  In the supermarket model there are n queues, each with a unit rate server.
Customers arrive in a Poisson process at rate \lambda n, where 0<\lambda <1.
Each customer chooses d > 2 queues uniformly at random, and joins a shortest
one. It is known that the equilibrium distribution of a typical queue length
converges to a certain explicit limiting distribution as n -> oo. We quantify
the rate of convergence by showing that the total variation distance between
the equilibrium distribution and the limiting distribution is essentially of
order n^{-1}; and we give a corresponding result for systems starting from
quite general initial conditions (not in equilibrium). Further, we quantify the
result that the systems exhibit chaotic behaviour: we show that the total
variation distance between the joint law of a fixed set of queue lengths and
the corresponding product law is essentially of order at most n^{-1}.
