Algorithmic trading (AT) strategies aim at executing large orders discretely, in order to minimize the order's impact, whilst also hiding the traders' intentions. Most AT evaluation methods range from running the AT strategies against historical data (backtesting) to evaluating them on simulated markets. The contribution of the work presented in this paper is twofold. First we investigated different types of agentbased market simulations and suggested how to identify the most suitable market simulation type, based on the specific market model to be investigated. Then we proposed an extended model of the Bayesian execution strategy. We implemented and assessed this model using our tool Al-TraSimBa (ALgorithmic TRAding SIMulation BAcktesting) against the standard Bayesian execution strategy and naïve execution strategies, for momentum, random and noise markets, as well as against historical data. On the basis of the results presented in the paper, we propose that momentum market is the most suitable model for testing algorithmic trading strategies, since it quickly fills the Limit Order book and produces results comparable to those of a liquid stock. Our experiments and analysis also revealed that: (i) the method of estimating priors proposed in this paper − within the Bayesian adaptive agent model − can be advantageous in relatively stable markets, when trading patterns in consecutive days are strongly correlated, and (ii) there exists a trade-off between the frequency of decision making and more complex decision criteria, on one side, and the negative outcome of lost trading on the agents' side due to them not participating actively in the market for some of the execution steps.