Modular Agent Network

Modular Agent Networks (MANs) are an important conceptual extension to model of Agent Networks (ANs)  [Guerrrero 2000]. A main contribution consists of the construction and simulation of hierarchical models in terms of ANs.

For better understanding of the hierarchical model is necessary to introduce the notion of heterogeneous system. A heterogeneous system is a complex entity constituted of sub-systems with different characteristics. Such systems are highly competitive, so that the interactions among these sub-systems can be extremely complex and have different nature.


The recent progresses obtained in efficiency in the domain of the complexity during the modeling and design of heterogeneous systems has been happening, basically, in function of the introduction of new languages and methodologies that bring additional levels of abstraction. This helps the designers to treat the complexity, continually growing, in appropriate levels of detail. Heterogeneous systems frequently show a complex behavior that cannot be completely or easily described in a simple formalism. Thus, is desirable the existence of another appropriate formalisms to these types of problems. The simulation of complex systems can be favored by a representation in multiple abstraction levels.

 

Hierarchy

The notion of the hierarchy is about the construction of structures capable to attribute resolution levels and/or abstraction to the model of a system.

 

Hierarchies in Agents Networks

In the context of ANs, constituted of places, arcs and objects, two possibilities of introduction of mechanisms of hierarchical structuring exist:


I) replacement of a sub-network by a super-place. The semantics of a sub-network is adapted to the semantics of a place. The composition is made by the connection of private input and output gates, using the notion of fusion of places. The components of the hierarchy have a strong joining, because the organization of the connections is defined directly in the configuration of places and arcs.

II) replacement of a sub-network for a super-object . The semantics of a sub-network is adapted to the semantics of an object. It can be said that in this case the joining is weak, because the connection of the gates follows the same principle of the sensor and effectors in a formal agent.

 

The structure of MANs is constituted by a grouping of instances of pages of sub-network connected between them. Under this point of view, one page can be faced like a type of abstract data. A page is a generic specification of a collection of places, arcs, sub-networks, interfaces and super-places that can be (invoked) instantiated.

Places and arcs in a MANs follow the original definition [Guerrero 2000]. Two other elements were added: super-places and interfaces (of sub-network).

 

Super-place : topological entity that represents an entire sub-network.

 

Interface:   presents a similar behavior associated to a conventional place, which is used for communication with mother-pages. This communication is based on a mechanism called places fusion, typically used in Hierarquical Colored Petri Nets (HCPNs) to implement the composition of hierarchical structures. Two or more places with a fusion relationship means, in fact, the same place - all the operations applied to one of them are reflected in all other places, as well as the properties (objects located in its interior, public and private gates).

 

Three important concepts are present in the construction of a Modular Agent Network:

 

Pageis a generic specification that indicates a certain configuration of places, arcs, interfaces and super-places. A page can include (or in a certain way to inherit) the specification of another page for the inclusion of a super-place of this other page.

 

Super-Place: it represents the incorporation of a page to the definition of another. Thus, a super-place is a reference to a page, in a similar format to a conventional place. It is possible to compare a page to a class in languages guided to objects.

 

Instance of Page: By other way, for simulate a Modulate Agent Networks(formed by a collection of interrelated pages) it is necessary to create an instantiation  tree that describes a collection of instances of pages, where each one of these instances receives one only identifier. This identification is justified because a same page can be instantiated multiple times inside the same net. One convention is adopted in which each page  instance receives an object identifier (oid). As a basic requirement, is considered that the system that implements the simulation process is capable to assign a unique oid to each page instance at the moment of its creation, as depicted below.

 

A page can include super-places of another pages, forming a hierarchy of pages. The only restriction is that any network graph, in which nodes are represented by the pages and arcs by the inclusion restrictions (created by super-places), must form a reticulate.

For the representation of hierarchies of pages, is used a similar format to the one adopted in UML (Unified Modeling Language) class diagrams. This artifact is denominated  a page diagram. An example is shown below.