# Congestion-Aware Geocast Routing in Vehicular Delay-Tolerant Networks
## 4 V-GRADIENT Design
### Dynamic Dropping Policy
\begin{table}
\begin{tabular}{c c} \hline \hline
**Map** & **The Downtown Part of the City of Helsinki** \\  & **[4500 m \(\times\) 3400 m]** \\ \hline Simulation time & 12 h \\ Movement model & Shortest Path Map-Based Movement \\ Type of nodes & Vehicles (cars) \\ Nodes’ speed interval & 10–50 km/h \\ Nodes’ message buffer size & 5 MB \\ Nodes’ wait time & 5–30 s \\ Message size interval & 500 kB–1 MB \\ Message generation interval & 30–90 s \\ Interfaces’ data rate & 250 kbps \\ Interfaces’ transmission range & 50 m \\ Initial Number of Copy Tickets & 3 \\ Message’s TTL & 150 min \\ Number of nodes & [20;50;100;200;300;400] nodes \\ ROI Radius & [200;400;600;800;1000] m \\ R\({}_{+ratio}\) & Vector of 100 evenly spaced points between 1 and 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Assigned parameters during the simulation procedure. Figure 1: Evolution of the average density level measured considering distinct density conditions. To exhibit the impact of the network density conditions and the ROIs' radius values on the additional dropping policy formulation, Table 2 includes the optimal \(R_{+ratio}\) values, bearing in mind the delivery ratio results obtained. It can also be seen in Table 2, that for a fixed number of nodes deployed in the network, the optimal \(R_{+ratio}\) expression can be modeled by an equation obtained through a power regression. The profile of such equations, following a trend depending on the number of nodes and consequently on the density level, also suggest a mathematical formulation of a variable threshold value associated with the extension of the buffer zone as shown in Equation (4). \[R_{+ratio}(R_{ROI},\rho_{t})=g(\rho_{t}){\cdot}R_{ROI}^{h(p)}. \tag{4}\]  
With respect to the formulation of the \(g(\rho_{t})\) and the \(h(\rho_{t})\) expressions, by selecting their corresponding target parameters presented in Table 2, it can be observed, as depicted in Figure 2, that both describe a well-modeled decay relative to the average density level, \(\rho_{avg}\), measured in simulations deploying a different number of nodes. In this sense, in scenarios characterized by extreme buffer congestion issues, the V-GRADIENT algorithm allows a dynamic adjustment of the range of the buffer zone for all messages carried by a particular node according to the estimated threshold expression presented in Equation (5), as a result of the best fit from Figure 2. Additionally, the buffer occupation level metric plays an important role in detecting the occurrence of congestion, providing nimbleness to the dropping policy operation. If we let ourselves picture a scenario where only a few messages are generated per hour, it can be concluded that, because no congestion issues arise, the drop policy should be less restrictive. For this reason, a \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **50 Nodes** & **100 Nodes** & **200 Nodes** & **400 Nodes** \\  & \(\rho_{avg}\)**= 0.3952** & \(\rho_{avg}\)**= 0.8329** & \(\rho_{avg}\)**= 1.6470** & \(\rho_{avg}\)**= 3.2884** \\ \hline \(R_{ROI}\) = 200 m & 9.5 & 8.6 & 8.1 & 7.9 \\ \(R_{ROI}\) = 400 m & 3.4 & 3 & 2.8 & 2.5 \\ \(R_{ROI}\) = 600 m & 2 & 1.7 & 1.5 & 1.4 \\ \(R_{ROI}\) = 800 m & 1.5 & 1.2 & 1.1 & 1.1 \\ \(R_{ROI}\) = 1000 m & 1 & 1 & 1 & 1 \\ \hline \(\hat{R}_{+ratio}\) & \(12,872{\cdot}R_{ROI}^{-1.366}\) & \(10,970{\cdot}R_{ROI}^{-1.360}\) & \(9460{\cdot}3{\cdot}R_{ROI}^{-1.348}\) & \(7649{\cdot}4{\cdot}R_{ROI}^{-1.320}\) \\ \hline \(R^{2}\) score & 0.9964 & 0.9932 & 0.9827 & 0.9706 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal \(R_{+ratio}\) values obtained for simulations considering different density conditions and distinct regions of interest (ROI) radius values. Figure 2: Regression-based model for the: (**a**) \(g(\rho_{t})\); and (**b**) \(h(\rho_{t})\) expressions.