The response time of solid state drives (SSDs) has dramatically reduced according to the spread of non-volatile memory express (NVMe) devices. These devices have response times of less than 100 micro seconds on average. The response time of all-flash-array systems has also drastically reduced through the use of NVMe SSDs. However, there are applications, particularly, virtual desktop infrastructure and in-memory database systems, that require storage systems with even shorter response time. Their workloads were found to contain many input-output (IO) concentrations. We define IO concentration by using a declarative style. Input-output (IO) concentrations are aggregations of IO accesses. They appear in narrow regions of the storage volume and continue for periods of up to about an hour. These narrow regions occupy a few percent of the logical unit number capacity, include most IO accesses, and appear at unpredictable logical block addresses. To drastically reduce the response time of these workloads, we developed automated tiered storage system called 'automated tiered storage with fast memory and slow flash storage' (ATSMF). The memory component of ATSMF is a memory with a non-volatile feature. The system predicts the remaining duration of IO concentration, calculates the response-time increase during migration and response-time decrease after migration, and migrates the IO concentrations if the response-time decrease after migration surpasses the response-time increase during migration. Experimental results indicate that ATSMF is at least 20% faster than flash storage only and its memory access ratio is more than 50%.