**Real-Time for the Real World ****™**

This site is about some of my research on real-time (including, but not limited to, computing) systems—particularly the general case of dynamically real-time systems subject to epistemic uncertainties. (My consulting practice web site is time-critical-technologies.com.)

This site is a condensed and simplified work-in-progress preview of a work-in-progress book about that research [Jensen 2018].

Both the book and this preview have two primary purposes:

First, to publicly more fully detail my time/utility function (TUF) model for expressing timeliness constraints of a real-time system’s actions, and the utility accrual (UA) model for expressing and seeking to assure feasible satisfactory timeliness of a system’s actions according to application-specific satisfaction criteria, in the presence of kinds and degrees of epistemic uncertainty; (traditional “real-time computing” concepts and techniques are a special case which can greatly benefit from the rigor of these general TUF/UA models).

Second, to outline one of my currently most important research goals—exploring the use of mathematical models of evidence and belief (such as the Transferable Belief Model based on Dempster-Shafer theory) as the basis for dynamic predictability of TUF/UA scheduling. Such models exploy rules for analytically combining uncertain information from multiple sources about the time-evolution of a real-time system’s, and its environment’s, properties and behaviors, to affect beliefs which govern

- decision-making—e.g., dynamically real-time resource management (particularly, scheduling) based on actions’ TUFs (and other pertinent parameters)
- and predictions—e.g., dynamic evidential beliefs regarding the actions’ and system’s timeliness in terms of TUF schedules’ accrued utility.

The TUF/UA paradigm for dynamically real-time scheduling has been previously summarized many times (e.g., in my Ph.D. students’ academic papers and theses)—but only incompletely and for certain cases, to appropriately scope the time and effort for our papers and the Ph.D. research. The details unveiled here have previously appeared only in my privileged documents for consulting and courses.

My uses as a consultant of mathematical theories of evidence and belief in conjunction with the TUF/UA paradigm for dynamic real-time systems are not currently publically available. Advocating that approach here helps enable open research on it by myself and others.

The terms and concepts used on this home page are carefully explained on the following pages.

This web site explains that a system is a *real-time* one *to the degree* that

- the
*timeliness of its actions—*i.e., when they occur with respect to some occurance time satisfaction criteria - and the
*predictability of that timeliness—*i.e., the manner and extent to which that timeliness is known, both in advance of, and during, system operation—again, with respect to some satisfaction criteria - are part of the
*logic*of the system (not performance metrics).

Thus, a lexicon and metric for that real-time degree is necessary for reasoning about such systems.

In the real-time computing community, the lexicon and degree are over-simplified as various vague and inconsistent notions of “hard,” “soft”, “firm,” and “non-” real-time. Those confused notions are insufficient for rigorous reasoning about timeliness and predictability of timeliness in non-trivial real-time systems.

A proper expressive and comprehensive lexicon, and a metric, for an expanse of that degree is provided by this site. An analogy is generalizing from the narrow focus on paint colors which are only either black or some grays or white, to recognizing and being able to logically reason about the whole spectrum of paint colors.

This site takes a scholarly approach to precisely define the concepts of *real-time* per se, and related concepts such as *predictability* and *hard/soft*, in terms of a *mental model* in a *framework*—*quality of service*—based on *first principles* about *latency *and* uncertainty *and* predictability. *

In particular, this site is oriented primarily toward the general case, which is *dynamically real-time *systems. “Dynamically real-time” refers to timeliness and the predictability of timeliness being dynamic, particularly (but not exclusively) due to inherent *uncertainties*—e.g., ignorance about, or non-determinism in—the system and its operational environment. Herein, “dynamic” is used to mean “dynamically real-time,” as opposed to other ways that systems can be dynamic (e.g., adaptive).

Inside the traditional real-time computing field, most systems are special cases at or very near the static corner-point of the real-time expanse.

Outside the field of traditional real-time computing, *most real-time systems have some kinds and degrees of dynamic real-time behavior by their actions*—i.e., may be anywhere on the real-time expanse except at its static corner-point.

Simple common examples of how real-time systems and their applications and their operational environments can have dynamic properties include (but are not limited to):

- unknown or changing system actions’ (e.g., tasks’) arrival times and operation (e.g., execution) times, potentially resulting in transient or persistent resource overloads;
- unknown or changing actions’ (e.g., tasks’) completion time constraints (such as deadlines) even during an action’s operation;
- unknown or changing actions’ conflicts for access to shared (hardware and software) resources;
- other unknown or changing aspects of the system’s operational environment.

The key to those examples is the term “*unknown*,” which can (but does not necessarily) encompass “changing.” The term “unknown” must be formally (e.g., mathematically) defined for instances of those dynamic property examples to be meaningful and subject to analysis. Some formal ways to make that definition are summarized later on this site.

Unknowns are often separated into “*known unknowns*” and “*unknown unknowns*.”

Both known unknowns and unknown unknowns are ubiquitous, including often being integral to dynamic real-time systems where timeliness and predictability of timeliness must nonetheless be satisfactory according to application- and situation-specific criteria.

Formal definitions of, and formal techniques for reasoning about, “unknowns” can be different for “known unknowns” vs. “unknown unknowns.” Those for the former, such as conventional probability theory based ones, can be (but are not necessarily) a subset of those for the latter. Various popular formalisms for reasoning about uncertainties are briefly summarized in the book and (necessarily less so) in this preview.

The formal approach this site emphasizes for reasoning about both known and unknown unknowns, particularly for making assurances about timeliness and predictability of timeliness in dynamic real-time systems, is to employ a general framework for modeling epistemic uncertainty—i.e., a mathematical theory of evidence or beliefs. Certain such theories have been shown to be more or less promising for dynamically real-time systems (including, but not limited to, military surveillance and combat systems) of interest to us and to our research and consulting sponsors.

The field of mathematical theories of evidence is a very deep one, used extensively in numerous different contexts. Simplistically, it can be thought of as a departure from the frequentist theory of probability, first to Bayesian theory, which was generalized to Dempster and Dempster-Shafer theory, modified to create the Transferable Belief Model, and further generalized to Dezert-Smarandache theory.

Using mathematical theories of evidence tends to be very application-specific, which is one essential motivation for a precise and comprehensive characterization of “real-time.”

The Real-Time pages of this site are a work-in-progress preview of my work-in-progress monograph “*An Introduction to Fundamental Principles of Dynamically Real-Time Systems*” [Jensen 2018].

An outdated list of selected papers authored by my research teams and myself, and published in professional society (IEEE, ACM) journals and conferences, is provided, and will be updated. Other sources for some of those are my Google Scholar page and my academia.edu page.

N.B. There still are pages from the previous (c. 2008-2012) version of this site which I have not yet updated and integrated (or removed).