VMS Help Sys Parameters, PRIORITY_OFFSET  *Conan The Librarian (sorry for the slow response - running on an old VAX)

    PRIORITY_OFFSET specifies the difference in priority required
    by the scheduler for one process to preempt the current process.
    A value of 2, for example, means that if the current process
    is executing at priority 1, a computable process at priority 2
    or 3 is not allowed to preempt the current process. However, a
    priority 4 or higher process can preempt the current process.
    This mechanism affects only normal priority (0-15) processes. The
    default value is 0.

    This special parameter is used by Compaq and is subject to
    change. Do not change this parameter unless Compaq recommends
    that you do so.