The increasing use of shared networking infrastructure such as the internet for livemedia transport introduces challenges in ensuring the low-latency, high-reliability,and lossless delivery. The unpredictable nature of these uncontrollable networkdomains complicates the optimal configuration of media transport services neededto meet stringent requirements of live media delivery.This thesis proposes a Graph Neural Network (GNN) based methodology topredict end-to-end delivery delay distribution characteristics for various mediatransport configurations. By modeling network topologies and learning fromsimulated data encompassing diverse path structures, retransmission mechanisms,and link states (delay and loss), the GNN model aims to accurately predit delaypercentiles.This predictive capability is intended as a foundational tool to simplify the searchfor optimal transport configurations and improve the dimensioning of playoutmargins. Ultimately, this work seeks to enhance the e!ciency and reliability oflive media transport over lossy IP networks, supporting the evolution towardsmore intelligent network management.