## 3 Materials and Methods
### Proposed ATM System Design and Implementation
#### 3.3.5 Machine Learning in ITM
\[\rm TV^{out}=\{\rm TV^{in}_{i}+(L/V_{i})\} \tag{4}\]

Let PV (\(\rm EV_{s}\)) be the deterministic probability of a platoon of N automobiles trying to form the frequency of event \(\rm EV_{s}\). Here, E is the event, and PV (\(\rm N\,|\rm EV_{s}\)) is the deterministic probability of a platoon of N automobiles providing the occurrence of event EVs. Finally, at the end of the evaluation portion, the probability \(\rm PV^{PrimaryV}\) (\(\rm N\)) that such a specific new vehicle will become the prime vehicle of a platoon of n automobiles mentioned in Equation (5). \[\rm PV^{PrimaryV}(N)=lim_{0-\infty}\ PV\ (EVs)*PV\ (N\,|\,EVs)*F_{V}(PV)dv \tag{5}\]

The results of PV (EVs) and PV (\(\rm N\,|\,EVs\)) can be determined by the speed distribution mapping (Figure 6). Mathematical Model Formulation for Proposed ATM

Let the vehicle congestion deterministic model CDM in a platoon of vehicles (\(\rm V_{i}\)) on the road (\(\rm R_{i}\)) be (I = 1... n). The Markov speed (\(\rm M_{speed}\)) property of any vehicle in a platoon. State space can be defined as {\(\rm S_{T0}\,\ldots\,\rm S_{Tn}\)}. A matrix (M) for state space can be defined as mentioned in Equation (6). Figure 6: Traffic flow space vs. time (incoming and outgoing vehicles). Here, a transition probability from the state P to Q can be defined as M\({}_{\text{PQ}}\). The top-speed vehicle on the road can be defined as TV\({}_{\text{top}}\). The state vector (B\({}^{(i)}\) TV\({}_{\text{top}}\)) for any ith vehicle mentioned in Equations (7)-(9). \[(\text{B}^{(i)}\text{TV}_{\text{top}})=(\text{B}^{(0)}\text{TV}_{\text{top}})^{ \star}\text{A}^{(i)} \tag{7}\]

\[(\text{B}^{(0)}\text{TV}_{\text{top}})^{\star}=(\text{\Omega}_{0},\text{ \Omega}_{1},\dots\text{ \Omega}_{n})^{\text{T}} \tag{8}\]

\[\text{\Omega}_{n}=\left\{ \begin{array}{c}1\ \left(\text{for}\text{TV}_{\text{ top}}\in\text{ S}_{\text{T}}\right)\\ 0\ \left(\text{for}\text{rest}\text{all}\right)\end{array} \right. \tag{9}\]

## 4 Discussion

The proposed ATM system was implemented on MATLAB simulator. The proposed system utilizes three primary entities (vehicles, infrastructure, and events) described in Table 2.

In order to validate the efficiency and accuracy of the proposed ATM system, various traffic scenarios were created for Linked automated vehicles (LAVs) as follows. (a) Only with linked LAVs (b) Where Only with Non-LAVs, (c) in which for LAVs and Non-LAVs, both types of vehicles are moving. Figure 7 shows the system design of the proposed ATM model for road-traffic conditions on the road with both the moving vehicles in a forward position. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Entity** & **Subunit** & **Property** & **Functionalities** \\ \hline Vehicles & Automobiles (2, 3, and 4 wheelers) & Vehicle ID, speed, vehicle type, lane & To recognize a vehicle \\  & Vehicle control unit & Manual and automatic & To determine the vehicle control type \\  & Road unit & Lane ID, Lane name, length, one & To determine the road unit \\ Infrastructure & Traffic light control unit, & ID, installation status, delay & To determine the traffic light control \\  & Street light unit & ID, installation status & To determine the street light unit \\ Events & Vehicle to Vehicle Communication & Vehicle speed, vehicle turn & To determine the V2V communication \\  & Vehicle to infrastructure & Signboard, pedestrian crossing, & To determine the V2I communication \\  & communication & traffic light, speed indicator & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Entities utilized in the proposed ATM system. Figure 7: System Design of proposed ITM. * **Only with LAVs--**This is the first scenario considering only LAVs. In this scenario, the intelligent traffic-management systems mainly divide the traffic into two segments. The first is the control segment (CS), and another is the merging segmentation (MS). The CS has a control entity named control unit (CU), which helps it to communicate with LAVs [62].