AREAS , NODES AND NETWORKS : Some Analytical Considerations

In spatial interaction modelling, trips between origins and destinations within the same areal zone have a predominant influence on both the value of the gravity parameter and on the associated pattern of flows. Despite this, the relevant highly sensitive intrazonal impedance values are usually based on approximate average intrazonal distances or times. This situation has been identified in the literature as the ‘self potential’ problem. In this paper, integration over continuous space within the origin-destination zones is applied to not only compute the intrazonal flows more accurately, but also to evaluate the interzonal flows along shortest path routes meeting the interzonal links at efficient intermediate points. In particular, this general approach permits more accurate corrections to the conventional model, allowing, for instance, the usual approximations in determining average trip length to contiguous zones to be overcome. In addition, all jobs can be taken as concentrated at zonal centroids which are also nodes of the transport network. Alternatively, for outer zones, jobs may be taken as dispersed throughout the zonal area. This latter option reflects the greater dispersion of service jobs within suburban areas. The eventual aim is to develop practical ‘rules of thumb’ for correcting the conventional analysis. Flows between areal zones and several facility nodes can occur along plausible alternative multi-destination paths, rather than via one ‘abstract’ interzonal path to one destination, as usually considered in conventional spatial interaction models. Such destination/path choice is easy to handle in the relatively uncongested conditions characterizing off-peak discretionary travel. This paper examines facility choice via alternative round trip routes, attempting to discern the influence of ‘intervening opportunities’ on the potential for multi-stop trips without having to fully identify the actual trip chain. Such intervening opportunities can only be properly considered along the alternative paths of the actual network, as specified above.