## 4 Energy-Efficient Dynamic Routing Using IDEAL Communication  
In this section, we describe the logic of the C-EEDR application in the context of the INTEGRATION [2], since we used it in our simulations for the evaluation. The INTEGRATION software is an agent-based microscopic traffic assignment and simulation software. It is capable of simulating large-scale traffic road networks at a time granularity of 0.1 s. This high time-resolution allows detailed analyses of many traffic theory phenomena, such as acceleration, deceleration, lane-changing, and car following behavior. It computes a number of measures of performance, including delay, stops, fuel consumption, hydrocarbon, carbon monoxide, carbon dioxide, and nitrous oxide emissions, and the crash risk for 14 crash types. The details of the INTEGRATION software can be found in [2].  
INTEGRATION, by default, models the C-EEDR application assuming IDEAL connectivity, i.e., all messages transmitted are received without loss or delay. This assumption simplifies the modeling process from the traffic engineering perspectives and provides an upper bound of the expected benefits of the application. The C-EEDR application is developed as a feedback system that assumes the vehicles are connected and equipped with GPS. Moreover, a vehicle is assumed to be capable of calculating the fuel consumption for each road segment it traverses and communicating this information to the central server. In INTEGRATION, the fuel consumption and emission rates of each vehicle are calculated every second, based on instantaneous speed and acceleration.  
Each vehicle accumulates this fuel consumption rate on each road segment it travels on. Then, whenever the vehicle exits that road segment, it updates the road segment's cost. Based on the IDEAL communication assumption, these updates are promptly added to the routing information at the central server in the cloud.  
The vehicle route is a sequence of connected road segments. Thus, if a route \(R_{i}\) consists of \(k\) road segments, the total route fuel consumption cost \(F_{R_{i}}\) is the summation of the fuel consumption of the constituting road segments, as expressed in the following equation:  
\[F_{R_{i}}(t)=\sum_{j=1}^{k}\;F_{S_{j}}(t) \tag{3}\]  
where \(F_{S_{j}}\) is the fuel consumption on the road segment \(S_{j}\) at time \(t\).  
Initially, \(F_{S_{j}}\) is computed based on the free-flow speed. Then, this value is updated based on the updates from probe vehicles. Based on the IDEAL communication assumption, whenever a vehicle exits a road segment \(S_{j}\), INTEGRATION uses the reported vehicle's fuel consumption \(F_{v}\) on this road segment to update the road segment's cost \(S_{j}\). It uses a smoothing factor \(\alpha\), as shown in Equation (4); a typical value of \(\alpha\) in INTEGRATION is 0.2.  
\[F_{S_{j}}(t+1)=(1-\alpha)\cdot F_{S_{j}}(t)+\alpha\cdot F_{v} \tag{4}\]  
where \(F_{v}\) is the estimated fuel consumption of vehicle \(v\) on the road segment \(S_{j}\). The fuel consumption cost is communicated to the central server when the vehicle leaves the road segment. Then, the routing algorithm uses all the communicated road segments costs to update the current ones using Equation (4).