Finding the biased-shortest path with minimal congestion in networks via linear-prediction of queue length

In this paper, we propose a biased-shortest path method with minimal congestion. In the method, we use linear-prediction to estimate the queue length of nodes, and propose a dynamic accepting probability function for nodes to decide whether accept or reject the incoming packets. The dynamic accepting probability function is based on the idea of homogeneous network flow and is developed to enable nodes to coordinate their queue length to avoid congestion. A path strategy incorporated with the linear-prediction of the queue length and the dynamic accepting probability function of nodes is designed to allow packets to be automatically delivered on un-congested paths with short traveling time. Our method has the advantage of low computation cost because the optimal paths are dynamically self-organized by nodes in the delivering process of packets with local traffic information. We compare our method with the existing methods such as the efficient path method (EPS) and the optimal path method (OPS) on the BA scale-free networks and a real example. The numerical computations show that our method performs best for low network load and has minimum run time due to its low computational cost and local routing scheme.