  We theoretically calculate the average fraction of frozen particles in
rectangular systems of arbitrary dimensions for the Kob-Andersen and
Fredrickson-Andersen kinetically-constrained models. We find the aspect ratio
of the rectangle's length to width, which distinguishes short, square-like
rectangles from long, tunnel-like rectangles, and show how changing it can
effect the jamming transition. We find how the critical vacancy density
converges to zero in infinite systems for different aspect ratios: for long and
wide channels it decreases algebraically $v_{c}\sim W^{-1/2}$ with the system's
width W, while in square systems it decreases logarithmically $v_{c}\sim1/\ln
L$ with length L. Although derived for asymptotically wide rectangles, our
analytical results agree with numerical data for systems as small as
$W\approx10$.
