  We introduce a new model to study the oscillations of opposite flows sharing
a common bottleneck and moving on two Totally Asymmetric Simple Exclusion
Process (TASEP) lanes. We provide a theoretical analysis of the phase diagram,
valid when the flow in the bottleneck is dominated by local stationary states.
In particular, we predict and find an inhomogeneous high density phase, with a
striped spatio-temporal structure. At the same time, our results also show that
some other features of the model cannot be explained by the stationarity
hypothesis and require consideration of the transients in the bottleneck at
each reversal of the flow. In particular, we show that for short bottlenecks,
the capacity of the system is at least as high as for uni-directional flow, in
spite of having to empty the bottleneck at each reversal - a feature that can
be explained only by efficient transients. Looking at more sensitive quantities
like the distribution of flipping times, we show that, in most regimes, the
bottleneck is driven by rare fluctuations and descriptions beyond the
stationary state are required.
