Considerations on traffic management in isolated intersections

The continuous growth in the number of motor vehicles in major cities, combined with a stagnant development of road infrastructure, has caused traffic congestion and a range of negative direct and indirect effects. Even if measures were proposed to improve the road infrastructure, such as increasing connectivity or the size of the roads, the benefits would only be temporary, as it is well known that any infrastructure improvement will attract new traffic. The aim of this study is to identify traffic management measures at conflict points in road infrastructure that can improve traffic flow parameters. The study categorizes conflict points as either saturated or unsaturated intersections in order to determine a precise mathematical model for the timing of traffic light cycles that is suitable for local traffic conditions. The theoretical assertions are supported by a case study and conclusions and recommendations are formulated for use in the practice of traffic lights at isolated intersections.


Introduction
The use of personal cars in most of the daily trips has accentuated the negative external effects and led to levels of congestion that are hard to bear for those involved (Dragu et al. 2017).Among the negative external effects induced by traffic congestion, we mention: chemical pollution, noise, additional social costs, effects on health, degradation of the landscape, increased risk of accidents and, implicitly, a decrease in the quality of life of the inhabitants (Banister, 2008;Banister, 1997).
In terms of health, traffic congestion causes excessive fatigue, cardiovascular disease, but even affects entire systems such as the respiratory system and the nervous system, resulting in a lower standard of living (Qadri et al, 2020).
In 2021, Bucharest was in eighth place in the world for traffic congestion, according to the annual index carried out by Tomtom.Road traffic congestion was estimated at 50%, up 8% from 2020 but down 2% from 2019 (https://www.tomtom.com/).
Although the term congestion is used extremely frequently, it has different interpretations from stakeholders who, with often divergent interests and points of view, interfere on the transportation market.We can name here: the person in charge of the transport infrastructure development strategy, the infrastructure user, the traffic engineer, the transport beneficiary and the transport economist.For each of them the notion of congestion has different meanings depending on the degree of involvement in the transportation process (Raicu, 2007).
The plan proposed by the Bucharest Metropolitan Transport Association (an NGO structure established with the agreement of the General Council of the Municipality of Bucharest) aims at creating 1303 (2024) 012047 IOP Publishing doi:10.1088/1757-899X/1303/1/012047 2 a complex public transport network that would solve the current congestion problems.The goal for 2030 is to increase the number of public transport users from 20% at present to at least 80%.This objective must be achieved in the area with the highest population density in the country -over 8000 inhabitants/km 2 .
From the data supplied by the Driving Licenses and Vehicle Registration Directorate of the Ministry of Internal Affairs -DRPCIV (https://www.drpciv.ro/),information was obtained regarding the number of vehicles registered in Bucharest.Table 1 shows the situation of the number of registered vehicles between 1990 and 2021.
Table 1.The number of registered vehicles between 1990 and 2021 From table 1 it is noticeable that the number of registered vehicles and occupied area (11m 2 /vehicle) has increased extremely fast and intensely.
The current main challenge of any urban system deals with the externalities produced by the road transportation system.It is well-known that about 50% of pollution is from road transport and, in particular, from internal combustion engines (De Luca and al, 2020).Within this context, different actions have been deployed in the last few decades to reduce pollution, such as acting on the vehicle technology or different types of fuels, and through different and sophisticated mobility/travel demand management policies (De Luca and Papola, 2001) or traffc flow control strategies.
Currently, Intelligent Transport Systems (ITS) are used at different levels (micro, meso and macro levels).The positive effect of their use is the reduction of time lost by traffic participants and the increase in the efficiency of the performance of a transport network, measured in the increase of transport capacity, but also of traffic safety (Ravish and Swamy, 2021).
As a result of the dynamic development of new technologies in the field of ITS, it became necessary to model transport processes in order to forecast traffic flow parameters.Thus, a widely used transport model concept was born to evaluate traffic flow parameters from the design phase (Darapalyuk et al, 2020).
The local control method is the most used road intersection coordination method, applied in most cases (Zhankaziev et al. 2018).This provides several modes of traffic control resulting from the traffic parameters of the intersection.This management method does not require the installation of expensive equipment, since traffic lights are the main control tool.

Intersection with unsaturated traffic
From the point of view of demand, road intersections at the same level can be classified into unsaturated intersections, saturated intersections and oversaturated intersections.When all the vehicles in the queue pass through the intersection during the green period, we are dealing with an intersection with unsaturated traffic.Saturated intersections are those in which, after the end of the green phases, there are still queues of vehicles, or in other words, during the duration of the green, all the vehicles in the waiting line fail to transit the intersection.If vehicle queues tend to lengthen and block upstream intersections, then the intersection becomes oversaturated and other methods of streamlining traffic, reducing the length of queues and delay times must be sought.Traffic saturation can occur on a single phase or on several phases (Darapalyuk et al, 2020).
Regardless of the traffic light time, there is a time interval when a saturation flow (qs) flows through the intersection, which represents the maximum possible flow, achieved when the distance between vehicles is the minimum safe distance and the speed is maximum and approximately constant.There is a time to called lost time and it corresponds to the time when the first vehicle in the line enters the perimeter of the intersection after the light turns green.This is partially recovered by extending the green duration to the yellow duration for the last vehicle in the line to leave the intersection andenteron green.The duration of the yellow light, tg, is also a lost time imposed by traffic safety.It represents the time required for the intersection to be cleared by the last vehicle entering the intersection at the end of the green time of a traffic phase.
The values of the saturation flows depend on the starting performance of the vehicles composing that flow and on the width of the traffic lanes (lb).For forward (qsi) and turning (qsv) directions, the saturation flux is given by relation (1) (Popa and Beloiu, 1999).
For lb, the minimum allowed value is 3,5 m and R is the average turning radius provided by the geometry of the intersection, but not less than 6,55 m, (5,3 + 1,25)m, 5,3m is the minimum value allowed for the innermaneuver in grange of long vehicles by EEC -UN Regulation no.36, adopted in Romania by STAS 12139/1 -91, and the maximum width allowed for road vehicles is 2,5m.
Determining the duration of the traffic light cycle for an intersection with unsaturated traffic involves the following steps: 1) Determination of lost time for traffic phases: 2) Determining the effective green time: (3) 3) Determining the green time required for crossing the intersection by a number of nv vehicles: where hu represents the time interval between two successive vehicles (hu =2s).The number of vehicles that transit the intersection during the green period is: (5) 4) Determining the critical flow (qcr) of vehicles that can transit the intersection during the green period: 5) Determining the total flow that transits the intersection in the interval of one hour in the F phases of the traffic light cycle: where it is obtained: is considered the cycle duration, then the expression for C is: The maximum allowed duration of C, resulting from comfort conditions, is 120s (to reduce waiting time).
From the analysis of relation (9) it can be seen that it is not valid for large flows.The limit value is obtained from the expression: which leads to values of the total traffic flow that transit the intersection equal to 1800 Ve /h, under the conditions where hu = 2 s There are antagonistic conditions in increasing the flow.One of the measures is aiming the increasing of the number of access lanes in the intersection, but this leads to an increase of the area of the intersection and implicitly an increase in the duration of the intermediate times, with consequences on the reduction of the flow of vehicles passing through the intersection.This is because it is known that the duration of a cycle is composed of the sum of the durations of green and the durations of intermediate times.
In conclusion, for a succession interval hu = 2s the maximum value of the sum of the flows transiting the intersection is 1800Ve/h for the intersection to be classified as unsaturated intersections.
maximum critical flow is assimilated to the saturation flow and is determined with the relation: The critical flow values depend on the cycle duration, while the saturation flow, which is obtained when the cycle duration tends to infinity, is a constant that does not depend on any of the parameters involved.The values of critical flow and saturation flow for 2, 3 and 4 operating phases are shown in table 2.
Table 2. Critical flow and saturation flow The variation of cycle time for Tp = 6s, hu = 2s and number of phases equal to 2, 3 or 4 is shown in Table 3.
Table 3 Experience has shown that a correctly sized traffic light cycle should have a minimum value of 35s for 2 phases and 45s for 3 or 4 phases and a maximum value of 120s, with the recommendation that for a 4-way intersection not to exceed 80s (Salter, 1989).
Plausible values are shown in Table 4. From the analysis of the data representing the cycle duration as a function of the sum of the hourly flows, it is observed that the relation for determining the cycle time provides different values depending on the number of operating phases of the traffic light installation.Two-phase operation is suitable for small flows while three -or four-phase operation for large flows, which corresponds to practical reality and increases traffic safety in intersections through the existence of separate traffic phases for left turns.

a. Intersection with saturated traffic
Determining the cycle time is done with the relationship: (Salter, 1989;Boroiu and Neagu, 2015) where k is a constant which for typical intersections has the value 1,5.Tp-the total time lost for the entire traffic light cycle, yi -ratios, for each access, between the actual traffic flow and the saturation flow.
The folowing relationship is used to determine lost time: whereTi is the intermediate time required for the phase change, ip the delay caused by inertia when starting and stopping the vehicle (approximatelly 2 seconds).
From the analysis of relation (13) it can be seen that this also has limits in application.The relation can only be applied under the conditions in which: In this case, the application limit cannot be rigorously determined, as in the case of unsaturated intersections because it depends on the sum of the y values that are given by the ratio of the access flow to the saturation flow.The more the number of accesses or phases increases, the more the inequality tends to no longer be respected and the relation for determining the cycle can no longer be applied.
After the green color appears, a certain amount of time is lost until the first vehicle enters the intersection, but after that the movement of the line of vehicles enters a steady state at an approximately constant rate called saturation flow (qs).
If at the end of the green period there are still vehicles in line, those that have crossed the stop line will continue their movement during the yellow period to clear the intersection.Thus, the flow of vehicles moves during the green period and partly during the yellow period, but the vehicle flow has a lower value than the saturation flow (qs).This can be seen in fig. 1.
After determining the cycle time (Cs), the total effective green time is distributed among the traffic phases in proportion to their corresponding y value.Thus, for an intersection with 2 phase operation (F1 NS direction and F2 EV direction) we can write: To make the transition from effective green duration to actual duration, the following relations are used: Figure1.Intersection release rate In the case of fixed traffic lights, it is necessary to reach a compromise regarding the duration of the traffic light cycles so that the traffic variations are satisfied by a single traffic light program that does not cause very long delays.
To make some comparisons and observations on the application of relation ( 13), an intersection with 4 accesses operating in 2 phases is assumed, the total lost time is 10s, equal values of the green time and the value of the saturation flow 1800 Ve/h on all 4 accesses.The calculated values of the cycle are presented in table 5.
Table 5.Values of the duration of the traffic light cycle  It is considered that a variation of the cycle time between 3Cs/4 and 3Cs/2 does not lead to an increase of delays by a maximum of 10%.The minimum value of the cycle is considered 25s and the maximum 120s.
Determining the duration of the cycle consists of going through certain stages.These are shown in fig. 3.

Conclusions
The paper presented some considerations regarding the dimensioning and regulation of traffic in isolated intersections.These modelings are differentiated according to the characteristics of the traffic in the area and the influence of exogenous factors of the system.The way of dimensioning the traffic light cycle for intersections with unsaturated traffic was critically analyzed and it was identified that the cycle duration determination relationship has application limits.It can be applied only in cases where the sum of the flows of vehicles requesting the intersection does not exceed the value of 1800 reference vehicles/h, for the case where the tracking interval between vehicles is 2s.This value can increase if the interval between successive vehicles decreases, but this fact leads to an increase in the degree of risk because any unexpected braking of one of the vehicles in the row can lead to accidents due to the failure to ensure the necessary braking space.It is observed that this value corresponds to the value of the traffic capacity of a lane in ideal conditions, which is reflected in the practical reality.
It was concluded that the saturation flow in the intersection has a constant value regardless of the value of the critical flow and the other parameters that define the traffic.Two-phase operation is suitable for small flows while three-or four-phase operation for larger flows, which corresponds to practical reality and increases traffic safety through the existence of separate traffic phases for left turns.
From the analysis of the methodology for determining the duration of the traffic light cycle for saturated intersections, it was concluded that this also has application limits, but these are more relaxed and depend on the number of phases, the number of accesses and obviously the ratio between the arriving flows and the flow of saturation related to each access.
In conclusion, the analytical models for dimensioning the duration of traffic light cycles have limitations in application and then, in the situation of increased values of traffic flows, a possible solution would be that of simulations using specialized programs and the realization of a grouping of traffic flows on arteries with large capacity and organization of traffic according to the green wave system.Another model for streamlining traffic is that of moving from the coordination of isolated intersections to the coordination of an entire congested area with an emphasis on giving priority to flows leaving the locality.This model requires specialized programs for routing and operational management of traffic that could also have an integrated function to inform users about the choice of the most appropriate moment to travel, which would lead to the flattening of traffic peaks and the rational use of the capacity of road infrastructures.

Figure 2 Figure 2 .
Figure 2 shows the variation of the average delay per vehicle as a function of the cycle duration,

Figure 3 .
Figure 3. Flow chart for the calculation of the duration of the cycle (Drapalyuk et al, 2020)

.
The variation of the traffic light cycle time depending on the size of the flows

Table 4 .
Plausible values of the traffic light cycle time