Random walks are the most fundamental process among various dynamical processes, and most previous works focused on binary networks. This work studies random walks on deterministic weighted scale-free small-world networks with a perfect trap. We derive an explicit expression of the mean first passage time on the network with a trap. Meanwhile, we present the evolutionary rule for the first passage time when the network grows. The study can be useful for understanding the random walks on weighted networks.

This paper proposed a novel routing strategy with two tunable parameters, [Formula: see text], [Formula: see text], based on the dynamic local information in a finite buffer network. The system behaves differently from that with a local routing strategy based on the degree with an adjustable parameter [Formula: see text]. Simulations show that, under dynamic local strategy, the maximal capacity of the network system increases with [Formula: see text] whereas it increases with the decrement of [Formula: see text] in the case of all the nodes having identical delivering ability. The dynamic local routing performs much better than the local routing, which is demonstrated by a larger value of the critical packet generation rate. We found that buffer coefficient has a limited impact on the performance of network system. We also demonstrate that a smaller [Formula: see text] would be better if we want to have an excellent traffic capacity considering the travel time, average path length and waiting time. Our study will be helpful to improve traffic performance in finite buffer networks.

Random walks on complex networks are of great importance to understand various types of phenomena in real world. In this paper, two types of biased random walks on nonassortative weighted networks are studied: edge-weight-based random walks and node-strength-based random walks, both of which are extended from the normal random walk model. Exact expressions for stationary distribution and mean first return time (MFRT) are derived and examined by simulation. The results will be helpful for understanding the influences of weights on the behavior of random walks.

The study of traffic dynamics on couple networks is important for the design and management of many real systems. In this paper, an efficient routing strategy on coupled spatial networks is proposed, considering both traffic characteristics and network topology information. With the routing strategy, the traffic capacity can be greatly improved in both scenarios of identical and heterogeneous node capacity allocation. Heterogeneous allocation strategy of node delivery capacity performs better than identical capacity allocation strategy. The study can help to improve the performance of real-world multi-modal traffic systems.

No abstract