Step 3 – applying the (λ) parameters

Step 3 involves application of the negative exponential equations to calculate the ‘raw accessibility indices’.

Once the series of paths was calculated from each measurement location to the multiple instances of the activity under consideration, the travel times along these paths were converted to a measure of accessibility called the ‘raw accessibility index’ (R). This was done by inputting the travel times into the negative exponential equations.

The raw accessibility index is described in figure 15.4.

Figure 15.4   Raw accessibility index

Travel time distribution equation:   R =eλ t

                R              =            raw accessibility index

                                                (percentage of people who would make a trip of length t)

                t               =            time in minutes

                λ              =              travel time distribution parameter

So for t = time in seconds use:        R =e–λ ( t / 60)      


The raw accessibility index range extends from 0 to 1. A score of ‘1’ means the destination site is immediately adjacent to the origin so has the maximum possible raw accessibility score.

This results in each measurement location having multiple raw accessibility indices, which record the percentage of people who would make the trip to each instance of the destination activity (figure 15.5).

Figure 15.5   Application of the travel time distribution equation to the series of path times

a) using an appropriate value for λ based on the mode and activity type

b) yields a series of values for the raw accessibility indices for the site being considered


Given the NZHTS (chapter 13) only yielded statistically significant results to allow the definition of the (λ) parameters by journey purpose for walking and private vehicle modes, the all-purpose (λ) parameters for walking, cycling, public transport and private vehicle in MUA were used in the calculation methodology (shown in table 15.1).

Table 15.1    All-purpose (λ) parameters

Transportation mode

All purpose (λ) parameters


0.077 (0.089)


0.069 (0.072)

Public transport

0.037 (0.041)

Private vehicle

0.080 (0.078)

Note: The figures shown in brackets are the actual values used for the case study and reflect earlier derived values based on trip legs rather than the more comprehensive methodology of trip chains described in chapter 13.