An operation is waiting for a destroy latch on an in-memory page. It’s used when a data page is removed from the buffer pool and added to the list of free buffer pages. No other latch type is compatible with this mode.

PAGELATCH_* latches are lightweight, non-configurable internal locks used by SQL Server’s storage engine to protect concurrent access to in-memory pages. For example, when the storage engine wants to access a data page in the buffer pool to send to the relational engine, it must first request a latch on that page. The latch is released once the operation has finished, and the duration is usually dependent on available memory.

If your system is experiencing latch waits, it may suggest there’s high contention for in-memory pages of tables or indexes. Latch contention is typically associated with tempdb pages, particularly Global Allocation Map (GAM), Shared Global Allocation Map (SGAM) and Page Free Space (PFS) pages. See: Under the covers: GAM, SGAM, and PFS pages (MSDN).

Investigate

• Check the DMV sys.dm_os_waiting_tasks to see if there’s a problem with a specific page. See: Page Latch Contention.
• Find out if you’re suffering from contention with TempDB. See: Breaking Down TempDB Contention.
• Check whether concurrent inserts into the same index range are causing the problem.  See: Diagnosing and Resolving Latch Contention on SQL Server (Microsoft Download Center).