  Traffic is a challenge in rural and urban areas alike with negative effects
ranging from congestion to air pollution. Ride-sharing poses an appealing
alternative to personal cars, combining the traffic-reducing ride bundling of
public transport with much of the flexibility and comfort of personal cars.
Here we study the effects of the underlying street network topology on the
viability of ride bundling analytically and in simulations. Using numerical and
analytical approaches we find that system performance can be measured in the
number of scheduled stops per vehicle. Its scaling with the request rate is
approximately linear and the slope, that depends on the network topology, is a
measure of the ease of ridesharing in that topology. This dependence is caused
by the different growth of the route volume, which we compute analytically for
the simplest networks served by a single vehicle.
