A computer system includes a CPU, a memory device, two expansion buses, and a bridge logic unit coupling together the CPU, the memory device and the expansion buses. The CPU couples to the bridge logic unit via a CPU bus and the memory device couples to the bridge logic unit via a memory bus. The bridge logic unit generally routes bus cycle requests from one of the four buses to another of the buses while concurrently routing bus cycle requests to another pair of buses. The bridge logic unit preferably includes four interfaces, one each to the CPU, memory device and the two expansion buses. Each pair of interfaces are coupled by at least one queue; write requests are stored (or “posted”) in write queues and read data are stored in read queues. Because each interface can communicate concurrently with all other interfaces via the read and write queues, the possibility exists that a first interface cannot access a second interface because the second interface is busy processing read or write requests from a third interface, thus starving the first interface for access to the second interface. To remedy this starvation problem, the bridge logic unit prevents the third interface from posting additional write requests to its write queue, thereby permitting the first interface access to the second interface. Further, read cycles may be retried from one interface to allow another interface to complete its bus transactions.