# Congestion-Aware Geocast Routing in Vehicular Delay-Tolerant Networks
## 4 V-GRADIENT Design
### Dynamic Replication Mechanism  
One of the main conclusions drawn from the analysis of the previous subsection relates to the benefits of the application of a moderate replication process outside the regions of interest, particularly if the vehicle's density is low and ROIs' dimensions are small. This is shown in Figure 3, where the size of the buffer zone \(R_{MAX}\) is determined through Equation (5). The replication mechanism inside the ROI should depend upon several parameters. For instance, if all nodes are interested in the messages, corresponding to a penetration rate of \(\sigma_{rate}=100\%\), the messages should be distributed to all nodes within the ROI and all nodes should contribute to spreading the message as fast as possible within the ROI. However, if only a small fraction of the nodes are interested in the messages, corresponding to a low penetration rate, the messages' TTL is small and the network is sparse, and the interested nodes may not be enough for efficiently spreading the messages, resulting in a low delivery ratio. Thus, the V-GRADIENT adopts two mechanisms for improving message dissemination in these situations. First, a flooding zone is defined, smaller than the ROI, where messages are flooded to every node, as in the epidemic protocol. Second, a ticket-based spraying heuristic, as proposed in [11] is used, where some nodes not directly interested in the message are selected to help to disseminate messages within the ROI or the buffer zone. If \(T\) tickets are assigned, the number of message replicas transmitted during the spray phase is \(2^{T}\), as in [11]. Naturally, if the network is sufficiently dense and/or the ROIs' radiuses are considerably large, messages will run out of tickets in locations closer to the ROI's center and no replication will occur outside of the ROIs. Notably, it was considered enough for the V-GRADIENT protocol to have \(T=3\) tickets assigned to all messages. Nodes using the V-GRADIENT have to estimate the penetration rate (\(\sigma_{rate}\)) of all distinct geocast groups in the network. When a contact opportunity arises between two nodes, they exchange geocast group identifiers, which they are interested in. This allows them to keep a dictionary with a count of the number of nodes contacted that were interested in each geocast group. By keeping a count of all established contacts also, the penetration rate (\(\sigma_{rate}\)) is simply the fraction of nodes contacted that were interested in each geocast group, as kept in the dictionary, over the total number of nodes contacted. Figure 3: Message flooding zone (light blue) and buffer zone size (dark blue) as compared to the size of the ROI (red). Figure 4 shows the evolution of the average penetration rate measured by nodes for three different geocast groups with penetration rates of 25%, 50%, and 75%, and for different density conditions of 40, 100, and 200 nodes in the Helsinki scenario. As can be seen, the nodes can have a fairly accurate idea of the real penetration rate for each geocast group, and the convergence speed is faster for denser networks and higher penetration rates, as this results in more frequent contacts between nodes. The V-GRADIENT uses the penetration rate metric to control the number of uninterested vehicles that should cooperate in forwarding messages of geocast groups of low penetration rates. The term control stems from the limited amount of shared resources available, which implies the management of a trade-off. The more forwarding load assigned to nodes that are not interested in messages results in an improvement in the delivery performance of such messages. In contrast, the resources spent on carrying and forwarding messages which the nodes have no interest in end up, inevitably, compromising the delivery of those in which they are interested. Thus, to allow a fair distribution of the forwarding load, the proposed algorithm for the V-GRADIENT defines a flooding region within the ROI whose area covers a portion of the ROIs directly linked to the penetration rate measured.