A function block containing a process-cache tag for storing process-cache tags in the pre-stage of a process cache and an FIFO queue for each tag entry are installed as a traffic controller. The traffic controller stacks packet groups, identified as being from the same flow, in the same FIFO queue. Each FIFO queue records the logged state of the corresponding process queues, and when a packet arrives at an FIFO queue entry in a non-registered state, only its first packet is conveyed to a function block for processing the process-cache misses, and then it awaits registration in a process cache. Access to the process cache from the FIFO queue is implemented at the time that registration of the second and subsequent packets in the process cache are completed. This allows packets other than the first packet in the flow to always access the process cache for a cache hit.