Topological analysis of a two coupled evolving networks model for business systems

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Abstract

In multi-agent systems, the underlying networks are always dynamic and network topologies are always changing over time. Performance analyses of topologies are important for understanding the robustness of the system and also the effects of topology on the system efficiency and effectiveness. In this paper, we present an example of a real-world distributed agent system, a digital business ecosystem (DBE). It is modelled as a two coupled network system. The upper layer is the business network layer where business process between different business agents happen. The lower layer is the underlying P2P communication layer to support communications between the agents. Algorithms for multi-agent tasks negotiation and execution, interaction between agents and the underlying communication network, evolutionary network topology dynamics, are provided. These algorithms consider the two network layers evolving over time, with effects on each other. Through a comprehensive set of discrete event simulation, we investigate the effects of different evolutionary principles inspired by random graph and scale-free network in complex network theory on the topological properties and performance of the underlying network. We also find several rules to design a resilient and efficient P2P network.

Introduction

Nowadays, cooperation between individual business entities is more and more important. In order to flourish, enterprises have to develop in the form of clusters. Therefore, the biological word, ecosystem, is widely used to describe the increasingly interrelated nature of enterprises as the organisms in a business ecosystem. In this business ecosystem, customers obtained goods and services of value. At the meanwhile, they also co-evolve their capabilities, role and tend to alone themselves with the future directions. The digital business ecosystem (DBE) is the enabling technology for the business ecosystem (Annex 1, 2003).

Although the Internet has changed our world dramatically, the concept of an Internet presence is still based on centralisation. A system like the Internet, starts to become an organism in itself which is more than the sum of its individual parts. The DBE is a type of business middleware designed and built to be distributed across the Internet rather than to reside on any one computer. It provides an open-source distributed environment for small and medium enterprises (SMEs), producing entirely new behavior in software. Moreover, with the Internet acting as the platform, applications can work together to perform complex interactions whether they are centrally provided or peer-to-peer applications. If DBE can succeed in business, it could be the precursor of many similar digital ecosystems that lead the world into the next revolution in information and communication technology – the knowledge society. Behaviors and performance of such complex ecosystems are worth studying (Darking et al., 2008, Mansell, 2006, Razavi et al., 2007, Sacha et al., 2007). In this paper, we present a two coupled network model as an example of a real-world distributed agent system. It consists of a business network layer where services exchanges take place in and a peer-to-peer (P2P) communication layer that supports the communication in the system.

P2P network becomes popular due to its advantage in file-sharing. However, these P2P networks have some shortcomings in efficiency and scalability. Many research work focus on routing algorithms and protocols to solve the problems. Most of these work rely on specific topologies for their analytic and simulation studies. However, it is important to be aware that topology determines how agents interact and cooperate with each other, and topology itself also has significant impact on the performance, scalability, and communication cost. Therefore, the underlying architecture of peer agents network must support sophisticated behaviors of agents. It is necessary to study structure and topology to construct complex systems involving multiple interacting agents and the way how they cooperate. Proper structured topology plays an important role in this issue. The topological models of multi-agent systems have been found to enhance agents communication efficiency (Androutsellis-Theotokis & Spinellis, 2004). The advantages and disadvantages of different topological models on have been compared and their effects on performance of agents network have been explored (Zhu, 2006). More specifically, for example, in Soumaa et al. (2006), the correlation of entities in business network have been found to be strongly depending on the type of the network. However, these work do not consider the topological models as dynamic topology networks and effects of communication of agents on the topology have not been studied. In our case, we consider an evolving business network involving multiple agents, whose communication and cooperation are supported by an underlying P2P communication network. Both of the networks are changing and interacting with each other over time. We investigate how the performance and network resilience of the P2P communication network depends on the network topology of the P2P network itself, and also dynamics and system requirements of business networks. Moreover, it is worth studying other networks such as our previous work on evolving e-mail networks (Wang & Wilde, 2004) and supply chains network (Thadakamalla, Raghavan, Kumara, & Albert, 2004).

Current research work on the agent network topology is still not systematic and is often based on the network graph provided. Besides simple graph topology such as mesh-like topology, star-like topology, topological theory in complex networks has been widely applied to complex agent networks recently. Based on the complex network theory, there are currently random graph, small-world and scale-free network as options for network topologies. The random graph was introduced by Erdös and Rènyi (1959), in which edges are distributed randomly and the presence or absence of any edge between two nodes in the network is dependent on a fixed connection probability p. Other networks, such as networks of movie actor collaboration (Barabàsi and Albert, 1999, Watts and Strogatz, 1998), science collaboration (Redner, 1998), WWW (Albert et al., 1999, Huberman and Adamic, 1999) and Internet (Faloutsos, Faloutsos, & Faloutsos, 1999) have been found that the degree distribution of them follows a power-law distribution with different exponent. They are the so-called scale-free networks. In 1999, Barabàsi and Albert presented in Barabàsi and Albert (1999) that the scale-free network behavior was found to be the consequence of two mechanisms: growth of nodes and preferential attachment to well connected nodes. After that, the scale-free networks were studied extensively (Ebel et al., 2002, Klemn and Eguiluz, 2002, Newman, 2001). Recent works (Lia and Kong, 2006, Sun et al., 2006) have further considered the influence of preferential attachment on evolving networks. Surveys on the studies of the territory can be found in Dorogovtsev and Mendes, 2002, Newman, 2003, Albert and Barabàsi, 2002. Many researchers have also studied the networks, such as models leading to random graphs and scale-free networks, how to improve network performance and robustness and so on (Beygelzimer et al., 2005, Chen et al., 2007, Wang et al., 2006).

As presented above, a lot of studies on complex networks illuminated how specific topologies or connectivity patterns are based on the construction and growth of such networks. Nevertheless, the topological study in the multi-agent field is still inadequate. Most of the related work applies a specific topology, such as random graph, small-world topology or scale-free topology to an agent network, which do not take the dynamic behavior of topology into account. Furthermore, these network topologies including random graph and the scale-free network, however, were found to have their own advantages on different aspects. For example the random graph is more robust to attack than scale-free topology, while is less robust to random failure (Albert, Jeong, & Barabàsi, 2000). Thus we cannot use one specific topology directly to construct our network. In this paper, we show that it is useful to apply their evolution principles to model the dynamic topology network. Through discrete event simulation and analysis, we find out that some evolutionary principles have strong effects on the performance and topological properties of the system.

The rest of the paper is organized as follows. The next section presents a two coupled networks model, with a business network and an underlying P2P communication network interacting with each other over time. Section 3 presents the experimental design of the topological experiment and Section 4 shows our experimental results. Finally, Section 5 finalizes with the conclusions of the work and the direction of the future work.

Section snippets

Two coupled networks model

In this section, we present an example of a real-world distributed agent system, a digital business ecosystem (DBE). It is a model based on the following real-world scenario: small and medium enterprises (SME) may be providers or consumers of services, who are all clients of the system. SME provider clients use the system to submit their services descriptions. The system server aggregate and recombine these services into service chains and form complex services. Based on the feedback from

Simulation

The simulation procedure consists of the initialization stage that build up the initial state of the network topology and evolving stage that model the dynamic topology network.

  • Stage I (initialization):

    • Firstly, we setup the P2P communication network by using Random graph model or Barabasi and Albert’s model.

    • Assume the number of SMEs in the network is numSMEs = 1000. Among these SMEs, several SMEs are randomly selected to initially register their services proxies in FADA nodes. The amount of these

Degree distribution

In this section, we study the degree distribution of P2P communication network by plotting the probability of nodes having k degree as a function of k. Fig. 3 shows the results when the network evolves to N = 600 nodes, where (1)–(8) refers to different cases as presented in Table 1.

Power laws have been found in many different fields of network, comprehensively presented in Albert and Barabàsi (2000). We are interested in determining whether the P2P communication network with its evolution

Conclusion and future work

In this paper, we presented an example of a real-world distributed agent system, a digital business ecosystem (DBE). It can provide an open-source distributed environment that can support the spontaneous evolution and composition of services for SMEs. It is modelled as a two coupled network system. The upper layer is an evolving business network involving multiple agents and the lower layer is the underlying P2P communication layer to support communications between the agents. Both of the

Acknowledgements

This work was supported in part by the project Digital Business Ecosystem, funded by the sixth Framework Programme of the European Commission. Contract No. IST-2002-507953 and the Natural Science Foundation of China under the project number 60773203.

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