently presented by the authors to other conferences, this work focuses on the role of the node capacity limitations and the maximum number of retries