We study the scaling properties of a georouting scheme in a wireless multi-hop network of @math mobile nodes. Our aim is to increase the network capacity quasi linearly with @math while keeping the average delay bounded. In our model, mobile nodes move according to an i.i.d. random walk with velocity @math and transmit packets to randomly chosen destinations. The average packet delivery delay of our scheme is of order @math and it achieves the network capacity of order @math . This shows a practical throughput-delay trade-off, in particular when compared with the seminal result of Gupta and Kumar which shows network capacity of order @math and negligible delay and the groundbreaking result of Grossglausser and Tse which achieves network capacity of order @math but with an average delay of order @math . We confirm the generality of our analytical results using simulations under various interference models.
In the context of @cite_15 , the number of relays a packet has to traverse to reach its destination is @math . Consequently, @math must be divided by @math to get the useful capacity: @math . In order to ensure connectivity in the network, so that every source is able to communicate with its randomly chosen destination, @math must satisfy the limit @math . This leads to Gupta and Kumar's maximum capacity of @math with hot potatoes'' routing.
@cite_15
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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 spl lambda (n) obtainable by each node for a randomly chosen destination is spl Theta (W spl radic (nlogn)) 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 transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is spl Theta (W spl radic An) bit-meters per second. Thus even under optimal circumstances, the throughput is only spl Theta (W spl radic 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.