We propose and study a simple stochastic model for the dynamics of a limit
order book, in which arrivals of market order, limit orders and order
cancellations are described in terms of a Markovian queueing system. Through
its analytical tractability, the model allows to obtain analytical expressions
for various quantities of interest such as the distribution of the duration
between price changes, the distribution and autocorrelation of price changes,
and the probability of an upward move in the price, {\it conditional} on the
state of the order book.