1. A method for responding to an input-output request from a host to effect a transfer to a specified location within a logical volume in a disk array storage device wherein a host operating system utilizes a first, uniquely identified, base unit control block corresponding to the logical volume to effect a transfer in response to the input-output request, said method enabling the host to send overlapped input-output request to the logical volume and comprising the steps of: A) within the host i) defining at least one related, uniquely identified unit control block that identifies the logical volume, ii) interrupting the operating system response to the input-output request by assigning one of the base and related unit control blocks to the input-output request, and iii) returning control of the response to the input-output request to the operating system identifying the assigned unit control block whereby the host operating system can issue overlapped input-output requests to the given logical volume, and B) within the disk array storage facility i) establishing a table for the logical volume with an entry input-output requests and corresponding parameters, and ii) testing the parameters for each new input-output request to the logical volume with respect to the parameters for input-output request entries in the table to determine which, of a plurality of control functions including enabling the processing of the input-output request by the storage facility, will be performed.