The current document is directed to an efficient and non-blocking mechanism for flow control within a multi-processor or multi-core processor with hierarchical memory caches. Traditionally, a centralized shared-computational-resource access pool, accessed using a locking operation, is used to control access to a shared computational resource within a multi-processor system or multi-core processor. The efficient and non-blocking mechanism for flow control, to which the current document is directed, distributes local shared-computational-resource access pools to each core of a multi-core processor and/or to each processor of a multi-processor system, avoiding significant computational overheads associated with cache-controller contention-control for a traditional, centralized access pool and associated with use of locking operations for access to the access pool.