0.8 0.6 0.8 g8≌5四 06 0.2 00.1020.304050.60.70.80.91 Delivery probability 0510152025303540 Figure 4: The distribution of delivery probabilities of links used in Srcr routes, at the bit -rates chosen by SampleRate. The median is 0.8, meaning that Srcr often uses links with loss rates of 20% or more (multi-hop TCP, loss matrix) 乏500 3. 4 Effect of density Mesh networks are only effective if the node density is sufficiently high. This section examines the effects of density y simulating different size subsets of Roofnet; subset size and density are roughly proportional, since the network area is about the same for all subsets 0 The simulations function as follows For each subset size 0510152025303540 n.a random set of n roofnet nodes are selected. An estimate Number of nodes of the multi-hop throughput between every pair in the subset is computed, using only members of the subset as potential forwarders. The throughputs are estimated along the route that gives the highest throughput with Equation 1 and the single-hop TCP data-set Figure 5 shows the simulation results. The z axes show the subset size. The top graph shows the fraction of node pairs in the subset that are connected by a route that pro- vides throughput of more than one kilobyte per second The middle graph shows the average throughput over all pairs. The bottom graph shows the average hop-count of the routes. The ticks in each vertical line show 25th. 50th and 75th percentiles over 100 random subsets 1015202530354 The network only starts to approach all-pairs connectiv Number of nodes ity when there are more than 20 nodes, corresponding to a density of about five nodes per square kilometer. As the lumber of nodes increases, the average throughput also in- Figure 5: The simulated effects of node density on creases. The increase in hop-count in the third graph sug connectivity and throughput. The a axes show the gests the reason: a denser network offers a wider choice of number of nodes in the network. From top to bot- short high-quality links, though using them causes routes t tom, the y axes show the fraction of node pairs that have more hops achieve throughput of more than one kilobyte per second; the average throughput over all pairs; and 3.5 Mesh robustness the average hop-count. Each bar shows the 25th This section investigates the benefits of the routing choices 50th, and 75th percentile over 100 random sub- afforded by a mesh architecture and omni-directional anten- sets. Increasing density causes the network to be more highly connected, and increases the average The most immediate measure of a mesh network's robust throughput; higher density allows routes to be con- ness is the number of potentially useful neighbors each node tructed from shorter, higher-quality hops.(Simu- has. Figure 6 shows a histogram of the number of neighbo lated from single-hop TCP) for each node, where a neighbor is defined as a node to which the delivery probability is 40% or more. Most nodes have0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Cumulative Fraction of Links Delivery probability Figure 4: The distribution of delivery probabilities of links used in Srcr routes, at the bit-rates chosen by SampleRate. The median is 0.8, meaning that Srcr often uses links with loss rates of 20% or more. (multi-hop TCP, loss matrix) 3.4 Effect of Density Mesh networks are only effective if the node density is sufficiently high. This section examines the effects of density by simulating different size subsets of Roofnet; subset size and density are roughly proportional, since the network area is about the same for all subsets. The simulations function as follows. For each subset size n, a random set of n Roofnet nodes are selected. An estimate of the multi-hop throughput between every pair in the subset is computed, using only members of the subset as potential forwarders. The throughputs are estimated along the route that gives the highest throughput with Equation 1 and the single-hop TCP data-set. Figure 5 shows the simulation results. The x axes show the subset size. The top graph shows the fraction of node pairs in the subset that are connected by a route that pro￾vides throughput of more than one kilobyte per second. The middle graph shows the average throughput over all pairs. The bottom graph shows the average hop-count of the routes. The ticks in each vertical line show 25th, 50th, and 75th percentiles over 100 random subsets. The network only starts to approach all-pairs connectiv￾ity when there are more than 20 nodes, corresponding to a density of about five nodes per square kilometer. As the number of nodes increases, the average throughput also in￾creases. The increase in hop-count in the third graph sug￾gests the reason: a denser network offers a wider choice of short high-quality links, though using them causes routes to have more hops. 3.5 Mesh Robustness This section investigates the benefits of the routing choices afforded by a mesh architecture and omni-directional anten￾nas. The most immediate measure of a mesh network’s robust￾ness is the number of potentially useful neighbors each node has. Figure 6 shows a histogram of the number of neighbors for each node, where a neighbor is defined as a node to which the delivery probability is 40% or more. Most nodes have 0 0.2 0.4 0.6 0.8 1 0 5 10 15 20 25 30 35 40 Fraction of Pairs Connected Number of Nodes 0 100 200 300 400 500 600 700 0 5 10 15 20 25 30 35 40 Average Throughput (kilobits/s) Number of Nodes 0 1 2 3 4 0 5 10 15 20 25 30 35 40 Average Number of Hops Number of Nodes Figure 5: The simulated effects of node density on connectivity and throughput. The x axes show the number of nodes in the network. From top to bot￾tom, the y axes show the fraction of node pairs that achieve throughput of more than one kilobyte per second; the average throughput over all pairs; and the average hop-count. Each bar shows the 25th, 50th, and 75th percentile over 100 random sub￾sets. Increasing density causes the network to be more highly connected, and increases the average throughput; higher density allows routes to be con￾structed from shorter, higher-quality hops. (Simu￾lated from single-hop TCP)