Method, device and computer readable storage media for managing storage system

A device for managing a storage system, comprising:

• at least one processing unit;
• at least one memory coupled to the at least one processing unit and storing instructions executed by the at least one processing unit, the instructions when executed by the at least one processing unit causing the device to execute actions, the actions comprising:
• determining a permitted concurrency number for respective access to multiple storage devices in the storage system by a multi-level cache device of the storage system, the permitted concurrency number being associated with a state of the multiple storage devices;
• in response to receiving an access request for the storage system, determining a cache device in the multi-level cache device corresponding to the access request;
• determining whether a current concurrency number of the cache device reaches the permitted concurrency number;
• and
• in response to determining that the current concurrency number fails to reach the permitted concurrency number, executing the access request for the storage system.