Optimum transmission radii for packet radio networks or why six is a magic number

Consideration is given to the capacity of packet radio networks in which the nodes are randomly located and which use slotted ALOHA as the access scheme, transporting messages through the network in a stored and forward fashion. It is shown that for a constant average degree in a random network it is possible to obtain a throughput proportional to the square root of the number of nodes on the network. It is also shown that the optimal average degree is approximately 6. Using a degree less than 6 causes drastic reduction in capacity of the network (the network also becoming disconnected) whereas exceeding 6 causes only gradual degradation (provided it is not a case of a degree which is an increasing function of the number of nodes).