A computer interconnect system uses packet data transmission over serial links connecting nodes of a network. The serial links provide simultaneous dual paths for transmit/receive. An adapter couples a CPU or the like at a node to the serial link. The adapter includes a packet memory for temporarily storing transmit packets and receive packets, along with a port processor for executing the protocol. Packets of data are transferred between the system bus of the CPU and the packet memory of a pair of data movers, one for read and one for write. The packet memory is accessed upon demand by the serial link, the port processor and the data movers, using interleaved cycles. To accommodate this access upon demand without request/grant cycles, parking registers are provided to store read or write data until a later cycle, and the data rate on the packet memory port is high enough to allow ample time for simultaneous use of both channels as well as packet processing and moving to and from the CPU.