Summary: When $n$ identical randomly located nodes, each capable of transmitting at $W$ bits per second and using a fixed range, form a wireless network, the throughput $\lambda (n)$ obtainable by each node for a randomly chosen destination is $\Theta(W/\sqrt{(n\log n)})$ bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmissionâ€™s range is optimally chosen, the bit-distance product that can be transported by the network per second is $\Theta(W\sqrt{An})$ bit-meters per second. Thus even under optimal circumstances, the throughput is only $\Theta(W/\sqrt n)$ bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance. The proof of lemma 4.8 is corrected in ibid. 49, No. 11, 3117 (2003).

##### MSC:

90B18 | Communication networks (optimization) |

94A05 | Communication theory |

68M10 | Network design and communication of computer systems |

60G35 | Signal detection and filtering (stochastic processes) |