Step 2 – solving for shortest path

The second step in the methodology involves calculating the ‘cost’ to travel from the measurement locations (origins) to the core+ activities (destinations), across each of the four transport mode networks.

The travel cost is modelled using travel time, rather than travel distance or real or perceived travel cost. This allows intersection delays and variable travel speeds such as walking and bus travel to be modelled in the same network and is a significant refinement on travel distance alone but other routing algorithms are available.

Of course not all route choice is based on least travel time and hence other variables such as cost would be useful to further test the accessibility results. Additionally, quality inputs such as those determined via community street reviews (Abley 2010) or via other mathematical models that predict walking quality (Abley and Turner 2011) provide an additional level of refinement. Other routing choice such as a cyclist’s preference for safety over speed is another refinement for cycle routing. The Abley Cycle Route-Choice Metric (ACRM) proposed by Rendall et al (2012) is an enhancement in this area. Refer to chapter 14 for details on the construction of suitable networks.

In order to limit the processing time required to perform the network analysis, it was necessary to set a limit for the maximum allowable journey time. This maximum travel time threshold was set to the 95th percentile trip duration calculated from the NZHTS data and by rearranging the travel time frequency function for the mode in question. The rearranged equation form is shown in figure 15.2.

Figure 15.2   95th percentile travel time equation

Solving y = eλt, for the travel time completed by less than 5% of NHTS respondents, yields:

0.05 = eλt


t =  -  ln(0.05) /  λ                               ; t = time in minutes


t = - 60 * ln(0.05) /  λ        ; t = time in seconds


While this approach is computationally efficient it results in a zero accessibility outcome for journeys beyond this threshold. A further enhancement of this methodology could be to calculate the travel time to the nearest destination up to a much higher threshold.

The shortest travel time path is calculated by each model to all activities that are within the maximum trip travel time (refer to figure 15.3)

 Figure 15.3  Calculation of shortest travel times

a) Find the shortest path to the closest destination (in terms of travel time)

b) Calculate the shortest paths by travel time to the remaining instances of the activity type


Steps 2 to 4 of this methodology are repeated 32 times, once for each of the eight activity types and four transportation modes.