Very slow cache processing: Is there any alternative?
If a large part of your time is spent with serialize then that might point to some broken code; as in things keep getting serialized to be stored in the cache/db but it keeps on having a cache miss, otherwise you should only see unserialize with heavy cache usage.

The pattern you're pointing to sounds like you have some code that is abusing the variables table. Inside variable_initialize() it runs array_map with serialize, and variable_set() calls serialize. I would check the max_allowed_packet value inside of MySQL; my preference is to set it to 32M.

If you can provide more details, I can give you a better answer. I will say that using PHP7 should give you a big speedup if you haven't done so.