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SQL Server 2019 introduced a new feature known as Memory Grant Feedback (MGF), which is part of the broader group of Adaptive Query Processing features. MGF adjusts the memory grant size for both batch and row mode operators, ensuring that the SQL Server engine is more efficient with its memory usage, thereby avoiding system performance degradation due to excessive memory grant. This feature is beneficial especially when running complex queries that require significant memory resources.

The way MGF works is quite straightforward. When a query is executed for the first time, the SQL Server Engine estimates the memory grant size required. If the actual memory required is significantly different from the estimated memory, SQL Server stores this information. When the same query is executed in the future, SQL Server adjusts the memory grant size based on the stored information, thus making the process more efficient.

-- Example of a simple query that can benefit from MGF in SQL Server 2019
SELECT * 
FROM Orders 
WHERE OrderDate BETWEEN '2021-01-01' AND '2021-12-31'
ORDER BY OrderAmount DESC;

In MySQL 8.0, memory allocation for queries is managed by optimizing the InnoDB storage engine. While it doesn't have an exact counterpart to SQL Server's MGF, it provides efficient memory management through advanced buffer pool instances and the InnoDB Buffer Pool Size configuration.

-- Example of setting the InnoDB buffer pool size in MySQL 8.0
SET GLOBAL innodb_buffer_pool_size = 134217728;

DB2 11.5 also optimizes memory usage by using a Self-Tuning Memory Manager (STMM). The STMM automatically adjusts the database memory configuration values to improve system performance. This automatic adjustment of memory allocation is done without requiring the database administrator to perform detailed system analysis and manual memory tuning.

-- Activating STMM in DB2 11.5
UPDATE DATABASE CONFIGURATION FOR sample USING SELF_TUNING_MEM YES;

In the world of cloud databases, Azure SQL and Azure Synapse also provide their own memory optimization features. Azure SQL uses a similar adaptive memory grant mechanism to SQL Server's MGF, while Azure Synapse uses memory-optimized tables and procedures to improve memory utilization and increase throughput.

In conclusion, efficient memory management is a crucial aspect of maintaining high database performance. Features like SQL Server's Memory Grant Feedback, MySQL's InnoDB Buffer Pool Size configuration, DB2's Self-Tuning Memory Manager, and Azure SQL's memory optimization mechanisms are all tools that help achieve this goal, making them indispensable for database administrators.