Structured modeling was not designed for simulation, but that has been no deterrence: more than a dozen papers have been written in this area. Some are evaluations of SML's suitability for simulation applications, while others are attempts to improve it for such purposes.

The consensus of the evaluative papers is that SML needs to become more expressive if it is to be useful for simulation, especially for discrete event simulation (DES). For example, Derrick [1988] examines 13 conceptual frameworks applicable to DES using a traffic intersection model as a common frame of reference. He concludes that although structured modeling (as embodied by SML) accommodates the static structure of a simulation model, it does not well accommodate dynamic structure. The same conclusion emerged for four other frameworks: the Entity-Relationship, Entity-Attribute-Set, object-oriented, and process graph method approaches.

My own evaluation of SML (Geoffrion [1989d]) takes an example-based look at three of the main concepts characteristic of simulation: (a) random variables and stochastic processes, (b) dynamic behavior rules describing the behavior of a system over time, and (c) the notion of an experimental plan addressing system behavior over time or over repeated trials. The examples are: Normal random variables and Poisson arrival processes for (a), the D/D/1 FCFS queueing system for (b), and Monte Carlo simulation of a simple structural mechanics problem, of the classical newsboy problem, and of critical path length for (c). In each case, the main SML modeling options are detailed.

My main conclusion regarding (a) and (b) is that much can be done within SML to deal with them, but that the complexity of the resulting models and/or the burden on the solver and its companion programs can easily become excessive if SML is not extended (e.g., to include random-valued attributes). The conclusion regarding (c) is that much could be done with a good model manipulation language designed to work in concert with SML or an extended version thereof. The paper advocates the design and implementation of such a language with certain capabilities, a project that I still believe would be very worthwhile.

Now we come to the efforts of others to improve SML's applicability to simulation. This always involves modifying structured modeling's semantic framework and SML, most obviously by allowing selected attribute elements to be random-valued (generated by known probability distributions). The first serious discussion of this extension appears in Maturana [1987], and there is work yet to be done to make it fully rigorous. One likely way to do so, proposed informally by my colleague John Mamer, would be to incorporate into the core concepts of structured modeling's semantic framework a sample space with a probability measure. This would yield statistical dependence of attribute and function element values as a consequence of the measure properties of the sample space and the structure of the model. A number of technical points need to be settled in connection with this setup, such as the assumptions (if any) needed to justify computing moments of element values by, in effect, repeatedly instantiating and evaluating a structured model that is "A-partially specified" (in the jargon of Geoffrion [1989a]). Then one would need to study how to perform such calculations efficiently in the simulation context.

Two adaptations of structured modeling to DES are particularly noteworthy.  See also Ma, Tian and Zhou [1998], which adds a logical formalism to SM for the purpose of describing dynamics.

Lenard [1992] sketches three DES-motivated extensions of SML, actually new kinds of elements: random attributes (see above), actions (which describe state transitions), and transactions (used to describe complex events in terms of a sequence of previously defined actions and transactions). Lenard [1993b] describes a prototype model management system based on these ideas that was implemented in a database environment (ORACLE 6.0). The database schema is not model-specific as in SML, but rather is fixed for all models. In addition, there are major restrictions of SML. The implementation (developed under contract to the U.S. Coast Guard) makes extensive use of the ORACLE tools SQL*Forms and SQL*Menu; in particular, most user interaction is through forms selected from a set of pop-down menus. Among the system's features is the ability to convert extended structured models to SIMSCRIPT II.5 code. The code generation is done entirely in SQL*Plus (ORACLE's version of the standard query language, SQL).

The approach taken by Pollatschek [1995] is quite different. It is elegant, powerful, and potentially applicable to domains other than DES. There is one extension of SML beyond random attributes, namely the addition of units of measurement (discussed in Section 2), and there are no restrictions of SML. The crux of this paper, however, is not in the extensions, although it is enabled by them, but rather in the idea of beginning the SML schema of every simulation model with a standard module (the same for all DES models) containing primitive and compound entities that essentially define a new simulation worldview proposed by the author.

This worldview, which of course must be obeyed by the balance of the model, contains semantics beyond the representational power of SML. These semantics can be used to build a processor capable of reading any such schema and producing simulation code, in a standard target simulation language like Simscript, that gives the dynamic behavior intended by the modeler. The translation process makes extensive use of the definitional dependency structure that is inherent in SML. The resulting code can then be fed to the target language processor, which serves as the solver.

The approach is a powerful one because the schema processor can work with richer semantics than are formally expressed in the schema itself. The extra richness comes by prior agreement of all concerned to accept the new simulation worldview, which regards simulation as involving model entity "associations" that exist in time and that follow one another according to certain rules. This worldview seems straightforward and natural, but needs to face the test of application in a variety of situations. The issue of generality and a pilot implementation are on the agenda for future work.

Pollatschek's approach abounds with intriguing issues for investigation, including its adaptation to domains other than DES. 

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