J. Cent. South Univ. (2019) 26: 893-904

DOI: https://doi.org/10.1007/s11771-019-4058-y

Dynamic signal control for at-grade intersections under preliminary autonomous vehicle environment

LUO Si-da(罗斯达)¹, ZHANG Shuai(张帅)²

1. Department of Civil and Environmental Engineering, Northwestern University, Evanston,Illinois 60208, United States;

2. Department of Strategy and Policy, Beijing Transport Institute, Beijing 100073, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Abstract: Autonomous vehicle technology will transform fundamentally urban traffic systems. To better enhance the coming era of connected and autonomous vehicles, effective control strategies that interact wisely with these intelligent vehicles for signalized at-grade intersections are indispensable. Vehicle-to-infrastructure communication technology offers unprecedented clues to reduce the delay at signalized intersections by innovative information-based control strategies. This paper proposes a new dynamic control strategy for signalized intersections with vehicle-to-signal information. The proposed strategy is called periodic vehicle holding (PVH) strategy while the traffic signal can provide information for the vehicles that are approaching an intersection. Under preliminary autonomous vehicle (PAV) environment, left-turning and through-moving vehicles will be sorted based on different information they receive. The paper shows how PVH reorganizes traffic to increase the capacity of an intersection without causing severe spillback to the upstream intersection. Results show that PVH can reduce the delay by approximately 15% at a signalized intersection under relatively high traffic demand.

Key words: dynamic traffic control; vehicle-to-signal; signalized intersection; preliminary autonomous vehicle environment

Cite this article as: LUO Si-da, ZHANG Shuai. Dynamic signal control for at-grade intersections under preliminary autonomous vehicle environment [J]. Journal of Central South University, 2019, 26(4): 893–904. DOI: https://doi.org/10.1007/s11771-019-4058-y.

1 Introduction

Intelligent transportation systems (ITS) have attracted the attention from transportation researchers and practitioners since 1980s. This advanced application is expected to meet the ever-increasing need for mobility in both developed and developing countries. Even in the developing world, cities have witnessed many ITS implementations that vary in technologies (e.g., car navigation, variable message signs, automatic plate recognition, etc). With the ongoing technological revolution, applications including vehicle-to- infrastructure communications (V2I) and vehicle- to-vehicle communications (V2V) are being on the horizon. In fact, vehicle-to-signal communication (V2S), one simplest instance of V2I, has been commercially deployed in the United States (https://apnews.com/34c22c1071434616a44653b042d9e869/carcompany-offering-red-light-readingvehicles-las-vegas).

V2S provides great opportunities to enhance the efficiency of signalized intersections. As acknowledged, it is the isolated signalized intersection that is a typical bottleneck in road networks and demands wise control strategies [1]. Efficiency improvement at signalized intersections is pivotal to relieving the worldwide notorious traffic congestion. Decades of research were focusing on improving the traffic condition by optimizing the cycle length, green allocation, lane designation, etc [2–6]. The reader could turn to WONG et al [7] for a comprehensive literature review. While great significance could be attached to coordinated signal control along a major roadway and area-wide control [8, 9], improving the performance of isolated intersections remains a fundamental issue. With the upcoming era of connected and autonomous vehicles (CAVs), more opportunities arise while gaining insights into the temporal and spatial resources of isolated signalized intersections becomes increasingly essential [10–12].

Specifically, technologies may bring more possibilities to the unconventional intersection design (UID). Compared with the ubiquitous conventional intersection design (CID), UID organizes traffic flow in an irregular manner to reduce vehicular conflicts at an intersection. Most UIDs lay emphasis on rerouting left-turning vehicles, thus producing generally a larger capacity than CIDs. Examples of UIDs include the continuous flow intersection [13–15], tandem design [16, 17], hook-turn intersection [18, 19], confraflow left-turn lane [20, 21], parallel flow intersection, superstreet, median U-turns, bowtie, jughandle, quadrant roadway, split intersection, etc (see e.g. http://www.dot.state.mn.us/trafficeng/ safety/ice/2007_ICE_Manual.pdf). The theoretical advantages of these UIDs are illustrated in the literature, yet one of their common disadvantages is that the designs are more or less counterintuitive to drivers. In addition, either permanent and dramatic change in the layout of intersections or abundant investment on new infrastructures is often required (e.g., installation of pre-signals in mid-block of streets is rather expensive). These issues could be resolved by information technologies.

The application of V2S could help organize traffic flow by offering vehicles the guidance on their trajectories without evident changes on infrastructure. This study proposes an UID which features a dynamic signal control strategy for at-grade intersections under preliminary autonomous vehicle (PAV) environment. PAV environment in this context means that the autonomy in driving needs not fully achieved, where autonomous vehicle technology can be classified into six levels [22]. Under PAV environment, drivers can let vehicles control themselves but still with drivers’ attentions to the road, thus V2S information can be largely followed by vehicles. With the help of V2S information, vehicles can have a knowledge of the appropriate velocity and lane to take while approaching a signalized intersection. It is worth noting that the debate is continuing whether signal control is needed for ultimate CAVs at intersections (https://www.caranddriver.com/news/a15347112/will-autonomous-cars-mean-no-more-traffic-lights/).Whatever the case may be, the focus here is the times where signal control is still necessary. The aim of this study is to offer a cost-effective control strategy for improving intersection efficiency in the near future.

2 Concept

A summary of parameters used throughout the paper can be seen in Table 1. Figure 1 depicts how PVH works. This example illustrates the behavior of traffic streams on an approach with three lanes on the road segment and four approach lanes. Right turns on this approach are ignored for simplicity following XUAN et al [16]. Little change could be observed compared with CIDs except for the information section and dynamic lane. PVH features information sections in the middle of the road. The information section, with the help of V2S, provides the cars that are passing the section with the speed and lane they should take before passing the intersection. It holds (slows down) through- moving vehicles and forbids them to enter the dynamic lane while left-turning vehicles are utilizing the dynamic lane, and vice versa. Although the dynamic lane design (see Figure 1) is not common in real-world applications, the rules on how to use the dynamic lane are written in road traffic laws in China.

Table 1 Notation

Figure 1 Mechanism of PVH:

The holding strategy is to slow down vehicles under certain circumstances. When the traffic light, for example, is red, there is no need for drivers to take a high speed that will simply result in a dramatic brake right before the stop bar. Holding these vehicles, letting them take a lower speed could bring no increase to their delays, but allow brilliant strategies to reduce the delay for some other vehicles in the traffic stream. For PVH, holding vehicles aims to alternately allow left turns or through movements to utilize the dynamic lane. As a result, more lanes can be used to discharge left turns and/or through movements during their green times. The location of information section is determined in a way that the cars between the stop bar and information section, called reservoir area, can be discharged within one green time. There are two reservoir areas, one for left turns and the other for through movements.

We propose how to determine the time for holding vehicles (holding time) and holding speed (v_h). To determine the holding time, a detector is installed at each information section to monitor whether a queue with zero speed spills back. The holding time takes the following conditions into consideration: 1) the reservoir area is full of queuing vehicles, or 2) vehicles cannot pass the intersection from the information section at road design speed (v_d) utilizing the green time left. Condition (2) is necessary because in some situations vehicles are not plentiful enough to queue up to the information section on the dynamic lane. When vehicles are held, V2S informs vehicles that the dynamic lane is closed to them and they must take the holding speed; otherwise, the dynamic lane is open and they should take the releasing speed (v_r). The releasing speed could simply be road design speed, so we have v_r=v_d and 0hd.

The determination of holding speed takes the next releasing time into account. The releasing time is when vehicles start to be free from getting held. While we assume that vehicles cannot change a lane if they are at zero speed, the holding speed should be set in order that vehicles can change to the dynamic lane as soon as they are released. That is, the queue has not propagated back to the information section when the next releasing time starts. This is the reason for holding vehicles of one movement–the queue may block the entrance to dynamic lanes if the spillback occurs quickly. For the releasing time, it starts when vehicles towards the other direction begin to be held. These criteria will be used in our simulation experiments that implement the proposed control strategy.

In Figure 1(a), the green for left turns just starts. Approach lanes are filled with cars at zero speed. Since left turns are full in the reservoir area, they have already been held. The left turns in the reservoir area begin passing the intersection at road design speed, and the left-turning vehicle at the information section takes the holding speed following V2S information. This vehicle, leading all left-turning vehicles behind, cannot pass the intersection even running at the design speed. Through-moving vehicles, meanwhile, can enter the dynamic lane to queue up behind the left turns.

After a period of time, the yellow for left turns start as shown in Figure 1(b). All left turns on the dynamic lane are discharged so the through vehicles behind will not be blocked. Through-moving vehicles wait for their green light. After a while, they are discharged using three lanes in Figure 1(c). The information provided for left turns still requires vehicles to take the holding speed and keep off the dynamic lane while the head of left-turn platoon has reached the stop bar. Left turns start to queue up.

In Figure 1(d), when the condition for holding through-moving vehicles is met, the dynamic lane starts to prevent through movements from entering. Meanwhile, the queue of left turns is about to reach the information section while left turns start to be released. Next, the light for through movements turns yellow in Figure 1(e). Similar to previous situations, all through-moving vehicles on the dynamic lane have been discharged. On the two through-moving approach lanes, vehicles are moving at their holding speed. Left turns are entering the dynamic lane and start to queue up. After a while, the light turns red on this approach in Figure 1(f). The queue of left turns on the dynamic lane grows, and then the reservoir area becomes full, so left turns get held while through movements get released. The system works in the same manner periodically. It is worth noting that the proposed dynamic control strategy is different from the idea of dynamic signal timing and/or lane assignment in the literature where either the signal timing or lane assignment changes with real-time traffic demand (see e.g. [23]).

Most approach lanes are still utilized in a conventional manner for PVH (e.g., n_l=1, n_t=2 in the previous example). In theory, the traffic stream could be organized in a more sophisticated way by V2S information so that more dynamic lanes can be used. Peculiar organizations of traffic flow, however, would be counterintuitive to drivers, thus causing safety problems. Even though the strategy is designated for PAV environment, drivers can still frequently take control of vehicles since they keep observing the driving environment. We consider that n–N is the maximum number of dynamic lanes that can be utilized (i.e., n_d≤n–N). The application condition of PVH is thus n>N. In other words, this study requires an approach to have more lanes than the road segment (see Figure 1 for example). This treatment of widening an approach is common over the world (e.g., Wilshire Blvd and S Figueroa St, Los Angeles, USA; Yingwu Ave and Hanyang Ave, Wuhan, China), especially in China where big intersections are ubiquitous.

In summary, PVH aims to increase the capacity of an intersection–it could yield the capacity as if there are n–N more regular approach lanes. The disadvantage, on the other hand, is that drivers are sometimes required to be in a counterintuitive lane. In general n–N≤2 holds in the real world, so the number of dynamic lanes is constrained to be at most two, which helps to alleviate the drawback. Furthermore, the PAV environment could offset the disadvantage since many drivers might allow their cars operate on their own in absence of emergencies.

3 PVH analysis

3.1 Spillback problem

Since vehicles may be held somewhere upstream the intersection, it is likely that the proposed design has a spillback problem. The spillback problem means that the design makes the queue, which is defined to be a vehicle platoon with zero speed in this study, reach the upstream intersection faster than CID does. A severe spillback problem is undesirable even if PVH relieves traffic congestion at the targeted intersection. In this section, we determine if the spillback problem exists, or under what condition there is no spillback problem for PVH.

Figure 2(a) shows the triangular fundamental diagram. Figure 2(b) shows the time-space diagram (s-t diagram). In Figure 2(b), △OAB and the faint lines inside the triangle is proportionally shrunk in size from Figure 2(a). Suppose the origin represents the upstream intersection of the approach with PVH implementation. The stop bar on this approach is located at d₀, while d is the location of information section.

Figure 2 Analysis of spillback problem:

To analyze the spillback, we consider when the first vehicle in a platoon reaches the information section (see trajectory OM), it starts to be held with the holding speed q₂/k₂ (see trajectory MF, MF//OD). Simultaneously, indicated by line MG a shock wave begins to propagate backward due to a change in traffic condition. We have MG//CD since the shock wave speed is physically (q₂–q₁)/(k₂–k₁). As soon as the first vehicle reaches the stop bar of the approach, another shock wave begins to propagate with line FG (FG//AB). Since these two shock waves have different speeds, they will meet at point G. Then, the two shock waves will end up with a superposition and have the speed indicated by GN. Clearly, GN//BC. If there is no information section (i.e., CID), the head of the platoon has a trajectory OE before it stops at the stop bar. Then, a shock wave with line EN begins to propagate. Now the task is to show EN//BC, or equivalently GE//BC to determine whether there is a spillback problem for PVH. This is because point G could lie between the approach and its upstream intersection, leading to the same effect caused by shock wave on the upstream intersection for PVH and CID. We have the following proposition:

Proposition 1: The three points E, G, N share a line. Equivalently in plane geometry: given that MF//OD, MG//CD, FG//AB, we have GE//BC.

Proof:

△OAD~△MHFOA×HF=AD×MH

△OAB~△EHFOA×HF=AB×EH

AD×MH=AB×EH

△ACD~△HMGAD×MH=AC×GH

AB×EH=AC×GH, and we obtain

BAC=GHE

△ABD~△HGEACB=HEG

BC//GE

Proof is over.

In order not to cause a spillback problem, point G should be above the t-axis. We consider the extreme situation that point G is right on the t-axis to find the condition for d and d₀. Let’s add an auxiliary line BI//GM where point I is on line OA. Since point G is on the t-axis, we obtain:

GE//BI

Let OC=x, then ;

As a result, when the two shock waves will meet before reaching the upstream intersection and turn into a single wave that has the same speed as that of the shock wave observed in CIDs.

Therefore, if the condition is met, the information section can be set without causing any spillback problem. However, sometimes the condition cannot be met since d is also affected by the number of vehicles discharged per cycle on the approach–vehicles queuing up in the reservoir area should exactly be discharged within one cycle. In this case, the shock wave with line MG will reach the upstream intersection earlier than that in CIDs. Nevertheless, the shock wave MG will not cause a problem as serious as that in CIDs since vehicles do not completely stop when they are hit by the wave. Even though the holding speed q₂/k₂ might be small, this nonzero speed could slow down the formation of a gridlock. In addition, the shock wave FG that brings vehicles zero speed reaches the upstream later than that in CIDs. Consequently, in this study no particular attention is paid to satisfy the

condition Optimization for the proposed scheme could be reasonably performed as an isolated intersection.

3.2 Optimal design

For the intersection design, we could consider the optimization for each approach independently through giving a fixed green time to each approach, and then focus on how to optimally assign green time to every approach of the intersection. In this study, we are interested in the optimization problem for one approach, and the second part aforementioned is beyond the scope of this paper, which follows the logic in XUAN et al [16].

The optimal design tackles the signal timing and lane designation on the approach controlled by PVH. A mixed integer nonlinear program is formulated. q is the maximum flow that can be discharged per hour and represents the capacity of the approach. n_l, n_t, g_l and g_t are four decision variables. n_d, q_l, q_t and q are unknown intermediate variables. The reader is referred to Table 1 for notations. To simplify the analysis, in the formulation PVH is approximated to be equivalent to opening up n_d new approach lanes, which means that the dynamic lane can be as fully utilized as regular approach lanes. Constraints (1) and (2) guarantee flow conservation. Constraints (3) and (4) state that q represents the capacity. Constraint (6) on the number of dynamic lanes was explained in Section 2. Constraint (7) is an inequality though the solution to the program should make this constraint binding since all green time should be utilized to achieve the maximum flow rate. This can be used to check the optimization results. Although the program includes integers and is nonlinear, we solve it by enumerating all feasible lane designations, leading to several linear programs as subproblems.

s.t.                       (1)

                  (2)

             (3)

             (4)

                (5)

                   (6)

                   (7)

                      (8)

                      (9)

g_l≥0                       (10)

g_t≥0                        (11)

Since Constraint (7) is binding at optimality, the optimal solution q^* can be given as

           (12)

The capacity of the approach increases linearly (nonlinearly) with the total green time (number of approach lanes). Furthermore, if effective traffic management is performed (e.g., strict enforcement on lane-changing behavior on approach lanes) to increase the saturation flow rate, it will largely benefit the intersection. We can gain more insight into how q^* is changed with n:

where two sides of the inequality equal each other when n_t=n_l=1. It follows that

                        (13)

Thus, q^* is always under the curve indicated by with the independent variable n when other factors are fixed. It shows that regardless of the turning proportion, the capacity of the approach with n lanes has an upper bound, which is a quadratic function of n.

3.3 Microsimulation

Simulation experiments are performed to determine the average delay on the approach. To implement the dynamic control strategy, it is crucial to track individual vehicles, where macroscopic traffic flow models should not be good options. Cellular Automata (CA) models are chosen for the microsimulation. In particular, a revised CA model is selected which can capture the lane-changing behavior in the traffic stream [24]. Most parameters are set following Ref. [24] while revisions are made to fit the proposed control strategy.

For the CA model on the road segment, two revisions are made. First, in the acceleration step, drivers desire to take the design speed to be as fast as possible. Second, the rules of discretionary lane changing, which is distinguished from mandatory lane changing in this study, are revised. Mandatory lane changing is performed when a vehicle has to change a lane (e.g., change to the dynamic lane as guided by V2S information) while discretionary lane changing occurs on road segment when drivers want to move faster. The CA model used on the approach, on the other hand, is much simpler since no discretionary lane changing is permitted and drivers follow the guided speed on approach lanes. In summary, the CA model on the road segment is described as follows:

Step 1: Acceleration v_n(t)=v_d.

Step 2: If d_nn(t), d_n,front}, v_n(t)=min{v_n(t), d_n,front}, discretionary lane changing is considered, go to step 3; else, skip to step 4.

Step 3: If d_n,back≥v_n,back(t–1)–v_n(t)+1 and rand()

n_,change, the lane changing is successful, skip to step 6; else, go to step 4.

Step 4: Deceleration: v_n(t)=min(v_n(t), d_n).

Step 5: Randomization: v_n(t)=max{v_n(t)–1, 0} with probability p.

Step 6: Position update: x_n(t+1)=x_n(t)+v_n(t).

For the CA model on the approach:

Step 1: Acceleration v_n(t)=v_d.

Step 2: Deceleration: v_n(t)=min{v_n(t), d_n}.

Step 3: Position update: x_n(t+1)=x_n(t)+v_n(t).

v_n(t) and x_n(t) denote the speed and position of vehicle n at time step t, respectively. d_n= x_n+1(t)–x_n(t)–1 is the spacing between vehicle n and its front vehicle. d_n,front and d_n,back denote the spacings between vehicle n and its two adjacent vehicles on the other lane, respectively. v_n,back denotes the speed of the adjacent vehicle behind vehicle n on the other lane. rand () represents a uniform random number between 0 and 1. p_n,change is the lane-changing probability. The time step used is 1 s. Note that in the CA model, the speed and position are discretized (i.e., v_n(t)=0, 1, 2, …).

Let’s take the CA model on the road segment for illustration purposes. d_nn(t), d_n,front} means that discretionary lane changing is considered by vehicle n when d_n is not large enough to take the design speed, and the distance from the adjacent vehicle front on the other lane is longer than that from the vehicle it follows. Both v_n(t)=min{v_n(t), d_n,front} and v_n(t)=min{v_n(t), d_n} guarantees no crash will happen in the traffic stream. d_n,back≥v_n,back(t–1)–v_n(t)+1 shows that if vehicle n performs lane changing, there will be no rear-end crash since the adjacent vehicle back on the other lane can at least take its speed at time step t–1 to avoid a crash at time step t. The rules of mandatory lane changing is simpler than the discretionary one. For brevity, mandatory lane changing is not explained here. The system keeps getting updated following the model until the simulation horizon is reached.

4 Results

The proposed optimal design model provides the signal timing and lane assignment. Using the timing result, we estimate the number of left- turning/through-moving vehicles that can be discharged per cycle. Along with a known minimum spacing between vehicles, the maximum length of a queue discharged per cycle is determined for left turns and through movements respectively, and then the information section can thereby be pinpointed as discussed in Section 2. Elaborated in the same section, methods to determine the holding/releasing time and holding/releasing speed for left turns and through movements are used for our simulation experiments. Note that these inputs of simulation cannot be determined by the proposed design model.

A road with two lanes on the road segment and three approach lanes is used for the simulation. Only one dynamic lane can be deployed here (i.e., n_d=n–N=1). Traffic demand is set 1800, 2200 and 3600 pcu/h, respectively (pcu is short for Passenger Car Unit)–the demand should not be too low in order to see the benefit of PVH. As for the left-turn proportion, the simulation is performed for ρ≤0.5, because essentially ρ>0.5 is symmetric to ρ≤0.5 in terms of the average delay on the approach. The saturation flow rate is 1800 pcu/(h·lane). The cycle length is set 100 s. The green (yellow) time is set 70 s (3 s) on the approach. For the first 2 s of yellow time, vehicles are allowed to pass the intersection in the simulation. The road design speed is set 30 km/h. The randomization parameter p=0.2 and the probability p_n,change=0.8 is used. Each cell corresponds to 7.5 m that represents the minimum spacing in the traffic stream.

The simulation, coded in C++ using object-oriented design, is repeated for 20000 times under each demand level and turning proportion. Within each time, the delay of each vehicle is recorded, and the average delay can thereby be obtained. All the experiments are performed on a PC equipped with an Intel 2.20 GHz CPU and 8.00 GB memory.

4.1 Benefits of PVH

The traffic flow model used in this study needs to be validated before investigating the advantage of PVH. To achieve this, the delay of CIDs obtained in the simulation is compared with that calculated by Webster formula [25]. The comparison is meaningful since Webster formula applies to evaluating the delay of undersaturated conventional signalized intersections. Accordingly, the comparison is performed under the demand level of 1800 pcu/h. Simulation experiments show that the CID gets oversaturated when the turning proportion is roughly above 0.4, though the approach is undersaturated for PVH. Thus, ρ is set less than 0.35 in this setting. Results are shown in Table 2. The average relative error between the delays is 8.6%. Therefore, the revised CA model should be acceptable for our purpose. Unfortunately, by no means can the model be proved suitable for simulating the proposed control strategy since no analytical delay formula in PVH environment is available.

Table 2 Validation of revised CA model

Then, comparisons can be made between the delay of PVH and CID where the comparison considers the average difference across various turning proportions. Table 3 shows that PVH can effectively reduce the delay. The delay reduction is most significant under 2200 pcu/h in terms of the relative difference. This makes sense since when the demand is 1800 pcu/h, it is probably too low to show the difference; when the demand is 3600 pcu/h, the approach is congested and even PVH cannot save it from oversaturation. In terms of absolute delay reduction, the most evident one can be observed under 3600 pcu/h. In summary, PVH is particularly beneficial when the demand is medium or high. The most significant delay reduction is approximately 15%. By increasing the capacity of the approach, PVH indeed brings benefits in saving travel time.

Table 3 Delay reduction for PVH

4.2 Fully autonomous environment

Although V2S information is indispensable to perform the proposed dynamic control strategy, a full CAV environment is not required. Yet, how the delay will change in fully autonomous vehicle environment (with the highest automation level [22]) remains to be explored. It is guessed that the intersection efficiency gets improved with increasing automation level. In fully autonomous vehicle (FAV) environment, people tend to perform working or entertaining activities in their cars. We believe that a decrease in the likelihood of discretionary lane-changing behavior could be observed. Additionally, the randomization effect in the revised CA model will no longer exist.

The delay in FAV and PAV environment is shown in Figure 3. It shows that FAV environment does further reduce the delay. When the demand is not high, differences between the delays are not so evident. A significant delay reduction can be observed under high demand level. It is promising to see the delay can be further reduced by approximately 18% in FAV environment. This could result from less disruption (e.g., lane changing) in the saturated traffic flow. On the whole, PVH could largely reduce the delay if implemented at signalized intersections, especially when drivers can be devoted to their own affairs and let vehicles handle all aspects of the dynamic driving task. The proposed control strategy could be effective in both the short and long term.

4.3 Other unconventional design

In this section, we compare the performance between PVH and tandem design. Tandem design makes use of the mid-block pre-signal to sort left turns and through movements, alternately permitting them to enter the tandem lane that works in essentially the same manner as the dynamic lane for PVH. For tandem design, one dynamic (tandem) lane is deployed here, and the optimal design is accomplished using the model in Ref. [16]. It is speculated that a key difference between the two UIDs is on the number of stops. Although much debate is on the reasonable speed threshold of a stop for this performance indicator, here we record one vehicular stop when the speed decreases to zero in the simulation.

Figure 3 Comparison between PVH under fully and preliminary autonomous vehicle environment:

Table 4 shows that the delay between PVH and tandem design is comparable. This is expected since both UIDs deploy a dynamic lane that can be utilized for both left-turning and through-moving vehicles. A slightly better utilization of the dynamic lane in tandem design might account for the minor difference in delay. Regarding the number of stops, PVH yields smaller numbers when the demand is low or medium. Since PVH asks vehicles to take the holding speed before entering the dynamic lane, its advantage in the number of stops is expected– the pre-signal in tandem design could incur additional stops for many vehicles. It is worth noting that the holding speed could be quite small (e.g. 5 km/h) under some scenarios.

Table 4 Comparison between PVH and tandem design

In theory, tandem design can have more dynamic lanes. Thus, tandem design could be more effective in terms of delay reduction, but there is difficulty in deploying too many dynamic lanes in real-world applications. A large number of dynamic lanes could lead to a mismatch between the entry and exit lanes at an intersection. In addition, the more the dynamic lanes are, the more counterintuitive it is to drivers and leads to greater discrepancy on intersection performance between the theory and practice [16], which also raises greater safety concerns. Last but not least, tandem design might trigger a spillback problem since it causes some vehicles to stop in the middle of the road.

5 Discussion

Although advantages of PVH could be seen, future applications require strict enforcement especially at early stage of the implementation. The concern is drivers’ intervention while vehicles approach the intersection under PAV environment. A violation of traffic regulations includes entering the dynamic lane without following the guidance of V2S information. As with other UIDs, these behaviors violating the regulations need to be strictly penalized. Driver compliance should be formed with strict rules enforced in early times after PVH is implemented. The suggestion is to record the license plates of misbehaved vehicles by video-based enforcement devices that can issue citations automatically. Nonetheless, these issues will spontaneously disappear when CAV technology becomes mature in future. We show that PVH can reduce the delay to a greater extent in fully autonomous vehicle environment. Although technologies in the era might be mature enough for practitioners to take traffic lights away, PVH could be useful in the near future.

In comparison with other UIDs, PVH may not be the most effective in terms of increasing the capacity of an intersection. However, the implementation cost of PVH is comparatively small. It requires no permanent change on infrastructure. UID candidates such as the continuous flow intersection, parallel flow intersection and superstreet involve the construction of concrete traffic islands that are used for organizing various traffic flows.

6 Conclusions

In this paper, a new dynamic control strategy, called periodic vehicle holding (PVH), for signalized intersections is proposed under PAV environment. Through holding left-turning and through-moving vehicles alternately, PVH deploys the so-called dynamic lane that exclusively discharges left turns (through movements) when the green light for left turns (through movements) is on. With V2S information, this strategy requires little change on infrastructure. PVH can increase the capacity of an intersection while capable of reducing the delay compared with CIDs, especially when medium or high traffic demand is observed. The average delay reduction is up to 15%. Moreover, PVH under fully autonomous vehicle environment can further reduce the delay by about 18% compared with that under PAV environment when the demand is high. PVH promises a cost-efficient control strategy in the near future.

To better implement the strategy, efforts are indispensable in future studies. One could extend this study to multiple approaches of an intersection. A critical issue is to consider the phase sequence problem, which affects the total delay at an intersection. In addition, comprehensive simulation experiments that integrate more traffic participants (e.g., buses, pedestrians and bicycles) or field tests could be performed. Up to now, the concept of PVH is fresh, thus how people including drivers, pedestrians and cyclists will react to the strategy is unknown. Field tests are encouraged when V2S information becomes available in order to evaluate the performance of PVH in the real world, preferably with a data-driven approach (see e.g. [26]).

Acknowledgments

The authors thank the colleagues in transportation programs at Northwestern University for their valuable comments and suggestions on innovative intersection designs. Furthermore, constructive comments and generous editorial assistances offered by two anonymous reviewers are greatly appreciated.

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(Edited by HE Yun-bin)

中文导读

初级无人驾驶环境下的平面交叉口动态信号控制

摘要：无人驾驶技术将会颠覆现有的城市交通系统。无人驾驶智能网联车的到来，对平面交叉口信号控制的效能提出了新的要求，相应的控制策略应能够很好地迎合智能车的特点。通过前所未有的信息手段，新兴的车路协同技术能够帮助降低信号交叉口的延误。本文提出了一种基于车辆-交通信号通讯的平面交叉口动态控制策略，适用于初级无人驾驶环境。当车辆靠近交叉口时，交通灯会给车辆发送诱导车速等信息，左转和直行车基于相应的信息会在交通流中被分开。本文阐述了这种动态控制策略如何重新组织交通流，在不对上游交叉口产生显著影响的情况下，来提升该交叉口的通行能力。结果表明，这种控制策略在较高的交通需求下，能够降低约15%的路口延误。

关键词：动态交通控制；车辆-交通信号；信号交叉口；初级无人驾驶环境

Received date: 2017-12-13; Accepted date: 2018-09-20

Corresponding author: LUO Si-da, Research Assistant; Tel: +1-847-8684981; E-mail: Sidaluo2015@u.northwestern.edu; ORCID: 0000- 0002-2803-956X