A connection apparatus that connects a plurality of storage units and a controller that establishes connection with the respective storage units in response to a connection request issued from each of the plurality of storage units and accesses the storage units includes a processor; and a memory, wherein the processor transmits a connection request selected based on priority information that represents priority associated with the connection among a plurality of received connection requests to the controller, the priority information being stored in the memory, and changes priority information included in a connection request received from a certain storage unit among the plurality of storage units so that the priority information has higher priority than the priority information included in connection requests received from the other storage units for a period where a connection request is successively received from the certain storage unit and a predetermined condition is satisfied.