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 the first kind or the second kind 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 receiving a read request designating an area of one of the logical volumes from the host, the processor is configured to assign an unused process in the plurality of processes managed by the process management information to the read request that was received, wherein the processor is configured to determine whether the data designated by the read request that was received is in the cache memory, based on a first identifier for identifying the area designated by the read request that was received 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 the first kind or the second kind of physical storage volumes providing the logical volume designated by the read request that was received is a first kind of physical storage volume, the processor is configured to store 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 the first kind or the second kind of physical storage volumes providing the logical volume designated by the read request that was received is a second kind of physical storage volume, the processor is configured to store a second identifier for identifying the process assigned to the read request that was received 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 is configured to store data retrieved from the part of the plurality of the first kind or the second kind of physical storage volumes in accordance with the read request that was received into the area allocated in the cache memory.