The applications running on Networks on-Chip (NoC) typically have to meet a minimum performance requirements to perform successfully. Employing differentiated services is a widely used approach to support QoS (Quality of Service) by relatively prioritizing traffic in the networks employing connection-less communication mechanisms. In this paper we present an analytical evaluation of the average message latency for wormhole-routed interconnect architectures exploiting a traffic prioritization mechanism to achieve differentiated services-based QoS. To verify the validity of the model we apply the method to the Spidergon NoC and compare the model against the results obtained from a discrete-event simulator developed using OMNET.