10 500 Most Effect 876543210 兰与 0 5 50100150200250 Number of Neighbors Number of links eliminated 1200 Figure 6: Histogram of the number of neighbors s as a “ neighbor if it has 1000 greater than 40% delivery probability for 1 megabit Fastest lt Most Effect per second packets. (loss matrix a800 400 987654321 Number of links eliminated Figure 8: Simulated average throughput and con- nectivity among all pairs versus the number of links elininated. Each curve shows the result of elimi- nating links in a particular order.(Simulated from Number of Distinct First Hops single-hop TCP) Figure 7: Histogram of the number of different first hops that Roofnet nodes use in all-pairs routes. most: Long x Fast deletes the link with the highest product (multi-hop TCP) of distance and throughput: Fastest deletes the link with the highest link throughput; and the Random line shows the average of 40 simulations in which links were deleted in many neighbors, though there are a few poorly-connected random orders nodes. Figure 8 shows that the best few links contribute notice- If a node never routes through one of its neighbors, the ably to average throughput, but that dozens of the best neighbor's value is questionable. For example, if most nodes links must be eliminated before throughput is reduced by routed through only one or two neighbors, it might be worth half. The fastest links are generally more important than the sing directional antennas pointing just at those neighbors long/fast links for throughput, though the first few long/fast Figure 7 shows a histogram of the number of unique first hop links are more important than the fastest links, and both neighbors used by each node when routing to all the other kinds are disproportionately important(deleting them low odes in the network. While some nodes do indeed route ers throughput faster than deleting random links ). On the hrough only one or two neighbors, the majority of nodes ther hand, the long/fast links are more con- Ise many more neighbors. In this sense Roofnet makes good nectivity than the fastest links use of the mesh architecture in ordinary routing Figure 9 shows the effect on throughput of cumulatively Another aspect of robustness is the extent to which the eliminating the best-connected nodes. The throughputs are network is vulnerable to the loss of its most valuable links. from the multi-hop density data set. The best-connected The graphs in Figure 8 shows how the average through- nodes are identified by looking for the nodes that appear put and connectivity among all pairs decreases as individual links are deleted. The results are simulated with Equation 1 Figure 9 shows that the best two nodes d the single-hop TCP data-set. Each line shows the cum for performance, since losing both decreases lative effect of a different deletion order. Most Effect deletes throughput by 43%. The penalties for losing ns more nodes the link whose absence decreases average throughput the re more gradual.0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 Nodes Number of Neighbors Figure 6: Histogram of the number of neighbors per node. A node counts as a “neighbor” if it has greater than 40% delivery probability for 1 megabit per second packets. (loss matrix) 0 1 2 3 4 5 6 7 8 9 10 0 5 10 15 20 25 Nodes Number of Distinct First Hops Figure 7: Histogram of the number of different first hops that Roofnet nodes use in all-pairs routes. (multi-hop TCP) many neighbors, though there are a few poorly-connected nodes. If a node never routes through one of its neighbors, the neighbor’s value is questionable. For example, if most nodes routed through only one or two neighbors, it might be worth using directional antennas pointing just at those neighbors. Figure 7 shows a histogram of the number of unique first hop neighbors used by each node when routing to all the other nodes in the network. While some nodes do indeed route through only one or two neighbors, the majority of nodes use many more neighbors. In this sense Roofnet makes good use of the mesh architecture in ordinary routing. Another aspect of robustness is the extent to which the network is vulnerable to the loss of its most valuable links. The graphs in Figure 8 shows how the average through￾put and connectivity among all pairs decreases as individual links are deleted. The results are simulated with Equation 1 and the single-hop TCP data-set. Each line shows the cumu￾lative effect of a different deletion order. Most Effect deletes the link whose absence decreases average throughput the 0 100 200 300 400 500 600 700 0 50 100 150 200 250 300 Average Throughput (kbits/sec) Number of Links Eliminated Random Long x Fast Fastest Most Effect 0 200 400 600 800 1000 1200 0 50 100 150 200 250 300 Disconnected Pairs Number of Links Eliminated Random Long x Fast Fastest Most Effect Figure 8: Simulated average throughput and con￾nectivity among all pairs versus the number of links eliminated. Each curve shows the result of elimi￾nating links in a particular order. (Simulated from single-hop TCP) most; Long x Fast deletes the link with the highest product of distance and throughput; Fastest deletes the link with the highest link throughput; and the Random line shows the average of 40 simulations in which links were deleted in random orders. Figure 8 shows that the best few links contribute notice￾ably to average throughput, but that dozens of the best links must be eliminated before throughput is reduced by half. The fastest links are generally more important than the long/fast links for throughput, though the first few long/fast links are more important than the fastest links, and both kinds are disproportionately important (deleting them low￾ers throughput faster than deleting random links). On the other hand, the long/fast links are more important for con￾nectivity than the fastest links. Figure 9 shows the effect on throughput of cumulatively eliminating the best-connected nodes. The throughputs are from the multi-hop density data set. The best-connected nodes are identified by looking for the nodes that appear in the most all-pairs routes. Figure 9 shows that the best two nodes are important for performance, since losing both decreases the average throughput by 43%. The penalties for losing more nodes are more gradual