A system and method can support queue processing in a computing environment. A lazy sorting priority queue in a concurrent system can include a priority queue and one or more buffers. The one or more buffers, which can be first-in first-out (FIFO) buffers, operate to store one or more requests received from one or more producers, and move at least one message to the priority queue when no consumer is waiting for processing a request. Furthermore, the priority queue operates to prioritize one or more incoming requests received from the one or more buffers, and allows one or more consumers to pick up the requests based on priority.