On the Capacity of Multihop Slotted ALOHA Networks with Regular Structure

In this paper we investigate the capacity of networks with a regular structure operating under the slotted ALOHA access protocol. We first consider circular (loop) and linear (bus) networks and then proceed to two-dimensional networks. For one-dimensional networks we find that the capacity is basically independent of the network average degree and is almost constant with respect to network size. For two-dimensional networks we find 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. Furthermore, we find that reducing the average degree (with certain connectivity restrictions) allows a higher throughput to be achieved. We also investigate some of the peculiarities of routing in these networks.