A DBMS maintains delayed and non-delayed messages within a non-delay shard and a delay shard that function as a pair. The DBMS stages non-delayed messages in enqueue-time order within the non-delay shard, and maintains a non-delay dequeue pointer that moves in physical order of the enqueued non-delay messages. The DBMS stages delayed messages in enqueue-time order within bucket shards of the delay shard. Each bucket shard, of a delay shard, represents a time span of delivery times, and messages are assigned thereto based on message delivery time. The delay dequeue pointer comprises a sub-routine to determine the message with the minimum delivery time within a current bucket shard with a time span that includes the current time. The DBMS delivers the next available message out of the delayed and non-delayed shards by comparing the delivery time of the next available message from each shard and delivering the earliest available message.