A Time/Utility Function (TUF), née Time/Value Function, specifies the application-specific utility that an action (e.g., computational task, mechanical movement) yields depending on its completion time. TUFs and their utility interpretations (semantics), scales, and values are derived from application domain-specific subject matter knowledge. An example (but not the only) interpretation of utility is an action's relative importance, which otherwise is independent of its timeliness. The traditional deadline represented as a TUF is a special case—a downward step of utility from 1 to 0 at the deadline time—e.g., timeliness without importance. A TUF is more general—it has a critical time, with application-specific shapes and utility values on each side, after which it does not increase. The various researcher and practitioner definitions of firm and soft real-time can also be represented as special cases of the TUF model. The optimality criterion for scheduling multiple TUF-constrained actions has historically in the literature been only maximal utility accrual (UA)—e.g., a (perhaps expected) weighted sum of the individual actions' completion utilities. This thus takes into account timeliness with respect to critical times. Additional criteria (e.g., energy, predictability), constraints (e.g., dependencies), system models, scheduling algorithms, and assurances have been added as the TUF/UA paradigm and its use cases have evolved. More expressively, TUF/UA allows accrued utility, timeliness, predictability, and other scheduling criteria and constraints to be traded off against one another for the schedule to yield situational application QoS—as opposed to only timeliness per se. Instances of the TUF/UA paradigm have been employed in a wide variety of application domains, most frequently in military systems.
Time/Utility Functions The TUF/UA paradigm was originally created to address certain action timeliness, predictability of timeliness, and application QoS-based scheduling needs of various military applications for which traditional real-time concepts and practices are not sufficiently expressive (e.g., for dynamically timeliness-critical systems not having deadlines) and load resilience (e.g., for systems subject to routine action overloads). An important common example class of such applications is missile defense (notionally). Subsequently, numerous variations on the original TUF model, the TUF/UA paradigm's system model, and thus scheduling techniques and algorithms, have been studied in the academic literature—e.g.,—and applied in civilian contexts.
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