All the existing real world networks are evolving, hence, study of traffic dynamics in these enlarged networks is a challenging task. The critical issue is to optimize the network structure to improve network capacity and avoid traffic congestion. We are interested in taking user's routes such that it is least congested with optimal network capacity. Network capacity may be improved either by optimizing network topology or enhancing in routing approach. In this context, we propose and design a model of the time varying data communication networks (TVCN) based on the dynamics of in-flowing links. Newly appeared node prefers to attach with most influential node present in the network. In this paper, influence is termed as and is applied for computing overall congestion at any node. User path with least betweenness centrality and most reputation is preferred for routing. Kelly's optimization formulation for a rate allocation problem is used for obtaining optimal rates of distinct users at different time instants and it is found that the user's path with lowest betweenness centrality and highest reputation will always give maximum rate at stable point.
@cite_3: Modern communication networks are able to respond to randomly fluctuating demands and failures by adapting rates, by rerouting traffic and by reallocating resources. They are able to do this so well that, in many respects, large-scale networks appear as coherent, self-regulating systems. The design and control of such networks present challenges of a mathematical, engineering and economic nature. This paper outlines how mathematical models are being used to address one current set of issues concerning the stability and fairness of rate control algorithms for the Internet.
@math is a matrix at time interval @math to @math . The given constraint states that a link can not send data more than its capacity @cite_3 . It is difficult and unmanageable to allocate a suitable utility function and optimal rate to distinct users in complex networks. Hence, Kelly has divided this problem into two simpler problems named as user's optimal problem and network's optimal problem @cite_3 . Let user @math decide an amount @math to pay per unit time, while @math is demanded a price @math for unit flow. Hence, user will acquire a flow, @math at time @math . User's optimal price for sending @math at time @math can be obtained using the optimization problem as On the other hand, network wants to maximize weighted log function of @math . Therefore, network optimization problem can be formulated as