Traffic dynamics in scale-free networks with limited packet-delivering capacity

We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node's packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node $i$ is proportional to $k_{i}^{\phi}$, where $k_{i}$ is the degree of node $i$ and $\phi$ is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter $\phi$ leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal $\phi$

Efficient routing on scale-free networks based on local information

In this letter, we propose a new routing strategy with a single free parameter $\alpha$ only based on local information of network topology. In order to maximize the packets handling capacity of underlying structure that can be measured by the critical point of continuous phase transition from free flow to congestion, the optimal value of $\alpha$ is sought out. By investigating the distributions of queue length on each node in free state, we give an explanation why the delivering capacity of the network can be enhanced by choosing the optimal $\alpha$. Furthermore, dynamic properties right after the critical point are also studied. Interestingly, it is found that although the system enters the congestion state, it still possesses partial delivering capability which do not depend on $\alpha$. This phenomenon suggests that the capacity of the network can be enhanced by increasing the forwarding ability of small important nodes which bear severe congestion.Comment: 4 pages, 7 figure

Theoretical approach and impact of correlations on the critical packet generation rate in traffic dynamics on complex networks

Using the formalism of the biased random walk in random uncorrelated networks with arbitrary degree distributions, we develop theoretical approach to the critical packet generation rate in traffic based on routing strategy with local information. We explain microscopic origins of the transition from the flow to the jammed phase and discuss how the node neighbourhood topology affects the transport capacity in uncorrelated and correlated networks.Comment: 6 pages, 5 figure

Efficient routing strategies in scale-free networks with limited bandwidth

We study the traffic dynamics in complex networks where each link is assigned a limited and identical bandwidth. Although the first-in-first-out (FIFO) queuing rule is widely applied in the routing protocol of information packets, here we argue that if we drop this rule, the overall throughput of the network can be remarkably enhanced. We proposed some efficient routing strategies that do not strictly obey the FIFO rule. Comparing with the routine shortest path strategy, the throughput for both Barab\'asi-Albert (BA) networks and the real Internet, the throughput can be improved more than five times. We calculate the theoretical limitation of the throughput. In BA networks, our proposed strategy can achieve 88% of the theoretical optimum, yet for the real Internet, it is about 12%, implying that we have a huge space to further improve the routing strategy for the real Internet. Finally we discuss possibly promising ways to design more efficient routing strategies for the Internet.Comment: 5 pages, 4 figure

Phase transition and hysteresis in scale-free network traffic

We model information traffic on scale-free networks by introducing the node queue length L proportional to the node degree and its delivering ability C proportional to L. The simulation gives the overall capacity of the traffic system, which is quantified by a phase transition from free flow to congestion. It is found that the maximal capacity of the system results from the case of the local routing coefficient \phi slightly larger than zero, and we provide an analysis for the optimal value of \phi. In addition, we report for the first time the fundamental diagram of flow against density, in which hysteresis is found, and thus we can classify the traffic flow with four states: free flow, saturated flow, bistable, and jammed.Comment: 5 pages, 4 figure

Scaling behavior of an artificial traffic model on scale-free networks

In this article, we investigate an artificial traffic model on scale-free networks. Instead of using the routing strategy of the shortest path, a generalized routing algorithm is introduced to improve the transportation throughput, which is measured by the value of the critical point disjoining the free-flow phase and the congested phase. By using the detrended fluctuation analysis, we found that the traffic rate fluctuation near the critical point exhibits the $1/f$-type scaling in the power spectrum. The simulation results agree very well with the empirical data, thus the present model may contribute to the understanding of the underlying mechanism of network traffics.Comment: 6 pages, 5 figure

The effect of bandwidth in scale-free network traffic

We model information traffic on scale-free networks by introducing the bandwidth as the delivering ability of links. We focus on the effects of bandwidth on the packet delivering ability of the traffic system to better understand traffic dynamic in real network systems. Such ability can be measured by a phase transition from free flow to congestion. Two cases of node capacity C are considered, i.e., C=constant and C is proportional to the node's degree. We figured out the decrease of the handling ability of the system together with the movement of the optimal local routing coefficient $\alpha_c$, induced by the restriction of bandwidth. Interestingly, for low bandwidth, the same optimal value of $\alpha_c$ emerges for both cases of node capacity. We investigate the number of packets of each node in the free flow state and provide analytical explanations for the optimal value of $\alpha_c$. Average packets traveling time is also studied. Our study may be useful for evaluating the overall efficiency of networked traffic systems, and for allevating traffic jam in such systems.Comment: 6 pages, 4 figure