A prefetch request having a priority assigned thereto is obtained, based on executing a prefetch instruction included within a program. Based on obtaining the prefetch request, a determination is made as to whether the prefetch request may be placed on a prefetch queue. This determination includes determining whether the prefetch queue is full; checking, based on determining the prefetch queue is full, whether the priority of the prefetch request is considered a high priority; determining, based on the checking indicating the priority of the prefetch request is considered a high priority, whether another prefetch request on the prefetch queue may be removed; removing the other prefetch request from the prefetch queue, based on determining the other prefetch request may be removed; and adding the prefetch request to the prefetch queue, based on removing the other prefetch request.