The Spatial Capacity of a Slotted ALOHA Multihop Packet Radio Network with Capture

In this paper we determine throughput equations for a packet radio network where terminals are randomly distributed on the plane, are able to capture transmitted signals, and use slotted ALOHA to access the channel. We find that the throughput of the network is a strictly increasing function of the receiver's ability to capture signals, and depends on the transmission range of the terminals and their probability of transmitting packets. Under ideal circumstances, we show the expected fraction of terminals in the network that are engaged in successful traffic in any slot does not exceed 21 percent.