Architectures and connection probabilities for wireless ad hoc and hybrid communication networks

Ad hoc wireless networks involving large populations of scattered communication nodes will play a key role in the development of low power, high capacity, interactive, multimedia communication networks. Such networks must support arbitrary network connections and provide coverage anywhere and anytime. This paper partitions such arbitrarily connected network architectures into three distinct groups, identifies the associated dual network architectures and counts the number of network architectures assuming there exist N network nodes. Connectivity between network nodes is characterized as a random event. Defining the link availability p as the probability that two arbitrary network nodes in an ad hoc network are directly connected, the network connection probability fN(p) that any two network nodes will be directly or indirectly connected is derived. The network connection probability fN(p) is evaluated and graphically demonstrated as a function of p and N. It is shown that ad hoc wireless networks containing a large number of network nodes possesses the same network connectivity performance as does a fixed network, i.e., for p > 0, limN→∞ fN(p) = 1. Furthermore, by cooperating with fixed networks, the ad hoc network connection probability is used to derive the global network connection probability for hybrid networks. These probabilities serve to characterize network connectivity performance for users of wireless ad hoc and hybrid networks, e.g., IEEE 802.11, IEEE 802.15, IEEE 1394–95, ETSI BRAN HIPERLAN, Bluetooth, wireless ATM and the world wide web (WWW).