Co-ordination of Joint Headways

Abstract

Bus-stops are often shared by several different services. Passengers may enjoy shorter waiting times I than if stops were specific to services because very often most of the services at the same bus-stop run on similar routes and will take the passengers close to their destinations. However, there may be times when after a long gap a few buses come at the same time. Such gaps are unpleasant for the passengers. Bus operators do not like this to happen either, as the buses would be unevenly loaded and this would cause other problems. Schedulers therefore try to co-ordinate the buses such that the intervals between bus arrivals on a common stretch of road are as evenly distributed as possible — at least theoretically in the timetables. Of course, any adjustment of timings will have to be justified cost-effectively, for example, the subsequent schedules should normally use the minimum number of buses. We shall call this kind of planning and scheduling exercise Headway Integration.

Departures at regular intervals (called headways) and extensively overlapping routes are characteristics of urban bus services in the U.K. and many other countries. For passenger convenience and satisfaction, and for operating efficiency, it is very desirable to achieve joint headways that are as regular as possible on overlapped stretches of routes. Currently available bus scheduling packages are not sufficient for this purpose. Most of them are good at minimising vehicle usage, but lack capability of retiming the trips necessary in co-ordinating joint headways.

This paper reports on an interactive heuristic approach that has led to the implementation of a computer system called HINT (standing for ’Headway Integration’) for co-ordinating joint headways. The approach centres on a set of system targets that reflect the current objectives such as what joint headways on which stretches of routes are desirable. The major role of the heuristics is to find quickly the best few solutions satisfying the system targets. The interactive utilities assist the scheduler to browse through the results yielded by the heuristics and analyse them in a systematic manner. More importantly, the scheduler can interactively exercise his expertise and local knowledge to override the default setup of system targets, and continually revise them in the light of further findings.

HINT has already been demonstrated to some bus operators in the U.K., who have shown much interest in it. Since HINT has been developed out of a research project on a specific computer installation, some conversion work would be needed before it can be generally available for commercial use.