  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. We study the diffusion limit of the price process and
express the volatility of price changes in terms of parameters describing the
arrival rates of buy and sell orders and cancelations. These analytical results
provide some insight into the relation between order flow and price dynamics in
order-driven markets.
