1. A storage system comprising: a plurality of processor units, which include two or more processor units that process an I/O (Input/Output) command from an external device; and a storage resource, which stores a load index determined for each LDEV, wherein the LDEV is a logical storage device, the load index of each LDEV is a static value that does not dynamically change in accordance with the number of I/O command relating to the LDEV, any of the plurality of processor units, based on the following (X1) and (X2): (X1) the load index assigned to each of the two or more processor units; and (X2) the load index of the target LDEV, selects, from among the two or more processor units, a processor unit which is to be an assignment-destination of an owner right for the target LDEV, and assigns this owner right to the selected processor unit, and the (X1) load index of the processor unit is a value based on the load index of one or more LDEV respectively corresponding to one or more owner rights that have been assigned to this processor unit.