  We present a phenomenological analysis of events with two high transverse
momentum ($p_T$) jets separated by a large (pseudo-)rapidity interval void of
particle activity, also known as jet-gap-jet events. In the limit where the
collision energy $\sqrt{s}$ is much larger than any other momentum scale, the
jet-gap-jet process is described in terms of perturbative pomeron exchange
between partons within the Balitsky--Fadin--Kuraev--Lipatov (BFKL) limit of
perturbative quantum chromodynamics (QCD). The BFKL pomeron exchange
amplitudes, with resummation at the next-to-leading logarithmic approximation,
have been embedded in the PYTHIA8 Monte Carlo event generator. Standard QCD
dijet events are simulated at next-to-leading order in $\alpha_s$ matched to
parton showers with POWHEG+PYTHIA8. We compare our calculations to measurements
by the CDF, D0, and CMS experiments at center-of-mass energies of 1.8, 7 and 13
TeV. The impact of the theoretical scales, the parton densities, final- and
initial-state radiation effects, multiple parton interactions, and $p_T$
thresholds and multiplicities of the particles in the rapidity gap on the
jet-gap-jet signature is studied in detail. With a strict gap definition (no
particle allowed in the gap), the shapes of most distributions are well
described except for the CMS azimuthal-angle distribution at 13 TeV. The
survival probability is surprisingly well modelled by multiparton interactions
in PYTHIA8. Without multiparton interactions, theoretical predictions based on
two-channel eikonal models agree qualitatively with fits to the experimental
data.
