  Random spatial models are attractive for modeling heterogeneous cellular
networks (HCNs) due to their realism, tractability, and scalability. A major
limitation of such models to date in the context of HCNs is the neglect of
network traffic and load: all base stations (BSs) have typically been assumed
to always be transmitting. Small cells in particular will have a lighter load
than macrocells, and so their contribution to the network interference may be
significantly overstated in a fully loaded model. This paper incorporates a
flexible notion of BS load by introducing a new idea of conditionally thinning
the interference field. For a K-tier HCN where BSs across tiers differ in terms
of transmit power, supported data rate, deployment density, and now load, we
derive the coverage probability for a typical mobile, which connects to the
strongest BS signal. Conditioned on this connection, the interfering BSs of the
$i^{th}$ tier are assumed to transmit independently with probability $p_i$,
which models the load. Assuming - reasonably - that smaller cells are more
lightly loaded than macrocells, the analysis shows that adding such access
points to the network always increases the coverage probability. We also
observe that fully loaded models are quite pessimistic in terms of coverage.
