We study vehicle waiting times at a traffic lane that is shared
by traffic from two directions. In contrast to crossovers, we
focus on instances where the vehicle passing time of the shared
infrastructure can be large. The motivation for this model arises
from our research on underground transportation systems. We
examine vehicle waiting times under periodic control
rules (i.e., the driving direction on the infrastructure is
switched between two directions according to a fixed time
schedule). We analyze both symmetric and asymmetric systems
(i.e., vehicle arrival rates as well as effective green and
red periods may be different for both directions). In fact,
we are dealing with a single server, two-queue polling system
with random setup times and periodic (nonexhaustive) service
discipline. We develop approximations for the mean waiting time
and we show by comparison to simulation results that the accuracy
is usually in the range of 1–2% for Poisson arrivals.
Also, we indicate how our approximations can be generalized
to compound Poisson arrivals.