  Traffic-light modelling is a complex task, because many factors have to be
taken into account. In particular, capturing all traffic flows in one model can
significantly complicate the model. Therefore, several realistic features are
typically omitted from most models. We introduce a mechanism to include
pedestrians and focus on situations where they may block vehicles that get a
green light simultaneously. More specifically, we consider a generalization of
the Fixed-Cycle Traffic-Light (FCTL) queue. Our framework allows us to model
situations where (part of the) vehicles are blocked, e.g. by pedestrians that
block turning traffic and where several vehicles might depart simultaneously,
e.g. in case of multiple lanes receiving a green light simultaneously. We rely
on probability generating function and complex analysis techniques which are
also used to study the regular FCTL queue. We study the effect of several
parameters on performance measures such as the mean delay and queue-length
distribution.
