The gradient-based routing algorithm considers the number of hops as the distance cost from a node to a sink is proposed by routing over lossy link (ROLL) [8]. In this paper, the height value at each node also implies the minimum hop
A. Distance Cost ModelA node defines a scalar field, called the node's height [13] by advertising packets. This is a common method to provide basic routing function and is used by several routing algorithms, e.g., the well-known shortest path first (SPF) algorithm [14]. A packet is forwarded on the link with the steepest gradient to the next nodes. Each node x maintains a distance cost with respect to all sinks (in a multi-sink scenario):industrial networks. Our proposal exploits two-hop information and enhances congestion detection ability owing to its monitoring of the buffer length at a node. The underlying concept of our algorithm is the construction of gradient field using three factors: number of hops, number of packets at one-hop neighbors and the minimum number of packets at two-hop neighbors corresponding to the previous node. The number of hops (distance cost) is built conventionally as in other gradient-based routing protocols that find the shortest paths for packets. The second and third factors address the queue length at neighboring nodes that may become the next forwarder. Once the queue length, changing with network traffic exceeds a threshold, it means that there is congestion at a node in the path toward a specific sink. The node asks its surrounding nodes to increase (or decrease) their gradient field so that packets can flow along other paths. Thus, this method leads to a trade-off between shortest paths and packet delays caused by congestion at overloaded nodes.The rest of this paper is organized as follows. In Section II, we build a system model with the total gradient field and outline how the local cost and global cost models are combined in our proposed scheme. In Section III, the implementation of our proposed algorithm is described in detail. The simulation model and performance evaluations are given in Section IV. Finally, Section V concludes this paper and infers some limitations and future work.(1) \71 (x) == hop_count.