In this paper, we study the optimization of network traffic by considering the effects of node buffer ability and capacity. Two node buffer settings are considered. The node capacity is considered to be proportional to its buffer ability. The node effects on network traffic systems are studied with the shortest path protocol and an extension of the optimal routing [Phys. Rev. E 74 046106 （2006）]. In the diagrams of flux-density relationships, it is shown that a nodes buffer ability and capacity have profound effects on the network traffic.
A delayed chasing model is proposed to simulate the chase behavior in the queue, where each member regards the closest one ahead as the target, and the leader is attracted to a target point with slight fluctuation. When the initial distances between neighbors possess an identical low value, the fluctuating target of the leader can cause an amplified disturbance in the queue. After a long period of time, the queue recovers the stable state from the disturbance, forming a straightline-like pattern again, but distances between neighbors grow. Whether the queue can keep stable or not depends on initial distance, desired velocity, and relaxation time. Furthermore, we carry out convergence analysis to explain the divergence transformation behavior and confirm the convergence conditions, which is in approximate agreement with simulations.
