In this report we demonstrate the outcomes of the research performed in the Air Transport Safety Institute of the Royal Netherlands Aerospace Centre (NLR). This research project constitutes the MSc Thesis of the writer, towards the graduation of the MSc Aerospace Engineering at Delft University of Technology (Air Transport & Operations). The subject of this project lies in the area of aviation safety and quantitative risk assessment. In specific, the study deals with the safety issue of fuel planning and fuel management in airlines’ operations (Commercial Air Transport). As the air traffic growths rapidly, it is a challenge to keep the current safety levels and further improve them, achieving the EU’s vision safety target, which is less than one accident per ten million flights by 2050. Amongst the various accidents and incidents categories, this project researches the accidents and incidents related to fuel. In specific, we investigate two fuel-related events; the probability that a flight lands with less than the minimum regulated fuel amount (called FRF - Final Reserve Fuel) and the probability of fuel exhaustion. So as to analyse and assess the safety risks, we followed the steps of the TOPAZ methodology. Based on previous research on the subject, an extensive hazards list was created, as well as an agent-based risk model was developed and implemented as a Stochastic Dynamically Coloured Petri Nets (SDCPN) model. The risk model was algorithmically implemented in JAVA programming language, in the direction of conducting Monte Carlo simulations. The first event's (FRF) probabilities were estimated through regular (straightforward) Monte Carlo simulation, whilst for the second (fuel exhaustion) regular Monte Carlo proved to be insufficient. Indeed, fuel exhaustion is a rare event and, consequently, an acceleration method was needed to be implemented. The acceleration method chosen is the Interacting Particle System (IPS). Finally, through the simulations, we estimate the probabilities of these rare events for several operational scenarios. The fuel-related risks were assessed for their acceptability, eventually proving that for all scenarios the risks are either tolerable or acceptable, while also the most prominent safety bottlenecks are identified and analysed.