Potential Accessibility in terms of Residents' Daily Activity

Abstract

This paper is concerned solely with graph theoretical modelling of potential accessibility measurement. Attempts will be made to establish a useful model to evaluate the potential accessibility in terms of residents' daily activity, and then to examine its usefulness with specific application to a hypothetical small island.Before proceeding further, a few definitions are in order. Potential accessibility is defined here for a vantage residence as access to all facilities (churches, banks, supermarkets etc.) in the region as a group. Therefore a residence with higher potential accessibility possesses a relatively higher advantage than the other residences as regards their daily activity. A trip is defined as a residence-to-residence circuit. A trip linkage is the spatial connection created when a resident moves from one facility to another or between his residence and facilities. Functional connectivity, which is a nonspatial concept, shows the frequency of opportunities to make trips. For example, the functional connectivity between residences and banks is higher than the functional connectivity between residences and hospitals, simply because the former trips are, on the average, more frequent than are the latter. A single stop trip is one in which the only trip linkages observed are between the residence and a single facility, whereas on a multistop trip, trip linkages are created between several facilities as well as between the residence and facilities (Figure 1).In order to build a reliable model, it is necessary to consider the following two important daily trip characteristics. First, a substantial portion of intraurban trips occurs on multistop journeys. According to Wheeler, trips involving more than one stop before returning home comprise a quarter to a third of all urban travel. Second, a trip linkage is a function of both distance (road and time distance) and functional connectivity. The shorter the distance, and the higher the functional connectivity, the stronger the trip linkage will be.The model is as follows:T=O·D+s1O·H·D+s2O·H2·D+……+sn-1O·Hn-1·D=n∑k=1sk-1O·Hk-1·D, where: T is the integral potential accessibility matrix (m×m), O is the accessibility matrix from residences to facilities (m×n), H is the accessibility matrix from facilities to facilities (n×n), D is the accessibility matrix from facilities to residences (n×m), s is the parameter, m is the number of residences, andn is the number of facilities.O·D shows the potential accessibility matrix in terms of single stop trips, O·H·D in terms of 2 stop trips and O·Hn-1·D in terms of n stop trips. Since daily trips are a mixture of single stop and multistop trips, we get the integral potential accessibility matrix by summing up the weighted potential accessibility matrices of single and p (p=2, 3, ……n) stop trips. The main diagonals of the matrix T indicate the integral potential accessibility of each residence.This model is then applied to a hypothetical small island with 19 facilities and 20 residences (Figure 5). Among these 19 facilities, there are two groceries and two supermarkets. In this analysis, the functional connectivity matrix is derived from a data set collected in 1949 in Cedar Rapids, Iowa, by the Traffic Audit Bureau.