A method and circuit arrangement process a workload in a multithreaded processor that includes a plurality of hardware threads. Each thread receives at least one message carrying data to process the workload through a respective inbox from among a plurality of inboxes. A plurality of messages are received at a first inbox among the plurality of inboxes, wherein the first inbox is associated with a first thread among the plurality of hardware threads, and wherein each message is associated with a priority. From the plurality of received messages, a first message is selected to process in the first thread based on that first message being associated with the highest priority among the received messages. A second message is selected to process in the first thread based on that second message being associated with the earliest time stamp among the received messages and in response to processing the first message.