  We use state-of-the-art density matrix renormalization group calculations in
the canonical ensemble to determine the phase diagram of the dipolar
Bose-Hubbard model on a finite cylinder. We consider several observables that
are accessible in typical optical lattice setups and assess how well these
quantities perform as order parameters. We find that, especially for small
systems, the occupation imbalance is less susceptible to boundary effects than
the structure factor in uncovering the presence of a periodic density
modulation. By analysing the non-local correlations, we find that the
appearance of supersolid order is very sensitive to boundary effects, which may
render it difficult to observe in quantum gas lattice experiments with a few
tens of particles. Finally, we show how density measurements readily obtainable
on a quantum gas microscope allow distinguishing between superfluid and solid
phases using unsupervised machine-learning techniques.
