# An Intersection Signal Control Mechanism Assisted by Vehicular Ad Hoc Networks
## 2 Information Collection for Far Vehicles
Then, it selects the closest vehicle in the direction of the packet forwarding as the next hop node to relay the ICP to. If the multi-hop connection through the whole road is active, which means the distance between any two successive vehicles is less than the transmission range of the VANET (\(R\)), the ICP can reach the RSU at the destination intersection smoothly. Then, the information of all vehicles on the road is packed and sent back to the source intersection RSU via their own networks (Figure 2a). Each intersection maintains a vehicle information table that records and updates the information of each running vehicle in real-time, and adds a time stamp (\(t_{s}\)) to record the time point of information gathering. When there is a small amount or an uneven distribution of vehicles on the road, the distance \(d\) between some pairs of successive vehicles may be greater than the transmission range \(R\), which means the ICP cannot continue to be forwarded right along the road and a network \"island\" occurs. In this case, the vehicle node that holds the ICP relays it back immediately to the source RSU via the original path. As shown in Figure 2b, the vehicles 3 and 4 are in the range of the \"island\" and cannot communicate with the two side RSUs. When the ICPs from the RSUs on both ends arrive at vehicle 2 and vehicle 5, respectively, and cannot be forwarded continually due to the distance between them being longer than \(R\), they are sent back at once. In order to solve this problem of incomplete information collection for all vehicles on the whole road, we need to estimate the states of vehicles in  
Figure 1: Impact of far vehicles on intersection signal decision-making: (**a**) intersection situation at \(t_{1}\) and (**b**) intersection situation at \(t_{2}\). Figure 2: Collection of real-time vehicle information through a vehicular ad hoc network (VANET): (**a**) end-to-end connecting using multi-hops and (**b**) breaking by “island.” RSU: roadside unit. the \"island\" range based on their available existing data. We take the condition in Figure 2b as an instance to describe the estimation process. First, the range of the \"island\" needs to be determined. We assumed that the center position of the left intersection is the zero point and the value of the position increases toward the right. Then, the value of the center position of the right intersection is _slen_, which is considered equal to the road length, and the \"island\" range is \((pos_{2}+R,pos_{5}-R)\), where \(pos_{2}\) and \(pos_{5}\) are the positions of vehicles 2 and 5, respectively, in the figure. Second, we estimated the velocity of the vehicle \(v_{e}\) in the \"island\" by considering the traffic density on the road [33] using Equation (1):  
\[v_{e}=v_{d}/\left\{1+a\times\left[\frac{n_{id}\times\left(\frac{slen}{pos_{- pos_{2}}}\right)}{n_{max}}\right]^{b}\right\} \tag{1}\]  
where \(n_{max}\) is the capacity of the road, \(n_{id}\) is the number of vehicles in the \"island,\" and \(a\) and \(b\) are adjustable parameters. Then, according to the \"losing duration\" \(t_{s}-t_{c}\) and the current position (\(pos^{\prime}\)) can be calculated, where \(t_{s}\) is the timestamp of its latest record and \(t_{c}\) is the current time. Moreover, as the vehicle movement is affected by the interactions with the vehicles around it and many other factors, which are hardly recognized quantitatively, such as the road condition, weather, driver's mental status, and even whether it is a light traffic flow. In some cases, the calculated positions of some vehicles are out of the \"island\" range (i.e., \(<pos_{2}+R\) or \(>pos_{5}-R\)). In other words, the estimated result is contrary to the actual situation. In this case, in order to make the result more accurate and realistic, we need to correct them using Equation (2), where we set the out-of-range estimated position as its nearest boundary value of the \"island,\" i.e., they are pulled back into the \"island\" where they really are:  
\[pos^{t_{c}}=