This deliverable has the objective to define a mathematical model for an optimised real-time management of railway traffic under Moving Block (MB). The formulated real-time traffic management model contains: i) a core module for the detection and the sub-optimal resolution of track occupation conflicts under MB and ii) a non-vital module for providing early-warning predictions of potentially hazardous MB traffic situations. The proposed real-time traffic management model includes a mathematical translation of requirements and constraints identified for both MB signalling within WP2 (namely deliverables D2.1 and D2.2) and the GNSS localisation and train integrity devices within WP3 (i.e. deliverables D3.1 – D3.3). An extensive literature review on real-time traffic management models and algorithms shows that so far research efforts have mainly focused on fixed-block and distance-to-go railway operations. Significant gaps still exist in the modelling of MB train operations, despite an increasing number of research works on MB signalling technology is observed since year 2003. A modelling gap analysis is here performed which indicates the need of enhancing existing real-time traffic management algorithms to better align them to the MB concept in terms of infrastructure representation and speed-headway functional dependency. To this end, the RECIFE-MILP real-time traffic management algorithm is enhanced. On one hand a finer infrastructure discretisation is implemented to offer a more suitable track representation under moving block which no longer uses fixed block sections. On the other hand, two different speed levels (namely maximum speed and scheduled speed) are introduced enabling a speed-dependent headway computation in either nominal or delayed traffic scenarios, thereby overcoming the limitation of speed-independent headways, typical of fixed-block traffic rescheduling models. A non-vital early-warning prediction model of hazardous MB traffic conditions is also proposed which includes a short- and a medium-term hazard identification method. In the short-term, potentially hazardous MB traffic condition are identified as violations of safety-critical threshold values of design variables relating to MB train operations (e.g. driving reaction times), the GNSS system (e.g. GNSS error or latency) and/or the GSM-R layer (e.g. MA communication delay). Safety-critical thresholds of the different design variables are identified by means of an extensive sensitivity analysis which uses a Stochastic Activity Network built for MB within WP2. In the medium-term warnings of potentially hazardous MB conditions are instead triggered whenever RECIFE-MILP detects track occupation conflicts in geographical areas with limited GNSS and/ or GSM-R signal availability, such as deep valleys or tunnels. The defined models contribute to the definition of an optimised automated Traffic Management System for Moving Block which can also support traffic dispatchers in preventively avoiding the occurrence of potentially dangerous MB traffic conditions. @en