Works on the use of WSNs for the monitoring and control of traffic flows have been pursued at different levels. (Goel et al., 2012) provided work on an adaptive traffic signal system with WSN technology. The proposed system was designed to give a clear way for emergency vehicles on the road to reach their destination. The system involved a traffic intersection that was smart enough to manage traffic flow anytime an emergency vehicle needed to pass through. Although actual implementation was not pursued, the work provided a great insight into the use of WSNs for a smart traffic light system.

(Yousef et al., 2010) also presented an adaptive traffic control system using WSNs but this time actual new techniques were provided for the controlling of traffic flow sequences. These techniques were dynam-ically adaptive to traffic conditions on both single and multiple intersections. The proposed system involved the usage of a WSN to instrument and control traffic signals roadways, and an intelligent traffic controller developed to control the operation of the traffic infrastructure supported by the WSN. This work gave a real deep insight and understanding on the design and traffic control algorithm for the proposed smart control lighting system.

In contrast to the previous sources where conventional WSNs were used with known sensing methods, (Bovik et al., 2010) presented a Wireless Visual Sensor Network scheme for the management of urban traffic flow. The approach was an innovative method into the way traffic flow can be controlled with the use of a complex visual sensor network that can automatically or semi-automatically deliver information on traffic flow more resourcefully. The proposal also represented an incredible opportunity into fast-forward technological innovations in many areas that include video acquisition and processing over wide geographic areas by smart cameras; and the integration of the information learned between cameras to reach aggregate understanding of the complex (traffic) scenes. Although complex, the technological proposals will have incalculable impact on society, the economy, and the fragile environment, when implemented.

Unlike previous literature and the subsequent sources of (Toepfer et al., 2015), (Collotta et al., 2012) and (Zhou et al., 2010) where deep insights were given on a traffic control system with WSNs, this paper attempts to exploit the realization of the ATM system for the conceptual evaluation of CO₂ emission at traffic intersections. It will be presented that through the relevant equations of CO₂ emission and arrival time per vehicle, CO₂ emission can be evaluated at a traffic intersection depending on the volume of cars at the intersection. With such assessment, further scrutiny can be made to reduce CO₂ emission with the implementation of an ATM system.

Consider the scenario of Figure 1 where there is a traffic intersection with four external approaches.

Directions 1 and 3 are opposite each other and so share the same green times, whereas directions 2 and 4 share the same signaling times. For simplicity, each direction consists of a single lane and turning lanes are not considered (David 2009), (Shih, 2013).

A network of sensors and traffic lights are deployed to make up the ATM system as shown in Figure 2.

As observed from Figure 2, traffic lights are deployed for each external approach and sensor nodes, connected through the overlap of their coverage, are placed on each approach path where the node closest to the traffic light (sink node) is connected in the same way.

From Figure 2, it can be seen that the system is made up of clusters of WSNs where the traffic lights are the cluster heads and sensor nodes are candidates of the cluster network. The candidates essentially detect vehicle activity and send relevant information such as the arriving, waiting, and departing times of motor vehicles to the corresponding cluster head. The traffic lights can then determine queue lengths for each approach and react accordingly. The primary goal of the network will be to determine the traffic signaling switch times that will minimize the average delay of vehicles at the intersection. A base station, deployed externally from the system can be used to manage all traffic lights.

At any given time and during motion, vehicles are emitting CO₂ which is proportional to their travel time (seconds), travel distance (m), and acceleration energy (m² /s² ) as modeled by the following equation by (Guan et al., 2007) and (Li & Shimamoto, 2011).

(1)

(2)

Where:

E_CO2= CO2 emissions (g);

K_C= Coefficient between gasoline consumption and CO2 emissions (g/cc);

D = Travel distance (m);

T = Travel time for the distance D (seconds);

A_ee= Acceleration Energy Equivalent (m²/s²);

v_k = The speed at time k (m/s);

σ_κ = When accelerating, this equals 1; otherwise, it equals 0.

Applying equation 1 to the condition of vehicle motion at an intersection implies that Aee=D=0. Therefore, equation 1 is simplified to:

(3)

Equation 3 is the relationship that is used in describing emission at the red phase of the signaling light where cars are on standby waiting to continue with their journey.

It is understood that the waiting time for all vehicles at the queue of the red phase are different. This is because cars are arriving at subsequent times to the queue which as a result defines the amount of emission per vehicle. To get an idea of the individual amount of CO₂ emitted by each vehicle at the red stage is to imply that the red phase has a length of (t₂-t₁) where t1 is the start of the red signal and t₂ is the end of the signal getting ready to turn to green. Therefore, let qwait=qwait(t₁,t₂). If j≤qwait or qwait(t₁) ≤ j≤qwait(t₂) which represents the position in the queue of a vehicle waiting, then at the beginning of the red phase, the wait time of the j th vehicle in the queue is:

(4)

Where is the arrival time of the j^th vehicle (David, 2009), (Shih, 2013). To be precise, determining the arrival times for each vehicle is the key in defining the total amount of CO₂ emitted at the intersection area.

For a more realistic approach, it is assumed that cars are arriving to an intersection randomly and unrelated. This makes the Poisson distribution process a more suitable model for arrivals in which in the process, inter-arrival times follow the exponential distribution with the probability density function (pdf) of (Yates & Goodman, 2004-07-26):

(5)

Where λ is the arrival rate in vehicles per minute per approach, and u(x) is the unit step function. The step function is required because negative inter-arrival times are impractical (David, 2009).

Equation 5 allows for a response that is instant and because realistically the traffic dynamics of a traffic scenario requires a minimum space between vehicles, the exponential distribution is shifted for a more practical interarrival time. Therefore, equation 5 is modified in (Luttinen, 1996):

(6)

Where space is the minimum space between vehicles in seconds. Consequently, vehicle arrival times can be generated by the following equation David ( 2009) & Pang-shi (2013):

(7)

Where at2 is the next arrival time; at1 is the previous arrival time; and γis the uniformly distributed random number between 0 and 1 (Ramanathan, 1993).