1. A storage system comprising: a processor executing a control program; a plurality of a first kind or a second kind of physical storage volumes providing storage resources to a plurality of logical volumes; a cache memory connected with the processor, the cache memory being configured to store a part of data held in the plurality of physical storage volumes; and a memory connected with the processor, the memory holding cache control information for indicating whether data designated by a write request or a read request from a host is held in the cache memory and process management information for managing use conditions of a plurality of processes each used to handle a write request or a read request, wherein, upon receipt of a read request designating an area of one of the logical volumes from the host, the processor assigns an unused process in the plurality of processes managed by the process management information to the received read request, wherein the processor determines whether the data designated by the received read request is in the cache memory, based on a first identifier for identifying the area designated by the received read request and the cache control information, wherein, in a case where the processor determines that the designated data is not in the cache memory and a part of the plurality of physical storage volumes providing the logical volume designated by the received read request is a first kind of physical storage volume, the processor stores the first identifier associated with an identifier for identifying an area allocated in the cache memory to the memory as the cache control information, wherein, in a case where the processor determines that the designated data is not in the cache memory and a part of the plurality of physical storage volumes providing the logical volume designated by the received read request is a second kind of physical storage volume, the processor stores a second identifier for identifying the process assigned to the received read request associated with an identifier for identifying an area allocated in the cache memory to the memory as the cache control information, and wherein the processor stores data retrieved from the part of the plurality of physical storage volumes in accordance with the received read request into the area allocated in the cache memory.