Effects of Randomly Added Links on a Phase Transition in Data Network Traffic Models Anna T. Lawniczak Alf Gerisch Kevin Maxie Dept. of Math. and Stat. Dept. of Math. and Computer Sc. Dept. of Math. and Stat. Guelph-Waterloo Physics Inst. University of Halle University of Guelph University of Guelph 06099 Halle (Saale), Germany Guelph, Ont N1G 2W1, Canada Guelph, Ont N1G 2W1, Canada gerisch@mathematik.uni-halle.de kmaxie@uoguelph.ca alawnicz@uoguelph.ca Abstract— We investigate how additional links added randomly to a network connection topology affect the phase transition from the free flow state to the con- gested state in packet-switching networks (PSNs). For the purpose of our study we have identified that the OSI Network Layer is the most important layer of the OSI reference model. For this layer we developed an abstraction for which we derived a time-discrete algo- rithmic simulation model. Using this simulation model we investigate the effects of various routing algorithms and connection topologies on the phase transition point. In this article we highlight the developed methodology and present some selected results. I. Introduction The global Internet, wireless communication systems, ad-hoc networks or sensors networks are some of the ex- amples of data networks of packet-switching type. These packet switching networks (PSNs) have experienced un- precedented growth that is going to continue in the fore- seeable future. Hence, understanding the dynamics of flow and congestion in PSNs is of vital importance. One of the important aspects of these dynamics is a phase transition from the free flow to the high congestion state indicated in terms of number of packet in transit in the network. Some aspects of this phase transition can be captured and inves- tigated by studying simplified models of PSNs [1, 2, 3, 4]. The aim of our work is to study how additional links added randomly to a network connection topology affect the phase transition from the free flow state to the congested state in PSNs. For the purpose of our study we have identified that the OSI network layer is the most important layer of the OSI reference model. For this layer we developed an ab- straction for which we derived a time-discrete algorithmic simulation model [5]. Using this simulation model we in- vestigate the effects of various routing algorithms and con- nection topologies on a phase transition point. In order to simulate our algorithmic models of PSNs we developed a C++ simulation tool, called Netzwerk-1 [6]. In this article we highlight only the developed methodology and present some selected results. For a more extensive treatment of the topic the interested reader is referred to [5]. This work is the continuation of the research commenced by some of the authors in [7, 8, 9], and it can be easily extended to study dynamics of more complex networks. II. Packet-switching network models There exists a vast amount of literature about PSNs, e.g. [10, 11]. Here we briefly review the material that is im- portant for the development of our PSN models and outline their construction. The detailed construction is described in [5]. The purpose of a PSN is to transmit messages from points of origin to destination points. In our models, we as- sume that the entire message is contained in a single “cap- sule” of information, which, by analogy to PSNs, is simply called a packet. In a real PSN, a single packet carries the in- formation “payload”, and some additional information re- lated to the internal structure of the network. Since our aim is to understand, for various routing algorithms, the effects of additional randomly generated links on network flow and congestion, we ignore the information “payload” entirely. Hence, in the considered models we assume that each packet carries the following pieces of information: time of its creation, its destination address and some information to assess the performance of a model. Our simulated network models consist of a number of in- terconnected nodes. Each node can perform two functions: that of a host, meaning that it can generate and receive packets, and that of a router (message processor), meaning that it can store and forward packets. Packets are created randomly at each node and independently from the other nodes. An incoming queue and outgoing queues are main- tained by each node to store packets on this node. We consider the case of one outgoing queue per switching node in this paper. We assume that each queue can be of un- limited size and observes a first-in first-out policy. Packets are routed according to the routing decisions made at each node independently from the other nodes. The creation and routing of packets is implemented by a discrete time, synchronous and distributed in space network algorithm. The structure of the networks considered and their routing algorithms are described in subsections which follow. 384 Proceedings of the Third International DCDIS Conference Copyright c 2003 Watam Press