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 (back testing) to evaluating them on simulated markets. The contribution of the work presented in this paper is twofold. First we investigated different types of agent-based 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 AlTraSimBa (Algorithmic Trading Simulation Back testing) against the standard Bayesian execution strategy and naive execution strategies, for momentum markets and random markets. The results revealed useful insights on the trade-offs 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.