A data processing apparatus and method are provided for arbitrating between messages routed over a communication channel. The data processing apparatus has a plurality of processing elements, each processing element executing a process requiring messages to be issued to recipient elements, and a communication channel shared amongst those processing elements over which the messages are routed. Arbitration circuitry performs an arbitration process to arbitrate between multiple messages routed over the communication channel. Each processing element issues progress data for the process executing on that processing element, the progress data indicating latency implications for the process. Arbitration control circuitry is then responsive to the progress data from each processing element to perform a priority ordering process taking into account the latency implications of each process as indicated by the progress data in order to generate priority ordering data. That priority ordering data is then output to the arbitration circuitry in order to control the arbitration process. This enables quality of service to be determined and allocated automatically between the various processes, without the need to know the requirements of the processes in advance, and the prioritization mechanism adapts dynamically to changes in communication between the processes.