Review: "A coverage model for improving public transit system accessibility and expanding access, A.T. Murray, Annals of Operations Research, 123, 2003, 143-156.

Jeremy Hubble - UPP 565 - March 14, 2005

A model for the optimal spacing of public transit stops is developed. This model was applied to Brisbane, Australia to determine optimal restructuring of the transit system to improve coverage and minimize travel times.

The base of the model is the stated preference for distance from a transit stop. In the sample used of Brisbane, a 400 meter standard is used. Thus, all locations within 400 meters of a transit stop have access to transit.

Three different “problems”  were used as the basis for allocating transit stops:

1. Location Set Covering Problem (LSCP) - seeks to minimize the number of stops in a system while keeping service to all currently served areas, and either keeping or removing current stops. This also helps to measure the efficiency of the transit system.
2. Maximal Covering Location Problem (MCLP) - maximizes the proportion of the population that has access to transit service. It can identify areas that are the most viable transit areas. Some current areas may be removed to poor viability, while being replaced with more viable areas. (It does not, however, account for political problems associated with removing transit service from areas.)
3. Hybrid Set Covering Problem (HSCP) - seeks to maximize new service provided by new transit stops. Constraints include continued transit service to each currently served area. 

In the case of a Brisbane, the bus system has 7543 stops, and serves 86% of the regional population. In performing the LSCP analysis, it was determined that only 1 in 10 transit stops were needed to conform to the 400 meter standard.

For adding new service, it was initially acknowledged that the spatial structure of the region made some areas unfeasible to serve. Thus, 'full' coverage would entail service to approximately 99% of the area. This could be accomplished by siting a stop on every intersection within the area, adding 11,766 new stops. However, this capacity would be excessive.

Using the HSCP analysis, an efficient transit coverage for all of Brisbane was determined. The siting of 685 "stop pairs", including 160 new stops and 525 existing stops would provide coverage to 98.88% of Brisbane. These 1370 total stops are significantly less than the number of stops currently in the system, even with the increased amount of coverage. The implication is that transit travel can be faster with the reduced number of stops, while still providing adequate service for people.

While the analysis provides theoretical means for siting bus stops, there are significant practical considerations that should be addressed also. Redundant transit stops may have different destinations. Furthermore consolidating stops of multiple transit lines may actually create more problems than it solves. (large backups at stops may slow the traffic, eliminating gains in efficiency.) Also, the nature of complete trips needs to be taken in to account. A 400 meter trip to the bus stop is not too bad. Adding another 400 meter trip at the destination makes things annoying. A few 400 meter trips for transfers in the middle of the journey, however, makes the trip excruciating. Planning an optimal network based on demographic data is a good start to planning new transit networks. However, the actual needs of transit riders should also be taken in to account.