Travel time is a necessary but not a totally sufficient condition for access to be achieved. Even so, starting with travel time analysis helps to identify locations with or without access for further analysis of cost, safety, quality and other variables affecting access to be considered later.

The number of people
willing to make a journey to a destination generally decreases as the length of
the journey increases; it also changes by transportation mode and journey
purpose. This effect is described as deterrence to travel. In transport
planning deterrence is modelled using *deterrence
functions*; these are mathematical models that have been fitted to travel
data derived from surveys. The accessibility of an activity decreases as the cumulative
deterrence of reaching the activity increases. Therefore, determining deterrence functions is an
important first step in developing any accessibility model.

The deterrence
function is often conveniently represented in transport planning with a *negative exponential *(decay) function
since this can be calibrated to fit observed travel behaviour using the form:

where λ is a constant that defines the slope of the decay curve. The tails of these types of curves often need to be curtailed to fit observed behaviour because there are observed maximum travel time thresholds and practical minimum travel time thresholds that need to be applied to all journeys to represent real travel choices.

Other curve fitting
methods can be applied, which may provide a better fit to the observed
trip-making data for travel time but are not as widely used and are much more
computationally intensive. De Vries et al (2004) identified that logistic decay
functions provide the best fit when modelling travel costs, particularly for
intermediate distances where commuting behaviour is highly elastic. The *weighted logistic decay* function follows
the form:

where *α* defines the *t*
value of maximum change and* **β* is a shape-fitting parameter.

However, the logistic decay function cannot easily be fit to data in
common software packages such as Microsoft Office Excel, nor is the formulation
widely enough applied in transport planning that there is a body of parameters available
for comparison with other countries. For these reasons the exponential decay
curve formulation has been selected for this research. Henceforth in this
report λ is termed the *travel time distribution* parameter.

λ parameters for walking, cycling, bus and private motor vehicle were developed by analysing data from the NZHTS. A description of the NZHTS, as extracted from the NZTA website, is presented in appendix C.

The NZHTS provides the best overall source of travel pattern data within New Zealand. Given the national coverage and size of the NZHTS, it is assumed participants in the NZHTS have a level of access to activities and spatial separation from activities that is representative of the entire population on average. The NZHTS data therefore provides a sound basis for developing a national methodology for measuring accessibility.

This chapter is separated into three subsections:

1 The methodology used to determine the value of λ parameters

2 The results of the analysis

3 A discussion of the results.