  We consider a simplified model of the continuous double auction where prices
are integers varying from $1$ to $N$ with limit orders and market orders, but
quantity per order limited to a single share. For this model, the order process
is equivalent to two $M/M/1$ queues. We study the behaviour of the auction in
the low-traffic limit where limit orders are immediately transformed into
market orders. In this limit, the distribution of prices can be computed
exactly and gives a reasonable approximation of the price distribution when the
ratio between the rate of order arrivals and the rate of order executions is
below $1/2$. This is further confirmed by the analysis of the first passage
time in $1$ or $N$.
