# Controlling Traffic Congestion in a Residential Area via GLOSA Development
## 2 Materials and Methods
### The Equations  
Our analysis includes _Highway Capacity Manual_ (HCM) equations [20]. These three equations indicate the travel time for a link or corridor calculated between two points, A and B, at different times according to the congestion hours. There are various reasons why time is used as a measurement standard:  
* Based on experience; time is the most essential factor influencing traffic flow on road segments.
* Additional congestion factors exhibit a close correlation with the time measurement index, following a similar pattern of peak and decline.
* Undoubtedly, time is the most straightforward variable to measure among congestion factors, rendering it valuable for practical applications.  
The travel time for traffic flow along a road segment is the duration spent on that segment under continuous traffic conditions. However, this ideal scenario is not practical due to intersections and signal lights in the urban road network.  
Consequently, traffic flow becomes intermittent on busy road segments, exhibiting two states: the driving state and the queue state. The travel time for intermittent traffic flow on the road segment is determined by both \"distance\" and \"speed,\" as per traffic flow theory. Therefore, the distance between points A and B is divided into two parts: the driving section and the queuing section.  
As illustrated in Figure 1B, a vehicle follows the path \((a\ )\) between points A and B. The traffic flow departs from the route point (A) at \(v_{a}^{m}(t)\), and upon reaching the path point (B), the vehicle enters a queue due to the influence of the signal light. If the queue length is \(L_{a}^{t}(t)\), the distance covered on road segment a is \(L_{a}^{m}(t)\), with the overall length of the road segment being \(L_{a}\):  
\[L_{a}=L_{a}^{m}(t)+L_{a}^{q}(t) \tag{1}\]  
where \(v_{a}^{m}\ (t)\), \(L_{a}^{m}\), and \(L_{a}^{q}(t)\) represent time-dependent functions. Similarly, it is posited that the time the vehicle spends traversing segment \(a\) is denoted as \(T_{a}^{q}\), the delay induced by thequeue (encompassing stop-and-go situations) is \(T_{a}^{d}\), and the total travel time on section a is designated as \(T_{a}(t)\); hence:  
\[T_{a}(t)=T_{a}^{m}(t)+T_{a}^{d}(t) \tag{2}\]  
were  
\[T_{a}^{m}(t)=\frac{L_{a}^{m}\ (t)}{v_{a}^{m}\ (t)}=\frac{L_{a}-L_{a}^{q}\ (t)}{v_{a}^{m}\ (t)} \tag{3}\]  
Equations (2) and (3) illustrate that to compute the road capacity \(T_{a}(t)\), it is necessary to ascertain both the travel time \(T_{a}^{m}(t)\) for the trip segment \(a\) the delay time \(T_{a}^{d}(t)\) of the queue component independently.  
The queue length \(L_{a}^{d}(t)\) can be used to calculate the travel time \(T_{a}^{m}(t)\).  
As a result, finding \(T_{a}^{m}(t)\) is turned into determining the real-time queue length \(L_{a}^{q}(t)\), which can then be studied and validated.  
According to the final two equations, the speed limit has no effect if congestion naturally slows traffic down to a lower speed yet imposes a hard limit on the maximum speed. Analyzing traffic flow is an important task for ensuring the efficiency of the road network. A crucial element in analyzing traffic flow is the road capacity, defined as the highest number of vehicles that can traverse a specific road section within a specified timeframe [21].