In an embodiment, a computer system comprises one or more co-packaged integrated circuits having a communication fabric that couples various agent circuits. The agent circuits transmit packets via the communication fabric, which can include command-data packets and command packets. In various embodiments, the communication fabric includes an arbitration circuit to arbitrate among packets to transmit on the fabric. The arbitration circuit may select a winning packet from one or more packets during an arbitration cycle based on a history of previously selected packets. The arbitration circuit may selectively implement, upon receiving a command packet and a command-data packet during a particular arbitration cycle and based on frequencies of particular buses of the communication fabric, one of at least two different arbitration schemes to select a winning packet for the arbitration cycle when an immediately preceding attribution cycle has no winning packet.