Are you aware of your z/VSE copy buffer usage ?
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Supervisor buffers (also called copy blocks) are use for I/O processing (CCW translation). The number of copy blocks to be allocated are defined with the SYS BUFSIZE command during IPL. See z/VS
You may verify the copy block usage of your system via the SIR Attention Routine (AR) command. Close to the bottom of the SIR command output on your console you can find the current copy block usage (COPY-BKLS), the high water mark (HIGH-MARK) and the maximum number of copy blocks (MAX). If your HIGH-MARK is close to the MAX value, you should consider to increase the number of copy blocks in your next maintenance window. Copy blocks are allocated in 24 bit storage (in the Supervisor area below 16 MB). Copy block shortage may cause system hangs.
There are situations where you may need to increase the number of copy blocks, e.g. if you start using VTAM 31-bit I/O buffers, or if you migrate from ECKD to SCSI devices.