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. - 

#include <Storages/MergeTree/MergeList.h>
#include <Storages/MergeTree/PinnedPartUUIDs.h>
#include <Storages/MergeTree/PartitionPruner.h>
#include <Storages/MergeTree/ReplicatedMergeTreeTableMetadata.h>
#include <Storages/MergeTree/ReplicatedMergeTreeBlockOutputStream.h>
#include <Storages/MergeTree/ReplicatedMergeTreeQuorumEntry.h>
#include <Storages/MergeTree/ReplicatedMergeTreeMutationEntry.h>
#include <Storages/MergeTree/ReplicatedMergeTreeAddress.h>
#include <Storages/MergeTree/ReplicatedMergeTreeQuorumAddedParts.h>
#include <Storages/MergeTree/ReplicatedMergeTreePartHeader.h>
#include <Storages/VirtualColumnUtils.h>
#include <Storages/MergeTree/MergeTreeReaderCompact.h>
#include <Databases/IDatabase.h>
#include <Databases/DatabaseOnDisk.h>
#include <Parsers/formatAST.h>
#include <Parsers/ASTDropQuery.h>
#include <Parsers/ASTOptimizeQuery.h>
#include <Parsers/ASTLiteral.h>
#include <Parsers/queryToString.h>
#include <Parsers/ASTCheckQuery.h>
#include <Parsers/ASTSetQuery.h>
#include <Processors/QueryPlan/BuildQueryPipelineSettings.h>
#include <Processors/QueryPlan/Optimizations/QueryPlanOptimizationSettings.h>
#include <IO/ReadBufferFromString.h>
#include <IO/Operators.h>
#include <IO/ConnectionTimeouts.h>
#include <IO/ConnectionTimeoutsContext.h>
#include <Interpreters/InterpreterAlterQuery.h>
#include <Interpreters/PartLog.h>
#include <Interpreters/Context.h>