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Director's discretionary time (DDT) is a time allocation (amount of potential observation time) whose use is left to a (scientific) director of an observatory or research telescope. Time allocation for observation on a major research telescope is often largely based upon evaluation of proposals, e.g., by a committee of scientists chosen for the purpose. Likely some specific amount of time is regularly allocated to maintenance of the equipment, which may vary from year to year due to planned major upgrade and maintenance projects. Often, a specific amount time is regularly left to the scientific director of the facility, who is presumed to be motivated and competent to choose observation projects of value. These may include types of observation considered experimental and speculative (e.g., the Hubble Deep Field), timely opportunities such as follow-ups to unexpected events such as transients, and observation whose value has been very recently revealed, such as early follow-ups to significant discoveries.
Note that within astrophysics, the abbreviation DDT is also seen meaning deflagration to detonation transition.