Millionen von Menschen werden allein in Deutschland täglich von
Bussen, Bahnen und Flugzeugen transportiert. Der öffentliche
Personenverkehr (ÖV) ist von großer Bedeutung für die
Lebensqualität einzelner aber auch für die Leistungsfähigkeit ganzer
Regionen. Qualität und Effizienz von ÖV-Systemen hängen ab von
politischen Rahmenbedingungen (staatlich geplant,
wettbewerblich organisiert) und der Eignung der Infrastruktur
(Schienensysteme, Flughafenstandorte), vom vorhandenen
Verkehrsangebot (Fahr- und Flugplan), von der Verwendung
angemessener Technologien (Informations-, Kontroll- und
Buchungssysteme) und dem bestmöglichen Einsatz der
Betriebsmittel (Energie, Fahrzeuge und Personal). Die hierbei
auftretenden Entscheidungs-, Planungs- und
Optimierungsprobleme sind z.T. gigantisch und "schreien"
aufgrund ihrer hohen Komplexität nach Unterstützung durch Mathematik.
Dieser Artikel skizziert den Stand und die Bedeutung des Einsatzes von
Mathematik bei der Planung und Durchführung von öffentlichem
Personenverkehr, beschreibt die bestehenden Herausforderungen und
regt zukunftsweisende Maßnahmen an.
Every day, millions of people are transported by buses, trains, and airplanes
in Germany. Public transit (PT) is of major importance for the quality of
life of individuals as well as the productivity of entire regions. Quality and
efficiency of PT systems depend on the political framework (state-run, market
oriented) and the suitability of the infrastructure (railway tracks, airport
locations), the existing level of service (timetable, flight schedule), the use
of adequate technologies (information, control, and booking systems), and
the best possible deployment of equipment and resources (energy, vehicles,
crews). The decision, planning, and optimization problems arising in this
context are often gigantic and “scream” for mathematical support because of
their complexity.
This article sketches the state and the relevance of mathematics in planning
and operating public transit, describes today’s challenges, and suggests a
number of innovative actions.
The current contribution of mathematics to public transit is — depending
on the transportation mode — of varying depth. Air traffic is already well
supported by mathematics. Bus traffic made significant advances in recent
years, while rail traffic still bears significant opportunities for improvements.
In all areas of public transit, the existing potentials are far from being exhausted.
For some PT problems, such as vehicle and crew scheduling in bus and
air traffic, excellent mathematical tools are not only available, but used in
many places. In other areas, such as rolling stock rostering in rail traffic,
the performance of the existing mathematical algorithms is not yet sufficient.
Some topics are essentially untouched from a mathematical point
of view; e.g., there are (except for air traffic) no network design or fare
planning models of practical relevance. PT infrastructure construction is
essentially devoid of mathematics, even though enormous capital investments
are made in this area. These problems lead to questions that can only be
tackled by engineers, economists, politicians, and mathematicians in a joint
effort.
Among other things, the authors propose to investigate two specific topics,
which can be addressed at short notice, are of fundamental importance not
only for the area of traffic planning, should lead to a significant improvement
in the collaboration of all involved parties, and, if successful, will be of real
value for companies and customers:
• discrete optimal control: real-time re-planning of traffic systems in case
of disruptions,
• model integration: service design in bus and rail traffic.
Work on these topics in interdisciplinary research projects could be funded
by the German ministry of research and education (BMBF), the German
ministry of economics (BMWi), or the German science foundation (DFG).