Final answer:
The function of the initiator is to prioritize running jobs, ensuring that critical tasks are allocated necessary resources within the mainframe system.
Step-by-step explanation:
The valid function of the initiator, in the context of job processing in mainframe environments like IBM's z/OS, is D. Prioritize running jobs. The initiator is responsible for starting and managing jobs within the system, and part of its duties is to prioritize these jobs based on predefined criteria. This ensures that critical tasks receive the necessary processing resources and helps in effective systems management. Functions such as avoiding program conflicts or dataset conflicts are typically handled by other components like the operating system's resource serialization mechanisms, while accessing TSO (Time Sharing Option) terminals is typically not a function of the initiator but would be related to the user's interactive sessions with the system.