## 1 Introduction  
The traffic in backbone networks has grown exponentially during the past two decades. With the ever-growing data-intensive applications relying on the Internet, the growth will be accelerated and the backbone networks will be increasingly overloaded. To adaptively select the optimal route for backbone network has been the main goal of research over decades [1; 2; 3; 4; 5; 6; 7]. However, as current routing strategies, such as OSPF, RIP, and EIGRP, use stationary channel measurement as criteria [8; 9], it is difficult to predict an optimized route that will stay optimal for a long time when the channel congestion situation keeps oscillating, especially during peak hours [2; 5; 10; 11; 12; 13; 14]. Based on the criteria of the current routing strategy, the optimal route selected often changes frequently in extremely congested networks. When a path is congested due to large amount of traffic flows, the latency soars and the router swaps to another path, and after that, the traffic redirected to the backup path makes the path congested and its latency increase sharply, and now the original path seems to be the optimal one again, etc. Such reroutings are a huge waste to computation resources and energy power, and the errouting delay may affect the quality of service (QoS) and user experience ultimately. Being able to reduce the number of reroutings by selecting a path that is consistently optimal over a relatively long time is thus important. How to model that a path is optimal over a long period of time so that it can work as a metric for the consistent optimal route is the question that we are trying to answer in this paper. Numerous solutions have been proposed for adaptive routing in backbone networks, but this question still exists in current telecommunication networks.  
There are two main trends in the current adaptive routing for backbone networks, using software defined networking (SDN) and/or artificial intelligence. Deemed as the next generation networking, SDN was adopted by most of the recent work on adaptive routing, taking advantage of the centralized control strategy [5; 6; 15; 16; 17; 18]. These works involve one or more centralized controllers in their design, collecting global knowledge of the network to achieve optimized QoS for the entire network. Artificial intelligence technologies, like machine learning, and especially deep learning and reinforcement learning, have been widely adopted in various aspects that need data to predict [5; 6; 17; 18; 19].  
In this paper, a metric of consistent adaptive routing is proposed to improve load balancing and achieve consistent adaptive routing by analyzing real-life backbone traffic and predicting future congestion situations. More specifically, the following contributions are made:  
* A Differential Path Congestion Consistency Model is proposed to describe the latency variation between two paths.
* Based on the model, a _Path Swap Indicator (PSI)_ is proposed to predict the future latency changing trend. Relying on learning the latest congestion situation and predicting the onset of a long-term and consistent channel deterioration, the routing strategy is able to make a long-term effective decision on the path switching, i.e., to switch the path if and only if the target path's condition will be better than the current one over a relatively long period of time.
* Experiments on a testbed built by the Docker network were carried out to evaluate the proposed strategy. The results are presented and analyzed in detail.