# DMRVR: Dynamic Milk-Run Vehicle Routing Solution Using Fog-Based Vehicular Ad Hoc Networks
## 4 Evaluation of the DMRVR Solution  
Our solution was executed with the OMNet++ and the SUMO software bidirectionally coupled. We used the Artery framework [53], applying the ETSI IT5-G5 setting, in accordance with European specifications, considering V2X communication, as the GeoNetworking and Basic Transport Protocol (BTP) alternatives [50]. Table 4 shows the parameters of the solution, which are based on the applications analyzed in [53; 54; 55; 56]. The SUMO Traffic model (LuST) developed for the City of Luxembourg was applied [57] reflecting specific mobility characteristics. By taking the City of Luxembourg as reference, depicting a common topology of mid-sized European cities, we were able to set up a realistic scenario. Traffic demand was inserted with realistic traffic information and mobility patterns. This has permitted calibrating and validating the model with regard to traffic flow situations. The model involved an area of 155.95 km\({}^{2}\), 930.11 km of roads, 88.79 km of highways, and a total of 203 traffic lights. A total of 4000 vehicles were considered along the running peak period from 8:00 a.m. to 6:00 p.m. [57]. We developed an algorithm with the Python language to set up the initial route. The _LogisticsService_ was setting in the RSU of the logistics operator. In the sequel, the _VehicleService_ \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Sent by Logistics Service**} \\
**Message** & **Fields** \\ \hline NotifyTardiness & id, sentTime, \\  & supplier, tardiness \\ NotifyRoute & id, sentTime, \\  & suppliers, cargoAmounts \\ NotifyAddSupplier & id, sentTime, \\  & suppliers, cargoAmounts, \\  & tardiness \\ \hline \multicolumn{2}{c}{**Sent by Pickup Vehicles**} \\
**Message** & **Fields** \\ \hline NotifyPosition & id, sentTime, vehicle, \\  & latitude, longitude \\ NotifyWithdrawal & id, sentTime, suppliers, \\  & supplierTardiness \\ NotifyPickup & id, sentTime, supplier \\ NotifyNonAttendance & id, sentTime, suppliers \\ \hline \hline \end{tabular}
\end{table} 
Table 2: DMRVR messages. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Field**} & **Type** & **Description** \\ \hline id & int & message unique identifier \\ supplier & int & supplier identifier \\ tardiness & int & supplier tardiness \\ sentTime & double & sent message time \\ suppliers & int [9] & supplier identifiers \\ cargoAmounts & double [9] & pickup cargo amount \\ supplierTardiness & bool & tardiness from supplier? \\ vehicle & int & vehicle identifier \\ latitude & double & pickup vehicle latitude \\ longitude & double & pickup vehicle longitude \\ sentTime & double & sent message time \\ \hline \hline \end{tabular}
\end{table} 
Table 3: DMRVR message fields. application was inserted in the simulation of the main vehicles, and in the operation of the auxiliary vehicles as well. The _LogisticsSercice_ and the _VehicleService_ framework applications include characteristics from the ITS-G5 Middleware proposed in the Artery scheme. The broadcast messages that cover a circular target area and were setup in GeoBroadcast (GBC) elements are specified according the ETSI ITS-GS. The GeoNetwork protocol leads the original node to rebroadcast the former element when it does not get the expected acknowledgment (_ack_) messages from the destination node. The messages in the DMRVR setting are organized to use this scheme. Intended to evaluate the impact of possible supplier tardiness occurrence, the _LogisticsService_ can estimate its \(p\) tardiness probability. Specifically for supplier (\(E_{i}\)), such probability \(p_{E_{i}}^{(td)}\) is represented by a negative exponential distribution, as depicted in Equation (7) [10]:  
\[p_{E_{i}}^{(td)}=exp(-T^{(up)}/t_{E_{i}}^{(td)}) \tag{7}\]  
where \(T^{(up)}\) is the imposed tardiness limit, and \(t_{E_{i}}^{(td)}\) is the expected supplier tardiness value, given the tardiness in fact occurs. When \(p\) is less than \(P_{E_{i}}\), the model assumes that the related supplier shows a tardiness value equal to \(t_{E_{i}}^{(td)}\) minutes.