## 3 The Proposed EGR Approach for Highway Traffic Environment
### Geocast Routing  
A description of the routing process of the proposed protocol is explained in this section. In a highway IoV traffic environment, the vehicles are intermittently connected and they show high-speed vehicle mobility. In addition, natural phenomena, such as shadowing fading, influence connectivity. These constraints make the routing a challenging task in a highway traffic environment. All of the individual links that make up the route for hop-by-hop message forwarding must remain accessible for the duration of the remaining link lifetime. Due to the special characteristics of the highway, we are forced to incorporate residual link lifetime and caching methodology into the proposed EGR. Considering these critical issues, we present the route construction approach using a scenario depicted in Figure 3 in which a sending vehicle \(N_{i}\) estimates the temporal residual link-lifetime using Equation (9) for each vehicle \(N_{j}\) moving in a forward direction and are in the forward transmission region AOB (FTA) and transmission ranges of sending vehicle \(N_{i}\). Herein, we define two useful functions \(argmax\)(U) and \(argmin\)(U) that are used in the following section. Figure 3: Selection of a vehicle for transmission. **Definition 1**. : _argmax(U) is the set of neighbouring vehicles belonging in a FTA for which U attains the maximum value._  
**Definition 2**. : _argmin(U) is the set of neighboring vehicles belonging in a FTA for which U attains the minimum value._  
_Case 1: When vehicles present in FTA of forward lane_  
Let \(t_{tx}\), \(t_{pr}\), and \(t_{po}\) denote the transmission time of a packet on the link, the propagation time of the packet that travels via the link from the locations \(\big{(}x_{i^{\prime}}^{\prime}y_{i}^{\prime}\big{)}\) and \(\big{(}x_{j^{\prime}}^{\prime}y_{j}^{\prime}\big{)}\) of the vehicle \(N_{i}\) and vehicle \(N_{j}\) at time \(t^{\prime}\), and the processing time of the packet at the receiving vehicle. Each packet is acknowledged to confirm its guaranteed delivery. The round trip time \(t_{rt}\), in which a packet delivered successfully is the sum of transmission time, twice the propagation time, and the processing time. It can be given by  
\[t_{rt}=t_{tx}+2\times t_{pr}+t_{po} \tag{10}\]  
For routing purpose, the sending vehicle \(N_{i}\) chooses a vehicle \(N_{j}\) among neighboring vehicles that lay in its forward region that should satisfy the following condition:  
1. The residual link lifetime \(T_{ll}\) of the radio link between both the vehicles is greater than the round trip time \(t_{rt}\). 2. The temporal distance between the sending vehicle \(N_{i}\) and vehicle \(N_{j}\) should be high. When the sending vehicle obtains temporal residual link-lifetime and temporal distance information about its neighboring vehicles, the sending vehicle \(N_{i}\) selects a neighboring vehicle with maximum \(d(t^{\prime})\) as the next forwarding vehicle such that  
\[ \begin{array}{c}N_{j}=argmax\big{(}d(t^{\prime})\times\mathcal{P}_{i,j}(d(t ^{\prime}))\big{)}\\ st.\ T_{ll}-t_{rt}>0\end{array}  \tag{11}\]  
where, herein, a vehicle with a maximum value of \(d(t^{\prime})\times\mathcal{P}_{i,j}(d(t^{\prime}))\) is retuned by the _argmax() function_. Choosing a vehicle \(N_{i}\) and \(N_{j}\) using the above logic gives a radio link between moving vehicles that will continue to be useful for satisfactory packet transmission. _Case 2: When vehicles present in FTA in the opposite lane_  
Opposite-lane vehicles are also considered to participate in the routing process, as they can reduce the delay. This is done by a source vehicle that transmits packets to a relay vehicle that is part of its transmission range and which is moving in a backward direction relative to the sending vehicle. As shown in Figure 4, for routing purposes, the sending vehicle \(N_{i}\) did not find any neighboring vehicles in its forward transmission region AOB.