A method for enabling overlapped input/output requests to a logical device using assigned and parallel access unit control blocks. Each I/O request interrupts an operating system to assign a base and related unit control block to the input/output requests. In addition a parallel access control block is associated with each unit control block for a logical volume and a parallel access main control block is established with a logical volume through which each of the base and related unit control block can be identified. An input/output request to a logical device interrupts the operating system to assign one of the base and one of the assigned unit control blocks to the input/output requests after which control transfers back to the operating system. At a disk storage facility, the input/output request is located in a table with other input/output requests and corresponding parameters. The disk array storage facility tests the parameters for each new input/output request to determine which of a plurality of control functions will be performed.