  We introduce a simple model of diffusive jump process where a fee is charged
for each jump. The nonlinear cost function is such that slow jumps incur a flat
fee, while for fast jumps the cost is proportional to the velocity of the jump.
The model -- inspired by the way taxi meters work -- exhibits a very rich
behavior. The cost for trajectories of equal length and equal duration exhibits
giant fluctuations at a critical value of the scaled distance travelled.
Furthermore, the full distribution of the cost until the target is reached
exhibits an interesting ``freezing'' transition in the large-deviation regime.
All the analytical results are corroborated by numerical simulations. Our
results also apply to elastic systems near the depinning transition, when
driven by a random force.
