Multi-class traffic flow on a partially space-shared road

Scarce urban space makes urban streets have to be partly shared by cars and cyclists. Traffic flow can be considerably influenced by cyclists, which are comparatively slower than cars. The fundamental diagram (FD) can change greatly, correlating to bike lane length and the cyclist flow. Models for the traffic dynamics on the space-shared streets are still lacking. This work fills the gap. This paper starts from proposing analytic formulas for the capacity, free-flow speed and critical density on a one-lane road, which together characterize the FD. The sensitivity of the FD to the bike lane length as well as the cyclist flow, using the analytical formulas, are presented. The given FD is satisfactory, compared with microscopic simulation results. Finally, we extend the research scope to a multi-lane road. It is expected that this work can benefit city designs and traffic operations.