SPECIAL SECTION ON SECURITY AND PRIVACY FOR VEHICULAR NETWORKS
Received November 27, 2017, accepted January 2, 2018, date of publication January 26, 2018, date of current version March 15, 2018. Digital Object Identifier 10.1109/ACCESS.2018.2794555
A Distributed Traffic Control Strategy Based on Cell-Transmission Model PENGFEI SHAO1 , LEI WANG 1 School
1,
WEI QIAN2 , QING-GUO WANG3 , AND XU-HUA YANG4
of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China 2 School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo 454000, China 3 Faculty of Engineering and the Built Environment, Institute for Intelligent Systems, University of Johannesburg, Johannesburg 2006, South Africa 4 College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou 310023, China
Corresponding author: Lei Wang (
[email protected]) This work was supported in part by the Natural Science Foundation of China under Grant 61473016 and in part by the National Research Foundation of South Africa under Grant 113340.
ABSTRACT This paper presents a distributed traffic control strategy based on cell-transmission model (CTM). In view of the drawbacks of the CTM in describing the evolution of traffic flow on the intersections under the control signals, we modify the CTM and propose a simplified model. A series of rules is designed with the help of the subgradient descent method to update the status of intersections. Unlike the conventional method, the traffic signal timing plan is found in a fully distributed manner. The evolution of traffic flow for several kinds of typical traffic states is studied through numerical simulation, and the validity and benefits of our method are evaluated against the most popular mixed-integer linear programing. INDEX TERMS Traffic signal control, distributed control, cell-transmission model. I. INTRODUCTION
Nowdays traffic control has become an essential ingredient in managing transportation systems. It is common in many modern cities that the road facilities do not rise proportionally in time with increase of population and vehicles. Massive vehicles on roads have brought about a sharp increase of traffic congestion, and further caused a series of social and economic problems [1]. One may try to construct more motorways but the cost is huge. Note that the traffic infrastructure has matured in major cities and it is hard to construct more roads. The existing road facilities should be fully exploited to ease traffic pressure but they have not been all utilized sufficiently yet [2]. Hence, it is vital to reduce the traffic congestion by designing various traffic control strategies. Obviously, an effective traffic control strategy can greatly ease traffic congestion, reduce air pollution and energy consumption, and give drivers with better safety and short travel time [3]–[5]. In the past decades, one research focus has been urban intelligent transportation systems (ITSs) with the development of intelligent control and computer technology [6]. ITS aims to provide innovative services for different modes of transportation and traffic management, and enable smarter use of transportation systems by individuals with better information and coordination. To this end, traffic control strategy is again essential in ITS [7]. Early works paid more attention to traffic signal control problem of single intersection [8], [9]. By assuming the
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adjacent intersections to be irrelevant with each other, most researchers optimized a special class of objective functions such as average queue length and average waiting time for single intersection. And, interrelation between adjacent intersections were simply ignored in this case. The method will lead to frequent stops without optimizing the offset between adjacent intersections. The offset is used in coordinated traffic control systems to reduce frequent stops at a sequence of junctions. Therefore, the flow in each road is actually affected by its surrounding roads and it is unreasonable to assume single intersection. In addition, this approach of traffic control becomes ineffective with increasing traffic demands gradually as these models built for single intersection perform worse in the area of high-density, unlike low-density. It is necessary for researchers to take numerous intersections into consideration. Recently, the majority of researchers have investigated the network transportation signal control (NTSC) [10], [11]. The aim of NTSC is to optimize the global performance with numerous intersections. Different objective functions yield different traffic signal timing plans, which are traffic signal switching schemes. Theoretically, these traffic signal timing plans do get a better traffic performance in traffic control. It is noted that the traffic signal timing problem is non-convex and it is usually NP hard. It may take long time to find an optimal solution even for simple transportation systems [12]. Then, many offline traffic control strategies have been proposed
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based on historical data by employing different optimization methods [13]–[16]. Obviously, they cannot adapt to the traffic demands change in real time. It has been verified by the historical data [17] that the traffic signal timing plan has a 3% attenuation in effectiveness every year. At present, traffic signal control systems including the Sydney coordinated adaptive traffic system (SCATS) of Australia and the split cycle offset optimizing technique (SCOOT) of England have been widely used worldwide, both of which belong to the centralized solutions. To reduce computing time, heuristic techniques are usually implemented to achieve close-to-optimal solutions such as simulate anneal arithmetic [14], genetic algorithms [15] and reinforcement learning method [16]. Though global optimization search algorithms are widely applied, they are hard for online decision making due to their lower operating efficiency. To enable effective online decision making, some researchers have focused on distributed algorithms of network transportation signal control. Note also that today widely deployed sensors can produce the real-time traffic flow. And such flow data can be collected, transmitted and processed with communication and computing technology. As a result, we can implement the traffic signal timing plan generated by intelligent controllers in real time [18]. Nowadays design of distributed traffic control algorithms has become a popular topic in the area of intelligent transportation systems. For example, a distributed algorithm for controlling traffic signal, adapted from backpressure routing which has been mainly applied to communication and power networks, has been shown to ensure the global optimality as it leads to maximum network throughout even in a fully distributed manner [19]. However, the algorithm may not cope with drivers response to traffic signals. McKenney and White [20] proposed an algorithm which is capable of controlling traffic signals using real-time traffic data from sensors and local communication between traffic signals based on a realistic traffic model. This distributed algorithm allows traffic signals to be updated frequently to match current traffic demand and it has a better performance than fixed signal plan controllers. One may see a comparison between their traffic signal timing plan with fixed timing plan, but cannot find theoretical support for the proposed model. Timotheou et al. [21] adopted the cell transmission model (CTM) which views the multiple-intersection traffic signal control problem as a mixed-integer linear program. This solution is facilitated by its own special structure of temporal and spatial decomposition with theoretical proof. Similarly, certain control diagram was given in [18]. This paper is dealt with design of the real-time traffic signal timing plan by a distributed method. In view of the drawbacks of the cell-transmission model in describing the evolution of traffic flow on the intersections under the control signals, we modify the cell-transmission model and propose a new model on the basis of it. A series of rules is designed with help of the subgradient descent method to update the status of intersections. Then, we derive traffic signal timing plan using 10772
subgraident descent method, which is a distributed algorithm. Unlike the previous methods optimizing traffic signal, this paper does not need to set constraint for structure of road network as a result of the simplicity for it. Meanwhile, we apply the idea of subgradient descent method to network traffic signal control, which make it more persuasive. Numerical simulation shows that this method works effectively under time varying traffic demands. The rest of this paper is organized as follows: Section 2 gives an introduction about the LWR model and the cell-transmission model (CTM). Section 3 presents a new simplified model. Section 4 describes an optimal design of traffic signal using subgraident decent method. Section 5 shows the numerical simulation with the comparison between the mixed-integer linear program and proposed method. Finally, conclusions are drawn in Section 6. II. PRELIMINARIES A. LWR MODEL
The LWR model has been widely used to predict temporary phenomena such as the build-up, propagation and dissipation of queues, see [22] and [23] for more details. The evolution rule of the LWR model is given by ∂ρ ∂f + = 0, (1) ∂x ∂t f = g(ρ, x, t), (2) where f denotes the traffic flow, ρ is the density, x and t are the position and time of vehicles, respectively, and g is the flow-density function. The function g between flow f and density ρ is a fundamental relationship in traffic flow theory. Fig.1 shows an analytical approximation for a macroscopic fundamental diagram (MFD) linking space-mean flow [24], density and speed on a large urban area, which will be used in our subsequent discussions. Similar empirical result is also shown in [25].
FIGURE 1. Relationship between traffic flow and density.
B. THE CELL-TRANSMISSION MODEL
Daganzo [26] adopted a simplified scheme to describe the relation based on the macroscopic fundamental diagram, which is given by f = min{ρVf , Q, W (ρjam − ρ)},
(3)
where Vf is the free-flow speed (free-flow represents the speed of vehicles when density is zero), W is the backward VOLUME 6, 2018
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propagation speed of disturbances when traffic is congested, and Q is the capacity flow into next section and ρjam is the jam density of traffic. By discretizing the time and space into a collection of equal-length cells and time intervals respectively, Daganzo divided roads into homogenous cells. The distance of a single cell is set as the distance traveled at free-flow speed by a typical vehicle in one time interval. As a result, all the vehicles in a cell can be assumed to advance to the next with each time interval under the situation of free-flow speed. Thus, the evolution of vehicles satisfies the following equation: ni+1 (t + 1) = ni (t),
(4)
where ni (t) is the amount of vehicles in cell i at time t. LWR model given in Eq.(1) and Eq.(2) is approximated by the following set of recursive equations: ni (t + 1) = ni (t) + fi (t) − fi+1 (t),
different boundary phenomena such as origin, destination, mergence, divergence, and general intersection cells [28]. Although, the standard CTM model cannot capture platoon dispersion, it is quite useful in modeling the spatial extent of queues and is more appropriate for signalized networks with closely spaced intersections as in urban environments.
(5)
fi (t) = min{ni−1 (t), Qi (t), (W /Vf )[Ni (t) − ni (t)]}, (6) where i indicates the cell i; i + 1 and i − 1 represent the downstream and upstream of cell i, respectively; fi (t) is the actual traffic flow out of cell i during time [t, t + 1); Ni (t) is the maximum number of vehicles, which can hold in cell i at time t; Qi (t) is the capacity flow into the downstream cell i + 1 at time t. Definitions of the others, including W and Vf , remain unchanged. It is important to tell the difference between fi (t) and Qi (t): the former is the actual flow while the latter Qi (t) is inflow capacity. The actual flow and inflow capacity are not in any similar pair. Inflow-outflow, actual flow-estimated flow are in such a pair. Basically, Eq.(5) describes the conservation of traffic flow of cell i: the number of vehicles in cell i at time t + 1 equals to the number of vehicles in cell i at time t minus those left, then, plus those entered. Eq.(6) states that the number of vehicles entering cell i at time t is limited by the three terms: vehicles at the upstream cell waiting to enter i, the capacity of the successor cell i, and the space left in the successor cell i when a queue is forming. Both Eq.(5) and Eq.(6) ensure flow conservation at cell i. C. RELATIONSHIP BETWEEN LWR AND CTM
Eq.(3) not only gives a technique to consider traffic in mergence and divergence, but also a suitable platform that has a simple solution for realistic networks, and more significantly, convergent approximation to the LWR model. A discretized version of the macroscopic approach approximates the flowdensity relationship by a piece-wise linear model as shown in Fig.2. Because Eq.(5) and Eq.(6) provide a numerical approximation to LWR equations, all the traffic phenomena demonstrated in the LWR model, such as kinematic waves, can be replicated in CTM [27]. The popularity of CTM is based on its simplicity, its capacity to capture phenomena that are found in first-order continuum flow models, and its ability to model VOLUME 6, 2018
FIGURE 2. Relation between traffic flow and density based on CTM.
III. DESCRIPTION FOR FLOW BASED ON CTM A. FLOW BETWEEN ROADS
It is well accepted that the speed-density model contains Green-shields model [29], Greenberg model [30] and Underwood model [31]. Assume that the traffic flow is continuous, the Green-shields model can be used to describe the average traffic density on the road: ρ ), (7) v = Vf (1 − ρjam where v is the travel speed of the continuous traffic flow on the road, Vf is the free flow speed on the road, ρ is the average density of the flow, and ρjam is the congestion density. Greenberg model is applied in the situation where the density of traffic flow is approaching the jam density in general: ρjam v = Vm ln , (8) ρ where Vm is the vehicle travel speed as the volume of traffic flow is maximum. When the density is quite small, the speed-density model reduces to Underwood model: −ρ
v = Vf e ρjam .
(9)
Obviously, the road density is inversely proportional to the speed. We assume that the vehicles which stop at the stop line on each section can form a continuous traffic flow after a short time with the traffic signals turning green from red. In this case, the relationship between density and speed will be quite different with traffic signals turning green. At this point, the speed-density model can bring us not only the direct indications but also inspirations: fi (t) = ρi−1 (t)Vf 1t,
(10)
where fi (t) is the number of incoming vehicles from the road i − 1 to the road i during 1t and Vf is the free flow speed on the road and 1t is green light time. When 1t or ρi (t) is big enough, the traffic flow to the next road will reach a threshold. 10773
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FIGURE 3. One-way network.
Taking the road network shown in Fig.3 into consideration, we obtain an iteration equation which defines the change of the vehicle density on the road i: ρi (t + 1) − ρi (t) =
fi (t) − fi+1 (t) , li
FIGURE 4. The road network for simulation.
(11)
where li is the length of road i. If there are traffic signals settled on the road, the situation would be quite different. Then, we introduce the variable θ controlled by traffic signals and add θ into the formula(10). We get the following formula: fi+1 (t) = ρi (t) Vf Ti θi (t),
(12)
where θi represents the duty cycle of the intersections i. And, Eq.(12) defines the actual traffic flow from road i − 1 into road i. Assumption 1: The cycle lengths of traffic signal, Ti , i = 1, 2 . . . n, are all equal and constant, denoted by T . Substituting Eq.(12) into Eq.(11) yields ρi (t + 1) − ρi (t) =
ρi−1 (t)Vf T θi−1 − ρi (t)Vf T θi , (13) li
Assumption 2: The lengths of road, li , i = 1, 2 . . . n, are all equal and constant, denoted by l. Through the above analysis, we establish a basic recursive method for the change of density on each road over time: ρ(t + 1) = ρ(t) +
Vf T A(t)ρ(t) + B, l
(14)
where T ρ(t) = ρ1 (t), ρ2 (t), · · · , ρi (t), · · · , ρn−1 (t), ρn (t) , −θ1 0 0 0 0 0 θ1 −θ 0 0 0 0 2 . . . . 0 . . 0 0 0 0 0 θ −θ 0 0 A(t) = i−1 i .. .. 0 . . 0 0 0 0 0 0 0 θn−2 −θn−1 0 0 0 0 0 θn−1 T B = δin , 0, · · · , 0, −δout ,
0 0 0 0 , 0 0 0
where δin and δout represent the numbers of vehicles flowing in and out at the entrance and exit, respectively, which can maintain the traffic volume of the road network. B. ROAD NETWORK
It is hoped that some of the strategies generated by this dynamic approach would shed light on improving some practices. Consider a road network of one-way streets without 10774
turning movements as shown in Fig.4 for comparison with the other optimization method. The road network shows that it is made up of 2 intersections and 7 sections of road. For ease of exposition, a simple network is used for illustration: • Entrance section, indicated by section set I - where exogenous traffic demands are introduced to the network. • Exit section, indicated by section set O - where traffic flows terminate and exit the network. • Intermediate section, indicated by section set M - which is neither an entrance nor an exit section. Each section belongs to only one of these three sets and is divided into three cells. The cells are numbered from the upstream direction of traffic flow and follow this nomenclature: cell (i, j) represents the jth cell in section i. The first cell of a section serves as an entrance to the section and there are a fixed number of vehicles into the first cell which belongs to Set I during an interval. Except the cells with special characteristics, including: Nij (t) - holding capacity (in this study, this is constant over time, so the time dimension can be dropped); Qij (t) - inflow capacity; Vf - free-flow speed; W - backward shock wave speed. By carefully relating the neighouring cells, the difference equations Eqs.(4)-(5) can be written for each cell in the network, though a cell neighbour may be in a different section. for example, for cell (i, 2), the difference equations are given by ni2 (t + 1) = ni2 (t) + fi2 (t) − fi3 (t),
(15)
fi2 (t) = min{ni1 (t), Qi1 (t), (W /Vf )[Ni2 (t)−ni2 (t)]}. (16) IV. OPTIMAL DESIGN OF TRAFFIC SIGNAL A. OBJECTIVE FUNCTION
In general, there are several measures of the effectiveness of traffic signal to adjust the traffic flow including throughout, stops, delay within a period of time and so on. Based on the current research status, we choose the total delay as the objective function. With the model in Eq.(14), we will take the total delay for all intersections for optimization. The cellbased model supplies us a more convenient way to define delay. For the arbitrary road i, vehicles flow in and out from previous road and latter road within time t − 1 to time t. Hence, delay is defined as the extra time beyond the free-flow VOLUME 6, 2018
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travel time vehicles staying in a cell, which is given by hi (t) = ni (t) − fi+1 (t).
(17)
As a result, our optimization task is to minimize the total delay of the entire network: XX F = min hi (t). (18) i
t
B. DISTRIBUTED SOLUTION
In the view of the above analysis, we formulate the derivation of traffic signal timing plan as an optimization problem given by min F =
n X
hi (θi (t)),
i=1
subject to θi (t) ∈
n \
Ai ,
(19)
problem mentioned above, we apply it into our model to get the following inequality: F(y) − F(θ ) ≥ sF (θ )0 (y − θ ).
(23)
Similarly, if the inequality holds for the arbitrary y(t) (y(t) ∈ Ai ), one has a set composed of a group of θi (t). And, the set is equivalent to that of the directions of subgraidents about the local objective function fi (t). It follows from the subgradient descent method that the iteration equation of θ with time is given by θi+1 (t) = θi (t) + αt sF (θi (t)).
(24)
For a discrete traffic model, the local objective function fi is not continuous and the subgraident descent direction at section i can be obtained from definition. The values of fi are compared at different θ to determine the maximum gradient descending direction, see Algorithm 1.
i=1
where each hi denotes the local objective function of section i, and each Ai is a closed set. In the true traffic condition, the local objective function hi is known to section i only. The distributed optimization methods minimize a sum of local objective functions only related to each agent, which is to be solved in a distributed way [32]. The total objective is to cooperatively solve the following optimization problem: min f (x) =
n X
fi (x),
i=1
subject to x ∈
n \
Xi ,
Algorithm 1 Subgraident Algorithm Input: t = 1, ni (1), rules of traffic flow between cells Output: θi (t), ∀ i = 1, 2 ∀ t = 1, 2 . . . n 1: some description 2: for θ1 (t) = {0, 1}, θ2 (t) = {0, 1} do 3: get ni (t), fi (t + 1) 4: compare fi (t + 1) for different θi (t) 5: choose a series of θi (t) 6: while t ≤ n do 7: return step 2 8: return θi (t), ∀ t = 1, 2 . . . n
(20)
i=1
where each local objective function fi (x): Rn → R is a convex function, and each Xi ⊆ Rn is a closed convex set, describing the local constraint set of agent i. We assume that the local constraint Xi and the local objective function fi are known to agent i only. In particular, for a given convex f : Rn → R and a point x¯ ∈ Rn , a subgradient of the function f at x is a vector sf (¯x )Rn such that sf (¯x )0 (x − x¯ ) ≤ f (x) − f (¯x ), ∀ x ∈ Rn ,
TABLE 1. Total delay difference between mixed-integer and subgraident method for each scene.
(21)
where ∂f (¯x ) represents the set of all subgradients of f at a given point x¯ , and it is referred to as the subdifferential set of f at x¯ . The inequality denotes the definition of subgraident of local objective function. For agent i, we have the following recursive equation: xi+1 (k) = xi (k) + αk sf (xi (k)),
(22)
where αk is the appropriate stepsize. Unlike the continuous system, the optimization problem (19) describes a discrete system. To solve the optimization problem (19), we define θ as a binary variable for simplicity. But, the idea of solving problems is consistent in the sense that both of them are to look for the maximum direction of local objective function descent. Inspired by the distributed constrained optimization VOLUME 6, 2018
V. SIMULATION STUDIES
In this section, we perform numerical simulation to show the effectiveness of our result with better dynamic timing plan. The parameters used in simulation are given by TAB.1. As a result of one-way road, the status of left traffic signal 10775
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certainly affects the adjacent, and we view both intersections as a whole. A comparison study shows that neighouring intersections do have an effect on green time allocation and regarding both adjacent intersections as a whole is reasonable. Comparing with mixed-integer linear program [27], which have built the formulation that works for the full range of traffic conditions, we have the following three outcomes for simulation scenes on the condition of different density. Scene 1: A heavy demand of 1800 vehicles waits to enter the first cell which belongs to the set I on the horizontal street, and the demand of 360 vehicles on the vertical street. The initial state of whole network is a half of jam density.
FIGURE 6. Delay over Time for Scene 2.
jam density. Fig. 6 shows the delay at each interval under the condition of empty density. Scene 3: a heavy demand of 1800 vehicles waiting to enter the first cell on the horizontal street, and the demand of 360 vehicles waiting to enter the first cell on the vertical street.The whole network is at jam density at the beginning. Fig. 7 depicts the delay at each interval under the condition of jam density.
FIGURE 5. Delay at Each Time for Scene 1.
Fig. 5 shows the results for scene 1. The fixed timing plan distributes the same green time to each junctions no matter the demands changes with time. And, mixed-integer linear programming creates green progression with dynamic bandwidths. Due to a different mechanism of adjusting traffic signal, our method is comparably less constraint on the cycle of traffic signal. By coordinating the adjacent junctions, we find the maximum direction of subgraident descent so that the majority of simulation time have a much better performance than the former. Furthermore, the total delay is less than that for the mixed-integer linear programming. The flexibility of timing plan deduced by the subgraident method reduces the total delay by more than 4.9%, a drop from 2092 veh to 1990 veh shown in Table.2. TABLE 2. Total delay difference between two methods.
Scene 2: a heavy demand of 1800 vehicles waiting to enter the first cell on the horizontal street, and the demand of 360 vehicles waiting to enter the first cell on the vertical street. The entire network is preloaded at a half of 10776
FIGURE 7. Delay at Each Time Both Two Approaches for Scene 3.
All the above three kinds of scenes yield better green time distribution under a series of demand conditions. It is shown in TAB.2 that our method has better improvement for half-density, which is similar to [33]. In general, the change of traffic flow occurs in the case where vehicles on a road suddenly increase when the road is in the medium density traffic originally. This situation is exactly the Scene 1 and the effectiveness on reducing the total delay is superior to the other two cases. During low-density period, it is relatively simple to create green progressions(Scene 2). This is the reason why the reduction in the total delay is much less than the others. For the jam density, the downstream intersection releases vehicles at the maximum rate and the upstream intersection gives traffic at the maximum rate during the early intervals. Eventually, when the traffic density was lowered to the optimum density, the plan switches to forward propagation which is the best strategy because it delivers vehicles to the downstream intersection just on time for the green signal. VOLUME 6, 2018
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VI. CONCLUSIONS
In this paper, we have developed a distributed traffic control strategy based on cell-transmission model for optimal network performance. Through the analysis to the evolution of traffic flow between intersections and study of the celltransmission model, we propose a simplified model on the basis of cell-transmission model to better describe the evolution of traffic flow. At the same time, the model avoids the drawbacks of cell-transmission model. A series of rules is designed with help of the subgradient descent method to update the status of intersections. The relaxed problem is distributedly solved by a subgraident descent algorithm after appropriate reformulation and decomposition of the problem in both space and time. Then, the resulting solution is exploited to attain traffic signal timing plans through distributed rounding. The simulation studying on different situations shows the proposed method works better than the benchmarked one. Extending the developed method to different traffic models and transportation problems will be our future work. REFERENCES [1] G. Dimitrakopoulos and P. Demestichas, ‘‘Intelligent transportation systems,’’ IEEE Veh. Technol. Mag., vol. 5, no. 1, pp. 77–84, Mar. 2010. [2] A. Kotsialos, M. Papageorgiou, C. Diakaki, Y. Pavlis, and F. Middelham, ‘‘Traffic flow modeling of large-scale motorway networks using the macroscopic modeling tool METANET,’’ IEEE Trans. Intell. Transp. Syst., vol. 3, no. 4, pp. 282–292, Dec. 2002. [3] N. H. Gartner, ‘‘OPAC: A demand responsive strategy for traffic signal control,’’ J. Transp. Res. Board, vol. 906, no. 906, pp. 75–81, 1983. [4] W. J. Feng, L. Wang, and Q. G. Wang, ‘‘A family of multi-path congestion control algorithms with global stability and delay robustness,’’ Automatica, vol. 50, no. 12, pp. 3112–3122, 2014. [5] K. L. Hong, ‘‘A novel traffic signal control formulation,’’ Transp. Res. A, Policy Pract., vol. 33, no. 6, pp. 433–448, 1999. [6] W. G. Spadafora, P. M. Paielli, D. R. Llewellyn, and J. G. Kramer, ‘‘Intelligent transportation system,’’ U.S. Patent 7 689 230, Mar. 30, 2010. [7] B. Zhou, J. Cao, X. Zeng, and H. Wu, ‘‘Adaptive traffic light control in wireless sensor network-based intelligent transportation system,’’ in Proc. IEEE Veh. Technol. Conf. Fall, Sep. 2010, pp. 1–5. [8] S. Shelby, ‘‘Single-intersection evaluation of real-time adaptive traffic signal control algorithms,’’ Transp. Res. Rec., J. Transp. Res. Board, vol. 1867, no. 1, pp. 183–192, 2004. [9] B. D. Schutter, ‘‘Optimal traffic light control for a single intersection,’’ in Proc. IEEE Amer. Control Conf., vol. 3. Jun. 1999, pp. 2195–2199. [10] S. Mikami and Y. Kakazu, ‘‘Genetic reinforcement learning for cooperative traffic signal control,’’ in Proc. 1st IEEE Conf. Evol. Comput., IEEE World Congr. Comput. Intell., Jun. 1994, pp. 223–228. [11] L. Adacher, ‘‘A global optimization approach to solve the traffic signal synchronization problem,’’ Procedia-Social Behav. Sci., vol. 54, no. 2290, pp. 1270–1277, 2012. [12] L. Adacher, A. Gemma, and G. Oliva, ‘‘Decentralized spatial decomposition for traffic signal synchronization,’’ Transp. Res. Procedia, vol. 3, pp. 992–1001, Jan. 2014. [13] Z. Ning, F. Xia, N. Ullah, X. J. Kong, and X. P. Hu, ‘‘Vehicular social networks: Enabling smart mobility,’’ IEEE Commun. Mag., vol. 55, no. 5, pp. 16–55, May 2017. [14] S. Publicover, C. V. Harper, and C. Barratt, ‘‘Hybrid simulated annealing and genetic algorithm for optimizing arterial signal timings under oversaturated traffic conditions,’’ J. Adv. Transp., vol. 49, no. 1, pp. 153–170, 2015. [15] J. J. Sánchez-Medina, M. J. GaláN-Moreno, and E. Rubio-Royo, ‘‘Traffic signal optimization in ‘La Almozara’ district in Saragossa under congestion conditions, using genetic algorithms, traffic microsimulation, and cluster computing,’’ IEEE Trans. Intell. Transp. Syst., vol. 11, no. 1, pp. 132–141, Mar. 2010. VOLUME 6, 2018
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PENGFEI SHAO received the B.E. degree in mechatronic engineering from China Agricultural University and the master’s degree in control theory and control engineering from Beihang University. His major research fields include modeling and control in complex networked systems.
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LEI WANG received the B.E. degree in automation and the Ph.D. degree in control theory and control engineering from Zhejiang University, Hangzhou, China, in 2004 and 2009, respectively. From 2014 to 2015, he was a Senior Research Fellow with the Department of Electrical and Computer Engineering, National University of Singapore, Singapore. He is currently an Associate Professor with the School of Automation Science and Electrical Engineering, Beihang University, Beijing, China. His current research interests include modeling and control in complex networked systems.
WEI QIAN received the B.E. degree in automation from Southeast University, Nanjing, China, in 2005, and the Ph.D. degree from the State Key Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, China, in 2009. He is currently a Professor with the School of Electrical Engineering and Automation, Henan Polytechnic University, Jiaozuo, China. His current research interests include time-delay systems, stochastic systems, networked control systems, and multiagent system.
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QING-GUO WANG received the B.Eng. degree in chemical engineering, the M.Eng. and Ph.D. degrees in industrial automation from Zhejiang University, China, in 1982, 1984, and 1987, respectively. He held Alexander-von-Humboldt Research Fellowship of Germany from 1990 to 1992. From 1992 to 2015, he was with the Department of Electrical and Computer Engineering, National University of Singapore, where he became a Full Professor in 2004. He is currently a Distinguished Professor with the Institute for Intelligent Systems, University of Johannesburg, South Africa. He holds A-rating from the National Research Foundation of South Africa. He has authored over 270 international journal papers and seven books. His present research interests are mainly in modeling, estimation, prediction, control, optimization, and automation for complex systems, including but not limited to, industrial and environmental processes, new energy devices, defense systems, medical engineering, and financial markets. He received over 12 000 citations with h-index of 63. He is a member of the Academy of Science of South Africa. XU-HUA YANG received the B.E. degree in automation from the China University of Petroleum, Dongying, China, in 1993, and the M.S. and Ph.D. degrees in control science and engineering from Zhejiang University, Hangzhou, China, in 2001 and 2004, respectively. He is currently a Professor with the College of Computer Science and Technology, Zhejiang University of Technology, Hangzhou. His current research interests include artificial intelligent, complex network system, intelligent transportation system, link prediction, and deep learning.
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