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Agent-Based Modeling of Systems of Systems

Jean-Baptiste Soyez, Gildas Morvan, Rochdi Merzouki, Daniel Dupont

arXiv:2609.27573v1cs.MA

TL;DR

SoSs combine autonomous component systems whose local goals may conflict with shared global goals, and existing approaches do not provide a sufficiently generic formalism for their complexity. The paper proposes a multi-level agent-based formalism for representing SoS structure, goals, and change. It argues that the formalism represents fundamental SoS characteristics and illustrates it with an InTrade IAV fleet case.

  • Problem

    Approaches that treat IAVs as simply more capable AGVs fail to capture the fleet’s organizational and functional complexity across levels.

    Source: §I · p. 1

  • Method

    The paper proposes a generic multi-level formalism using IRM4MLS to represent SoS organization, goals, and component systems.

    Source: §I · p. 2, C. Influence Reaction Model for… · p. 5

  • Results

    The authors argue that generated agent-based models respect directed SoS characteristics, including geographic distribution and component-system addition or deletion.

    Source: E. Respecting Fundamental… · pp. 11–13

  • Takeaways & Limitations

    The formalism is presented as a basis for modeling, simulating, and controlling directed SoS, illustrated with an InTrade IAV fleet.

    Source: §V · p. 13

Abstract

from arXiv · show

This paper deals with the generic modeling of systems of systems (SoSs) using agent-based modeling. SoSs are large-scale systems, including numerous-possibly heterogeneous-interacting component systems evolving in a dynamic environment. The aim of this paper is to provide generic formalism allowing to represent and control the whole complexity of a SoS using agent-based simulations. In particular, organizational aspects of SoSs are managed with the Agent-Group-Role model. Functional aspects, guiding SoSs to accomplish their global goals, are handled via a functional specification. Multilevel aspects are modeled with the Influence Reaction Model for Multilevel Simulation (IRM4MLS) agent-based meta-model. Models generated using this formalism encompass static and dynamic aspects of SoSs. They consider reorganization of SoSs caused by changes of goals or subsystem capacity. All these elements are illustrated in this paper using a SoS case study of Intelligent Autonomous Vehicles initiated by the Intelligent Transportation for Dynamic Environment (InTraDE) European project to automate the port container logistic.

I. INTRODUCTION

The paper frames SoSs as autonomous, heterogeneous component systems that must cooperate toward global goals despite their independent local goals. It argues that existing approaches do not adequately capture their organizational and functional complexity, motivating a generic formalism.

I. INTRODUCTION

  • SoS component systems operate independently toward local goals but must cooperate to achieve global goals that may conflict with those local goals.The paper characterizes SoSs as large-scale systems of numerous communicating components.Source: §I · p. 1
  • Treating Intelligent Autonomous Vehicles as merely more capable Autonomous Guided Vehicles misses the fleet’s organizational and functional complexity across levels.The paper uses the InTrade port-container fleet as its illustrative case.Source: §I · pp. 1–2
  • The paper proposes a formalism that divides SoS complexity into levels and organizations to represent static and dynamic aspects.Its goal is a modeling tool for engineering and operating SoSs.Source: §I · p. 2

A. Related Works

  • Prior approaches vary from interface, locality, policy, and connection models,,, to data-focused evaluation [11] and hypergraphs lacking generic evolution mechanisms [12].An ABM reconfiguration approach [14] lacks functional goal specification and has no convergence guarantee.Source: A. Related Works · p. 2

B. Contributions

The paper develops a generic multi-level formalism for representing SoS organization and goals, including reconfiguration as goals or environments change. It grounds the approach in an operational SoS definition and illustrates the paper’s structure and scope.

B. Contributions

  • The contribution combines a generic, operational SoS definition with a formalism for representing system structure and organizations, illustrated on a directed InTrade IAV fleet.IRM4MLS provides multilevel modeling, while organizational and functional representations support plans and structures for global goals.Source: B. Contributions · p. 2
  • Control mechanisms are proposed to preserve SoS characteristics as the environment or global goal changes.The paper describes detecting mission incapacity and reporting it to an authoritative CS, followed by mission reallocation or organizational change.Source: B. Contributions · pp. 2–3

C. Plan

  • The paper proceeds from SoS definitions and types to multi-agent modeling, then presents static and dynamic MASoS elements and their links to system-level goals.Its second section also introduces graphical notation for SoS.Source: C. Plan · p. 3, §II · p. 3

A. SoS Definition

  • An SoS is defined as autonomous, potentially heterogeneous component systems with a global goal, able to cooperate on missions no single component can accomplish.The definition includes geographic distribution and adaptation to changes in environment, goal, or membership.Source: A. SoS Definition · p. 3
  • The paper’s operational definition highlights five characteristics: operational and managerial independence, geographic distribution, emergent behavior, and evolutionary development.Its IAV examples include reallocating a failed vehicle’s mission to another capable CS.Source: A. SoS Definition · p. 3

B. Types of SoS

The paper focuses on directed or acknowledged SoSs with hierarchical, nested levels. It introduces a graphical representation of component systems and positions multi-agent modeling as a way to represent systems at different granularities.

B. Types of SoS

  • The paper focuses on directed and acknowledged SoSs, distinguishing them by central management and the degree to which component systems retain independent ownership and objectives.Directed SoSs subordinate CS operational modes to central purposes; acknowledged SoSs have designated management while CS retain independence.Source: B. Types of SoS · p. 4

C. Graphical Representation and Particular CS

  • The graphical notation represents component-system inclusion and communication links across levels, including elementary and top component systems.A CS that temporarily violates SoS characteristics may be treated as a virtual component system; the example includes IAVs joined as a platoon.Source: C. Graphical Representation and… · p. 4

III. MULTI-AGENT SYSTEMS (MAS)

  • The paper models component systems as agents and introduces IRM4MLS to represent complex systems at different granularity levels.CS agents are intended to exhibit the autonomy and independence of the CS they represent.Source: §III · p. 4, C. Graphical Representation and… · p. 4

A. MAS Definition

The section defines agents and multi-agent systems through their capabilities, environment, and interactions. It then relates agent-based modeling to complex systems and reviews organizational and multilevel approaches relevant to SoSs.

A. MAS Definition

  • An agent acts in and perceives an environment, communicates with other agents, pursues objectives using resources and competencies, and behaves according to its perceptions and communications.Its representation of the environment may be partial or absent.Source: A. MAS Definition · pp. 4–5
  • A MAS comprises an environment, situated objects, agents, relations, operators for manipulating objects, and operators for representing their effects and world reactions.Agents are active objects within the system.Source: A. MAS Definition · p. 5

B. Agent-Based Modeling of Complex Systems

  • MAS are used to simulate parallel interactions among autonomous entities, which are common in complex systems such as SoSs.HLA coordinates different simulations on one platform while representing independent entities across organizational levels [30]; PADAWAN nests agents and environments to represent aggregate organization [31].Source: B. Agent-Based Modeling of Complex… · p. 5
  • Related approaches address SoS organization through AGR groups and roles,, holonic CRIO decomposition [35], and Moise+ mission allocation [16],.HMAS combines holonic organization and norms to coordinate independent entities while respecting system integrity during change [37].Source: B. Agent-Based Modeling of Complex… · p. 5

C. Influence Reaction Model for Multi-Level Simulation (IRM4MLS)

IRM4MLS represents SoSs as entities interacting across multiple levels, separating organizational scales or aspects to make system complexity easier to apprehend and compute. Its model supports cross-level relations, level-specific states, and hierarchical or complementary relationships among levels.

C. Influence Reaction Model for Multi-Level Simulation (IRM4MLS)

  • IRM4MLS models SoSs as complex systems whose elements interact across levels, helping separate organizational scales or aspects to make complexity easier to apprehend and compute.The model is described as a multilevel agent-based meta-model for entities situated at different levels.Source: C. Influence Reaction Model for… · p. 5
  • IRM4MLS represents cross-level influence and perception through separate directed graphs, capturing interactions and their results without bias.Influence links let agents in one level affect another; perception links let them perceive another level's state.Source: C. Influence Reaction Model for… · p. 5
  • Each level has a state comprising environmental characteristics and influences, while agents may act across levels and level schedules can run independently.The environment can be modeled as an agent without internal state that produces influences; microscopic agents can aggregate into higher-granularity organizational agents.Source: C. Influence Reaction Model for… · p. 6
  • A hierarchical graph represents inclusion by edges, allowing lower-level agents to aggregate upward, and complementarity by symmetric edges between same-scale levels.Complementary levels can represent different aspects of the same entities.Source: C. Influence Reaction Model for… · p. 6

IV. AGENT FORMALISM TO REPRESENT SOS

The formalism addresses gaps in MAS representations of SoS organization, hierarchy, missions, and global goals. It specifies both static organizational and multilevel elements and dynamic mechanisms for initialization and capacity evolution.

IV. AGENT FORMALISM TO REPRESENT SOS

  • MAS definitions omit organizational and hierarchical concepts for representing which component systems integrate or allocate missions, and do not account for SoS multilevel structure in global goals.The paper says these omissions make it harder for an SoS to reason about reorganization to fulfil its goals and to express managerial independence, evolutionary development, cooperation, and coexistence.Source: §IV · p. 6
  • The formalism supplies static organizational descriptions and a multilevel environment, plus mechanisms for SoS initialization and capacity evolution.It also sets out elements intended to show that models built with the formalism respect fundamental SoS characteristics.Source: §IV · p. 6

A. Static Apects

The static formalism combines AGR organization with a multilevel description of component systems, capacities, groups, and goals. It connects group formation and mission allocation to functional requirements and the decomposition of a highest-level goal into lower-level missions.

A. Static Apects

  • AGR represents component systems as individuals or aggregations, organizing them into groups where roles support reasoning about mission distribution toward an allocated goal,.An agent can play roles in multiple groups; roles specify context-dependent behavior and status within a group.Source: A. Static Apects · p. 6
  • A capacity describes the means an agent or group has to accomplish a task, and indicates whether actions can reach a target state under a given level state.Capacities should be quantified as concrete action results rather than goal states; the example sets minimum individual and aggregate carrier capacity requirements.Source: A. Static Apects · p. 6, 2) Group of CS Modeling · p. 7
  • A component-system specification records its super-system, roles, lower-level component systems, operational groups, role assignments, and capacity function.The capacity function indicates whether the system can reach a goal state from the current state; the hierarchy represents increasing abstraction, approximation, and scale.Source: 1) CS Modeling · p. 7
  • Group specifications define playable roles and levels, role compatibility within and across groups, role-count bounds, and capacity bounds for agents and role populations.The specification also indicates when a group at a higher level must be instantiated by a component-system agent composed of lower-level systems.Source: 2) Group of CS Modeling · p. 7
  • A global goal is a desired system-and-environment state at the highest level, optionally bounded by a time limit.The goal can be divided into missions by functional, geographic, or other criteria, including according to levels.Source: 3) Multi-level environment and goal… · pp. 7–8
  • For each inclusion link, a function translates a higher-level goal state into lower-level goal states that can be allocated as component-system missions.The paper notes that component systems at a given level may have several ways to fulfil a higher-level goal.Source: 3) Multi-level environment and goal… · p. 8

B. Illustration of Static Aspects

The static illustration models the port’s IAV fleet at multiple levels, with component systems organized into groups and assigned roles. It specifies how those roles and group requirements relate to component capacities.

B. Illustration of Static Aspects

  • The model represents the fleet at four levels, from individual IAVs at l0 to the whole fleet at l3.The detailed example focuses on CS2,2 and its under CS CS4,0, CS5,0, and CS6,0.Source: B. Illustration of Static Aspects · p. 8
  • CS2,2 represents a quay fleet and plays quayTransporter and quayTransmitter roles, while CS4,0, CS5,0, and CS6,0 are its individual-IAV under CS.Its capacity function considers the capacities of CS2,2 and its under CS.Source: B. Illustration of Static Aspects · p. 8
  • Group g1 requires at least one quayTransporter and one quayTransmitter, and permits a CS agent to play both roles simultaneously.A CS agent assigned a role in a gs1 group cannot play a role in another group defined by gs1.Source: B. Illustration of Static Aspects · p. 8
  • A quayTransporter must carry at least one container per hour, and a quayTransmitter must transmit at least two messages per second.The whole population of quayTransmitters must also meet a cumulative transmission-capacity requirement.Source: B. Illustration of Static Aspects · p. 8
  • The g3 group specification applies a similar role-and-capacity structure to individual IAVs at a different level and scale.CS4,0, CS5,0, and CS6,0 each play transporter and transmitter roles and have no under CS.Source: B. Illustration of Static Aspects · p. 9

C. Dynamic Aspects

The dynamic formalism forms or reorganizes component-system groups to meet the SoS’s goals as goals, missions, or component capacities change. It includes mechanisms for capacity changes and for handling component systems that lose their CS status.

C. Dynamic Aspects

  • Two mechanisms support global-goal feasibility during SoS evolution: forming groups with suitable capacity and responding to component-system capacity changes.The paper notes related work on construction, reconfiguration, and capacity management that does not address system control,,,.Source: C. Dynamic Aspects · p. 9
  • At initialization or after a goal change, the SoS instantiates groups whose capacities and available agents match the goal needs, using group specifications.The creation process forms groups from higher-level needs down to elementary CS agents.Source: 1) SoS Creation · pp. 9–10
  • The functional specification represents SoS goals, missions, plans, and the mapping from missions to attached goals.Missions are sequences of CS-agent actions; goals are decomposed into subgoals across levels, with missions allocated to CS agents.Source: 1) SoS Creation · p. 9
  • The reconfiguration algorithm decomposes a CS goal into subgoals, selects a suitable group specification and CS-agent definitions, then instantiates agents and allocates missions.It returns a configuration respecting SoS characteristics or reports that no available configuration exists.Source: 1) SoS Creation · p. 10
  • When a CS loses capacity, it first attempts local reorganization; if that fails, it informs its super CS, propagating the response up to the top CS.If the top CS can no longer reorganize, it can inform the modeler that the SoS has failed and no means remain to reach the global goal.Source: 2) Capacity Evolution · p. 10
  • In the example, a failed IAV prevents its platoon from delivering 40-feet containers, but the quay fleet reorganizes by switching IAVs while maintaining its structure.The platoon itself cannot reorganize using its remaining under CS.Source: 2) Capacity Evolution · p. 10
  • When component systems lose CS status after aggregation, the model replaces their CS agents with virtual CS agents that retain potential-CS status.The virtual agents remain relevant to the super CS’s evolution and capacities and can represent non-virtual CS again if the aggregation link is removed.Source: 3) Particular case of virtual CS… · pp. 10–11

D. Illustration of Dynamic Aspects

The dynamic illustration starts with only the top CS and elementary CS present, then builds the intermediate structure around a functional specification. The completed model’s specification records goals, missions, their decomposition, and goal links.

D. Illustration of Dynamic Aspects

  • The illustration uses the mission distribution shown for the SoS to demonstrate its dynamic modeling process.The passage points to Fig. 10 for the mission distribution and to the earlier SoS example.Source: D. Illustration of Dynamic Aspects · p. 11
  • Before construction, the model contains the top CS, all elementary CS, and only the SoS’s global goal allocated to the top CS.It also includes levels, hierarchical, influence and perception graphs, CS-agent definitions, group specifications, and a nearly empty functional specification.Source: D. Illustration of Dynamic Aspects · p. 11
  • Once built, the functional specification lists goals and missions across levels, with plans decomposing higher-level goals into subgoals.It also maps missions to the goals they serve.Source: D. Illustration of Dynamic Aspects · p. 11

E. Respecting Fundamental characteristics

The paper translates SoS characteristics into conditions on component-system agents and illustrates whether those conditions hold in the IAV example. Its account of evolutionary development includes adding or deleting agents and responding to missions that become impossible.

E. Respecting Fundamental characteristics

  • The formalism’s agent-based models are presented as respecting directed SoS characteristics.The section translates the characteristics into model conditions and illustrates them with the IAV SoS.Source: E. Respecting Fundamental… · p. 11
  • CS4,0 is operationally independent, whereas CS1,0 is not because it shares resources with CS2,0.Operational independence is defined through component systems having their own private resource variables.Source: E. Respecting Fundamental… · p. 11
  • CS4,0 is geographically dispersed, but CS1,0 and CS2,0 are not because the leader’s position determines the follower’s position.The model permits information exchange but not physical links between component-system agents to accomplish missions.Source: E. Respecting Fundamental… · p. 12
  • CS2,2 can fulfill its missions only through cooperation among CS4,0, CS5,0, and CS6,0, which perform their own missions.This illustrates emergent behavior as joint action needed for a global mission that no single component system can realize alone.Source: E. Respecting Fundamental… · p. 12
  • Evolutionary development covers adding or removing a CS agent and detecting that a mission cannot be fulfilled; an impossible mission is freed for reallocation or reorganization.If a deletion affects a super CS’s capacity, the loss is communicated through influences and the SoS is reorganized.Source: E. Respecting Fundamental… · pp. 12–13
  • The illustrated SoS changes through deletion of CS3,0 and later addition of CS3,0 and CS4,0; the CS3,0 in the later state need not be the same agent.The model requires new agents to enter groups whose roles do not affect the capacity of the CS formed by the group.Source: E. Respecting Fundamental… · pp. 12–13

V. CONCLUSION AND FUTURE WORK

The paper presents an operational SoS definition and a generic multilevel, multi-agent formalism for centrally managed SoS in changing environments. It illustrates the approach with an IAV fleet and identifies extensions involving parallel levels, other simulation tools, and improved group formation.

V. CONCLUSION AND FUTURE WORK

  • The formalism defines SoS through five component-system characteristics and models centrally managed SoS as they evolve in environments that affect component capacities.The characteristics are operational and managerial independence, geographic distribution, evolutionary development, and emergent behaviour.Source: §V · p. 13
  • The model represents SoS at multiple levels and in groups, with elements offered to support the approach's validity.Source: §V · p. 13
  • The InTrade IAV case links a MaDKit SoS model with SCANeRstudio to observe how low-level events can affect vehicles and higher-level scheduling.The described simulation is being implemented; Fig. 16 shows UDP communications between SCANeRstudio and MaDKit, while Fig. 15 depicts an IAV platoon in SCANeRstudio.Source: §V · p. 13, Figure 16 · p. 13, Figure 15 · p. 13
  • Future work could couple the model with Flexsim CT to represent container-terminal traffic flow and provide semi-realistic inputs at a higher level.The paper describes coupling with simulation tools other than SCANeRstudio as a development direction.Source: §V · pp. 13–14
  • IRM4MLS levels are currently used to simulate different granularities, but can also represent parallel aspects such as IAV diagnosis and driving.The paper notes that these functions could lead to different SoS structures.Source: §V · p. 14
  • Further work could improve group formation by choosing group specifications and component agents according to SoS robustness or mission quality.Source: §V · p. 14
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