Ordering logic ensures that data items being processed by a number of parallel processing units are unloaded from the processing units in the original per-flow order that the data items were loaded into the parallel processing units. The ordering logic includes a pointer memory, a tail vector, and a head vector. Through these three elements, the ordering logic keeps track of a number of “virtual queues” corresponding to the data flows. A round robin arbiter unloads data items from the processing units only when a data item is at the head of its virtual queue.