On the capacity of multihop slotted ALOHA networks with regular structure

The capacity of networks with a regular structure operating under the slotted ALOHA access protocol is investigated. Circular (loop) and linear (bus) networks are first examined, followed by consideration of two-dimensional networks. For one-dimensional networks, it is found that the capacity is basically independent of the network average degree and is almost constant with respect to network size. For two-dimensional networks, it is determined that the capacity grows in proportion to the square root of the number of nodes in the network, provided that the average degree is kept small. In addition, it is found that reducing the average degree (with certain connectivity restrictions) permits a higher throughput to be achieved. Some of the peculiarities of routing in these networks are also studied.