In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. The model seeks to capture a number of features suggested by recent empirical analysis of limit order data, such as; fat-tailed distribution of limit order placement from current bid/ask; fat-tailed distribution of order execution-time; fat-tailed distribution of orders stored in the order book; long memory in the signs (buy or sell) of trades. The model developed here extends the earlier one of Chiarella and Iori (2002) in several important aspects, in particular agents have heterogenous time horizons and can submit orders of sizes larger than one, determined either by utility maximisation or by a random selection procedure. We analyze the impact of chartist and fundamentalist strategies on the determination of both the placement level and the placement size, on the shape of the book, the distribution of orders at different prices, and the distribution of their execution time. We compare the results of model simulations with real market data.