Abstract:
Accessibility analyses are conducted for a variety of applications,
including urban planning and public health studies. These
applications may aggregate data at the level of administrative
units, such as provinces or municipalities. Accessibility between
administrative units can be quantified by travel distance. However,
modelling the distances between all administrative units
in a region is computationally expensive if a large number of
administrative units is considered. We propose a methodology
to model accessibility between administrative units as a homogeneous
Markov chain, where the administrative units are
states and standardised inverse travel distances act as transition
probabilities. Single transitions are allowed only between
adjacent administrative units, resulting in a sparse one-step
transition probability matrix (TPM). Powers of the TPM are taken
to obtain transition probabilities between non-adjacent units.
The methodology assumes that the Markov property holds for
travel between units. We apply the methodology to administrative
units within Tshwane, South Africa, considering only major
roads for the sake of computation. The results are compared to
those obtained using Euclidean distance, and we show that using
network distance yields more reasonable results. The proposed
methodology is computationally efficient and can be used to
estimate accessibility between any set of administrative units
connected by a road network.
