On the Connectivity of Finite Wireless Networks with Multiple Base Stations

Connectivity is a basic quality of a network since it is required to obtain useful information out of the network. Research literature has mainly focused on the connectivity of wireless networks having a single connected network. However, due to diverse factors, it is feasible that a wireless network will have multiple base stations or sinks, i.e. it will have infrastructure. In this paper we analyze the connectivity of wireless networks with infrastructure and provide formulas to calculate the probability of having a connected network considering finite number of node platforms. With infrastructure the requirements for having a connected network may be relaxed since there can be more than one single-connected component of a network. Using combinatorics arguments we analyze the connectedness of a one- dimensional network over a line segment as a function of the available infrastructure-base stations and wireless nodes. This paper contains definitions for connected subnetworks that form a connected communication network; it also presents a one-dimensional network model and provides probability formulas for network connectivity for any given base stations arbitrary locations and the number of nodes. Through simulation we show the large increase in the probability of having a connected network when comparing a deployment with two base stations versus one with just one base station. This is of strong relevance when designing a wireless network.