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 determine their influence on calibration of the value of the gravity parameter itself. In addition, whereas all trips are assumed to have destinations corresponding to nodes of the transport network, interzonal trips, starting from dispersed origins, are assigned shortest path routes to join the interzonal links at efficient intermediate points. In the analysis, further approximations incurred in evaluation of the sets of origin/destination flows between contiguous zones are also identified. The eventual aim is to develop practical ?rules of thumb? for correcting the conventional analysis. Flows between areal zones and facility nodes may occur along several plausible alternative paths, rather than via one abstract ?interzonal? path, as usually considered in conventional spatial interaction models. Such destination/route choice is easy to handle in the relatively uncongested conditions characterizing off-peak discretionary travel. This paper examines facility choice via alternative routes, as well as attempting to discern the influence of ?intervening opportunities?. It is indicated how intervening opportunities may influence discretionary travel positively, in contrast to their identified negative influence on the probability of choosing the final destination in journey to work travel. Such intervening opportunities can only be considered meaningfully along the alternative paths of the actual network, as specified above.