  We study dynamic matching in a spatial setting. Drivers are distributed at
random on some interval. Riders arrive in some (possibly adversarial) order at
randomly drawn points. The platform observes the location of the drivers, and
can match newly arrived riders immediately, or can wait for more riders to
arrive. Unmatched riders incur a waiting cost $c$ per period. The platform can
match riders and drivers, irrevocably. The cost of matching a driver to a rider
is equal to the distance between them. We quantify the value of slightly
increasing supply. We prove that when there are $(1+\epsilon)$ drivers per
rider (for any $\epsilon > 0$), the cost of matching returned by a simple
greedy algorithm which pairs each arriving rider to the closest available
driver is $O(\log^3(n))$, where $n$ is the number of riders. On the other hand,
with equal number of drivers and riders, even the \emph{ex post} optimal
matching does not have a cost less than $\Theta(\sqrt{n})$. Our results shed
light on the important role of (small) excess supply in spatial matching
markets.
