Never rise to speak till you have something to say;

and when you have said it, cease. -- John Witherspoon


When the effective leader is finished with his work,

the people say it happened naturally. -- Lao-Tzu, Tao Te Ching

Chapter 10


We presented a sufficient and practical framework, UNIFY , for effective Multi-Representation Modelling (MRM). MRM, the joint execution of multiple models, is a significant challenge facing model designers. Previous approaches have been unsuccessful in helping model designers overcome this challenge; these approaches they do not satisfy all of our requirements for effective MRM. The techniques and processes that are part of UNIFY help designers to overcome the challenge of executing multiple models jointly by enabling consistency maintenance among the concurrent representations of the models. UNIFY is a sufficient approach for achieving effective MRM because it satisfies the requirements for effective MRM. UNIFY is practical because designers can apply it in conjunction with a familiar model specification methodology. UNIFY is a significant contribution to the practice of modelling and simulation.

Previous MRM approaches such as aggregation-disaggregation and selective viewing can fail to achieve effective MRM for many applications because they do not satisfy critical MRM requirements. These approaches encounter many problems such as temporal inconsistency, chain disaggregation and thrashing, which render the approaches ineffective for many applications. Our fundamental observations about jointly-executing models address the causes of these problems. These observations indicate that maintaining consistency among the representations of jointly-executing models can eliminate or reduce the problems encountered in other approaches.

UNIFY , our approach for achieving effective MRM, involves maintaining consistency among concurrent representations. The techniques and processes in UNIFY address consistency maintenance in concurrent representations. The viability of UNIFY rests on the assumptions that designers can (i) select mapping functions to capture application-specific aspects of attribute relationships, (ii) select policies to resolve the effects of concurrent interactions by understanding their semantics, and (iii) make time-steps compatible. These assumptions are reasonable because without them, no approach can capture the application-specific semantics of jointly-executing models. Alternative approaches fail to achieve effective MRM despite making similar assumptions.

UNIFY aids designers in incorporating MRM effectively in their applications. Effective MRM leads to the design of multi-models that satisfy their users' requirements. We provided guidelines for designers so that they can apply our techniques and processes to achieve effective MRM within their applications.

10.1 Contributions

Our work benefits the practice of modelling and simulation. UNIFY is the first known framework for effective MRM. The focus of UNIFY is to execute multiple models jointly. UNIFY is intended for designers who desire to incorporate MRM into their applications. These designers can construct MRM solutions for their applications by applying the techniques and processes within UNIFY .

The main contribution of our work is UNIFY -- a framework for the joint execution of multiple models. We formulated three requirements for MRM: multi-representation interaction, multi-representation consistency and cost-effectiveness. We showed how alternative MRM approaches do not satisfy these requirements, while UNIFY does. The contributions of our work are the following:

  1. 1. Fundamental Observations about MRM
  2. 2. UNIFY
    1. a. Multiple Representation Entities (MREs)
    2. b. Attribute Dependency Graphs (ADGs)
    3. c. Properties and requirements of mapping functions
    4. d. Process for constructing Consistency Enforcers (CEs)
    5. e. A Taxonomy for Interactions
    6. f. Process for constructing Interaction Resolvers (IRs)
  3. 3. A Cost Study of various MRM approaches
  4. 4. Guidelines for MRM designers

We presented the fundamental observations to show how problems arise in the joint execution of multiple models [Reyn97]. We made these observations after studying the joint execution of many models. The fundamental observations address the causes of ineffectiveness in jointly-executing models, such as inconsistency among their representations and dependent concurrent interactions. Addressing the fundamental observations forms the basis of any approach to effective MRM, such as UNIFY .

MREs are an approach for maintaining concurrent representations of jointly-executing models [Nat95]. An MRE permits interactions at all representation levels, yet is internally consistent. MREs eliminate or reduce many problems seen with alternative MRM approaches, such as aggregation-disaggregation and selective viewing. MREs eliminate chain disaggregation, temporal inconsistency, mapping inconsistency, transition latency and thrashing, and reduce network flooding. MREs require a means of capturing the relationships among multiple representations and policies to resolve the effects of concurrent interactions. Provided these requirements are satisfied, MREs reduce the MRM problem to the problem of maintaining consistency among concurrent representations when interactions at multiple representation levels occur.

ADGs and mapping functions capture relationships among concurrent representations. ADGs are a technique to capture dependencies among attributes in an MRE, whereas mapping functions capture application-specific information about the dependencies. ADGs permit designers to express how attributes in representations are dependent on one another, and how the execution of a multi-model affects the representations of each model. Mapping functions translate attributes from one representation level to another. ADGs and mapping functions can be used to construct a CE for an MRE. A CE is responsible for maintaining an MRE consistent at all observation times. When an interaction changes the value of an attribute, a CE traverses an ADG and invokes the appropriate mapping functions in order to maintain consistency in an MRE. We demonstrated the construction of a CE by showing how to construct an ADG and select mapping functions for an MRE. We showed how to assign static and dynamic semantics to dependencies captured by an ADG by classifying dependencies into four types and weighting them. We presented requirements and properties of mapping functions. We discussed how an ADG can be traversed in order to propagate the effects of an interaction. Finally, we presented an algorithm for the operation of a CE.

We presented one taxonomy for classifying interactions semantically and resolving their dependent effects [Nat99]. We presented four characteristics of interactions and showed how to classify interactions into four classes based on these characteristics. We showed how serialization, the traditional approach for resolving the effects of concurrent interactions, can be inappropriate for dependent concurrent interactions. Based on our taxonomy, we presented policies for resolving the effects of classes of dependent concurrent interactions. Our taxonomy is applicable to interactions in a variety of modelling and simulation applications. We believe that in any application where concurrent interactions may be dependent on another, such a taxonomy is applicable and can be used to resolve the effects of concurrent interactions. We demonstrated the construction of an IR and presented an algorithm for its operation.

We presented the first cost study comparing various MRM approaches [Nat97]. The study compares simulation and consistency costs for UNIFY and alternative approaches. We showed how simulation and consistency costs vary for the different approaches. Lastly, we showed that UNIFY reduces the total of simulation and consistency costs.

The fundamental observations, MREs, ADGs and our taxonomy of interactions enable designers to incorporate effective MRM in their applications. Providing designers with techniques and guidelines to achieve effective joint execution of multiple models is our main contribution to modelling and simulation.

10.2 Future Work

In the future, we expect to eliminate a few of the assumptions we made in UNIFY and apply UNIFY to applications in a variety of domains. Eliminating some of the assumptions we made in our work would make UNIFY more beneficial to model designers. Applying UNIFY to more applications, would provide us with greater experience with regard to MRM.

A critical assumption we made was that designers can make the time-steps of jointly-executing models compatible. Jointly-executing models executing with compatible time-steps can be temporally consistent. Application-independent guidelines for making time-steps compatible would be a desirable addition to UNIFY . Alternatively, providing techniques for maintaining temporal consistency among jointly-executing models that execute with incompatible time-step would eliminate a critical assumption in UNIFY .

Another assumption was that designers can select mapping functions to translate attributes among representations. We specified requirements and properties of mapping functions as guidelines for selecting them. However, specifying requirements and properties in greater detail, perhaps for classes of applications, would enable designers to select mapping functions with greater ease.

Yet another assumption was that designers can select policies for resolving the effects of concurrent interactions after classifying the interactions. We showed how to classify interactions and select policies for resolving classes of interactions. Providing sub-classes of interactions would enable designers to refine the classification of the different kinds of interactions in various applications. Refined classification may lead to refined policies for resolving the effects of concurrent interactions.

An area of future work would be applying UNIFY to a larger variety of models. Applying UNIFY to a wide variety of models would increase our understanding of MRM. We would like to apply UNIFY to models in areas such as economics, weather prediction and graphics. Applying UNIFY to such models would enable us to specify detailed requirements and properties of mapping functions and to refine the classification of interactions. Also, we would like to study the implementation of applications that employ UNIFY to incorporate MRM. Such studies details may reveal connections between requirements and properties of mapping functions, policies for resolving concurrent interactions and the implementation of modules for enforcing consistency and resolving interactions. UNIFY can gain widespread acceptability if it is applied successfully to a large number of multi-model applications.