Symptoms: all threads in BackgroundScheduledPool busy, lot of tasks in replication queue, none of the tasks is executing. 

![Screenshot from 2021-04-16 16-21-44_](https://user-images.githubusercontent.com/1549571/115193796-e767d600-a0ec-11eb-887c-5c9c2412e50c.png)

Related to #16895

Possible workarounds (poor options): increasing the background_schedule_pool_size to huge values, or restart server every time when that happens etc. - 

virtual bool partIsAssignedToBackgroundOperation(const DataPartPtr & part) const = 0;
    
    
    
    
    virtual MutationCommands getFirstAlterMutationCommandsForPart(const DataPartPtr & part) const = 0;
    
    bool movePartsToSpace(const DataPartsVector & parts, SpacePtr space);
private:
    
    
    
    struct CurrentlyMovingPartsTagger
    {
        MergeTreeMovingParts parts_to_move;
        MergeTreeData & data;
        CurrentlyMovingPartsTagger(MergeTreeMovingParts && moving_parts_, MergeTreeData & data_);
        ~CurrentlyMovingPartsTagger();
    };
    using CurrentlyMovingPartsTaggerPtr = std::shared_ptr<CurrentlyMovingPartsTagger>;
    
    bool moveParts(const CurrentlyMovingPartsTaggerPtr & moving_tagger);
    
    CurrentlyMovingPartsTaggerPtr selectPartsForMove();
    
    CurrentlyMovingPartsTaggerPtr checkPartsForMove(const DataPartsVector & parts, SpacePtr space);
    bool canUsePolymorphicParts(const MergeTreeSettings & settings, String * out_reason = nullptr) const;
    std::mutex write_ahead_log_mutex;
    WriteAheadLogPtr write_ahead_log;
    virtual void startBackgroundMovesIfNeeded() = 0;