Connecting the newly generated distribution points back to their source nodes requires constructing a graph which weighs energy expenditure in two urban processes via their correlated network properties:
1. Characteristic Path (Trip) Length - which measures the average distance to move material from a particular source to each distribution node attached to it, and as a result influences the likeliness that the trip be taken on foot or via the use fossil fuel based transportation.
2. Total Network Length - which reflects the cost for the construction and ongoing maintenance of city streets (or other urban infrastructure)
Unfortunately, these properties are inversely proportional to each other. Direct connection of each distribution node to its source node provides the shortest possible characteristic trip length (diagram x.5). However the resulting network structure fails to take advantage of node adjacencies and is therefore highly wasteful of material and is high in maintenance. The overall network length of such a network is significantly longer than say a minimum spanning tree which instead links each vertex to its closest (or lowest weighted) neighbour. Such a network uses the least material to connect all vertices however results in an extremely high percentage of detour between nodes as measured by comparing the direct path length, to the newly constructed path length.
To construct a network topology that would provide the highest benefit for cost, we require a hybrid which identifies a range of solutions within which the trade-offs are reasonable - neither trip lengths nor total network length are dramatically increased by decreasing the other.
Our solution is a parametric tool which allows a user to step by step increase the amount of allowable detour and measure the effect on characteristic trip length and overall network length. Allowable detour is controlled by the measure of the angle drawn between: A the point to be connected, B the source node and C the closest neighbour vertex to A. If the angle α < the specified angle threshold, the new node is allowed to connect through the neighbour, if not it checks the next closest neighbour between it and the source and repeats until cycling through all the points between it and the source. If no neighbour is found within the angle threshold the new node connects directly to the source.
(αd) Detour Angle, Branching Angle, Allowable Detour angle, allowable angle threshold?
(T) Average Trip Time
(N) Total Network Length
Method & Observations
A Network Paths script component was written which takes the set of source and distribution points generated in the simulation as inputs and connects them with a branching network with the wholesale node at the 'source' and retail nodes at the branching junctions. Topology of the paths was varied by adjusting the Detour Angle. Two sample tissues were selected for testing the effects of the Network Paths component: D=220 | F=0.85 and D=220 | F=0.95. These were selected in order to compare the difference in networks required to connect tissues of the same density but with very different Open Space Ratios, and therefore many more wholesale nodes.
Evaluation & Conclusions
What we see is that by increasing the Detaour Angle, N decreases in overall length while T, Average Trip Time increases. What we are interested in is the rate of change in these values and the range within which the trade-offs are reasonable. This should be evident in a point in the graph which exhibits a high degree of curvature or a sudden steep drop-off in the slope.
In the first tissue, the detour angle affects significantly the values measured. The angle 30 is considered the critical value where the returns trails off. In the second tissue, the ranges of values for both the overall network length and the average trip time are much narrow, therefore changing the detour angle has less effect on the network . This is accounted for by the fact that the number of wholesale nodes is considerably larger than in the first case while the number or retail nodes remains almost the same.