The description and analysis of emergence in complex adaptive system has recently become a topic of great interest in the field of systems, and lots of ideas and methods have been proposed. A Sign-based model of Stigmergy is proposed in this paper. Stigmergy is widely used in complex systems. We pick up “Sign” as a key notion to understand it. A definition of “Sign” is given, which reveals the Sign's nature and exploit the significations and relationships carried by the “Sign”. Then, a Sign-based model of Stigmergy is consequently developed, which captures the essential characteristics of Stigmergy. The basic architecture of Stigmergy as well as its constituents are presented and then discussed. The syntax and operational semantics of Stigmergy configurations are given. We illustrate the methodology of analyzing emergence in CAS by using our model.

Large-scale effects of locally interacting agents are called emergent properties of the system. Emergent properties are often surprising because they can be hard to anticipate the full consequences of even simple forms of interaction. In this paper we address the following questions: how do heterogeneous agents generate emergent coordination, and how do they manage and self-organize macroscopic orders from bottom up without any central authority? These questions will depend crucially on how they interact and adapt their behavior. Agents myopically evolve their behavior based on the threshold rules, which are obtained as the functions of the collective behavior and their idiosyncratic utilities. We obtain the micro-macro dynamics that relate the aggregate behavior with the underlying individual behavior. We show agents' rational behavior combined with the behavior of others produce stable macro behavior, and sometimes unanticipated cyclic behavior. We also consider the roles of conformists and nonconformists to manage emergent macro behavior. As a specific example, we address an emergent and evolutionary approach for designing the efficient network routings.

This paper proposes a traffic-adaptive dynamic routing method, which we have named RAG, for connectionless packet networks. Conventional traffic control methods discard the packets which cause congestion. Furthermore, conventional routing methods propagate control messages all over the network for gathering global topology information, and this causes more congestion. In contrast, RAG estimates traffic conditions all over a network without any communication between nodes and makes the best use of free links so that packets make detours to avoid congestive sites. RAG adopts distributed control based on game theory (non-communication, non-zero-sum, two-person). With RAG, nodes play a packet-forwarding game without any communication with each other, and each node controls ordering and routing of the forwarding packets based on the node's individual payoff table which is dynamically reconstructed by observation of surrounding nodes. Nodes cooperate with each other, except for punishment for disloyalty. Repetition of these local operations in nodes aims at the emergence of the gradual network-global traffic balancing. The results of experiments in comparison with the conventional shortest path first (SPF) routing method show that the throughput is about 1.58 times higher with the new method.