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- Publisher
- Hindawi Publishing Corporation
- ISSN
- 0197-6729
- eISSN
- 2042-3195
- DOI
- 10.1155/2023/6599484
- Publisher site
- See Article on Publisher Site
Abstract
Hindawi Journal of Advanced Transportation Volume 2023, Article ID 6599484, 28 pages https://doi.org/10.1155/2023/6599484 Research Article A Collaborative Method on Reversible Lane Clearance and Signal Coordination Control in Associated Intersection 1,2 3,4 5 3 4 Xiaolan Xie , Luxi Dong , Huinan Gu, Hailing Li, and Lieping Zhang College of Information Science and Engineering, Guilin University of Technology, Guilin 541006, China Guangxi Key Laboratory of Embedded Technology and Intelligent System, Guilin 541004, China College of Earth Sciences, Guilin University of Technology, Guilin 541006, China College of Mechanical and Control Engineering, Guilin University of Technology, Guilin 541006, China Hualuyiyun Technology Co., Ltd., Nanjing 211800, China Correspondence should be addressed to Luxi Dong; 281667195@qq.com Received 7 October 2022; Revised 9 February 2023; Accepted 21 April 2023; Published 5 May 2023 Academic Editor: Socrates Basbas Copyright © 2023 Xiaolan Xie et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. To improve trafc efciency and utilization of road resources and alleviate trafc congestion caused by imbalance of bidirectional trafc fow, in view of the conversion conditions of reversible lane function, the operating characteristics of associated in- tersections under dynamic reversible lanes are analysed in terms of capacity, and a reversible lane control model is constructed basedonshort-termtrafcfowprediction.Onthisbasis,thereversiblelanesegmentclearingtimeandupstreamanddownstream signal control strategies under diferent states are studied. Te collaborative control model of reversible lane clearing time and signal timing of associated intersections is established to obtain the optimal time for reversible lane function switching. Finally, using Chaoyang Road, Beijing, as an example, the efectiveness of the proposed model is verifed by the simulation indexes of averagevehicledelayandreversiblelaneclearingtime.Teresultsshowthattheoptimizedclearingefciencyexceeds15%andthe optimized average vehicle delay is reduced by more than 10%. Combined with the future trafc state, the trafc capacity and saturation fow are greatly improved, and the intelligent reversible lane control is better achieved. some time periods, rather than bidirectional comprehensive 1. Introduction trafccongestion.Tedeep-seatedcauseoftrafccongestionin In the case of limited supply of urban road resources, it is a considerable part of the city is mainly the imbalance between a feasible way to reform the supply side of trafc resources by the supply and demand of trafc fow, that is, the trafc fow making full use of existing trafc resources and improving ratio in diferent directions in road sections or intersections is trafc capacity and trafc efciency through new technologies signifcantly diferent in diferent periods, leading to the im- and management methods. In recent years, due to rapid ur- balance of supplyand demand ofspatial resources and adrastic decrease in trafc efciency. Tis state is manifested by the banization, work areas are in the city center while residential areas are in the suburbs, resulting in unbalanced trafc dis- imbalance of diferent turning trafc fows at intersections and tribution during the morning and evening rush hours, a trafc theasymmetryofbidirectionaltrafcfowsatroadsections.For phenomenonknownastidaltrafc.Tidaltrafcnotonlycauses intersections, signal control schemes can optimize the dynamic severe congestion in one direction but also leaves the trafc distribution of time resources, which is often limited by static infrastructure in the opposite direction underutilized, resulting spatial resources. However, even though the signal control in a waste of resources and detrimental to people’s travel. timing is optimized, the corresponding improvement is very On the other hand, according to the analysis of the char- limited [1]. Terefore, the reversible trafc management is an acteristics and regularities of trafc congestion, there is a large important approach which can efectively combine signal proportion of one-sided one-way trafc congestion during timing and lane functions to solve the unbalanced problem of 2 Journal of Advanced Transportation diferent turning directions of trafc fows at intersections. At Over the past decades, many diferent forms of reversible the road level, the imbalance between supply and demand of roads have been used around the world to satisfy various trafc fows in the morning and evening peak is solved by needs [6, 8]. For trafc congestion at intersections, Wong reversible lane control. At the intersection level, the imbalance and Wong presented a lane-based optimization method for between supply and demand of trafc fows between associated theintegrateddesignoflanemarkingsandsignal settingsfor road links and within the entrance lanes is addressed by isolated junctions [3]. Wang and Deng analyzed infuencing combing with reverse lane control and signal control, which factors in the process of reversible lane setting according to improves the utilization of existing spatiotemporal resources the mixed network design problem [9]. For traditional re- and releases trafc pressure in the road network. versible lane control aspect, Wang et al. combined variable Numerous theoretical and simulation studies have been speed limits and car-following control with vehicle- conducted on trafc systems in order to solve congestion infrastructure communication to propose a reversible lane problems and achieve high trafc efciency (e.g., Li and Sun signal control scheme [10]. Zhao and Zhou proposed an [2]). And the implementation of reversible lanes which ad- implementation method during the changing of lane as- justs road resources from the light trafc fow direction to the signment [11]. In terms of reversible lane management heavy trafc fow direction is an efective measure to solve the research, Suwansirikul et al. discussed the management tidal trafc congestion problem, which greatly improves the technology of reversible lane control [12]. Su et al. studied operational efciency of the whole road network system the operational advantages of dynamically using short withoutchangingtheroadstructure,controlfacilities,andthe stretches of opposing lanes for left-turn movements [13]. trafcinfrastructure(e.g.,WongandWong[3],JiangandBao Kotagi and Asaithambi evaluated reversible lane operation [4], Yu and Tian [5], and Golub [6]). Te current paper using a microscopic simulation model developed in mixed attempts to contribute to studies of trafc congestion con- trafc of urban undivided roads [14]. For convenience of sidering reversible lane control as well as signal timing, which application, many professional transportation organizations arewidelyusedtosolvetheproblemofunbalancedtrafcfow havealsodevelopedguidelinesforoperatingreversiblelanes, [7]. Tis paper tries to analyse the interactive relationship such as AASHTO [15], ITE [16], and FGSV [17]. attribute variation and clearing time of reversible lane and In summary, many existing studies try to improve the signal timing of associated intersection by constructing performance of single intersection for the purpose of in- a dynamic collaborative control model to achieve a perfect tersection congestion alleviation. Several studies are based on integration of the interaction and intrinsic mechanism be- the ideal assumption that the capacity of the road section is tween imbalance states with supply and demand of trafc absolutely proportional to the number of lanes, which aim to fows and the real-time dynamic reversible lane trafc signal maximize intersection capacity by increasing the number of control scheme andimprove theglobal trafcefciency ofthe lanes. However, the above models proposed so far are mainly whole trafc system. Tus, this paper aims to establish applicable to the traditional timing tidal lanes or reversible a collaborative control model of reversible lane clearing time guidance lanes. Tere have been few dynamic control models and signal timing of associated intersections to achieve the designed for real-time dynamic reversible lanes. global optimal time for reversible lane function switching under complex conditions and dynamic adjustment of lane attributes based on trafc state and signal control scheme 2.2. Research on Reversible Lane Switching Control Strategies mapping characteristics to achieve full spatiotemporal trafc under Diferent Situations. Several optimization models supply and demand balance of associated road links. Te have been proposed to produce the optimal operating proposed method can efectively utilize spatiotemporal re- strategiesforreversiblelanedynamiccontrol.Mostofthem sources in the road network and fexibly and dynamically formulate the optimal decision for reversible lanes as handle the balanced demand of trafc fows during diferent a network design problem and optimize a target system time periods to alleviate trafc congestion. performance index, such as opening time, assignment, Te remainder of this paper is organised as follows: safety evacuation design, and optimized control of re- Section 2 provides a literature review related to reversible versible lanes. In terms of the opening time of reversible lane and signal control. Te reversible lane function lanes, Levin and Boyles proposed a cell reversal model switching control is described in Section 3. Section 4 based on dynamic reversible lanes and scheduled in- presents the analysis of reversible lane clearing time. Te tersection control [18]. Assi and Ratrout built an optimi- optimized control strategies of reversible lane are proposed zation model for hypothetical massive trafc demand in Section 5. Te integrated collaborative control model is combinations using an objective function of minimizing constructed in Section 6. Te performance of the proposed intersection delay [19]. Shang et al. designed a combined model is evaluated and verifed through actual cases in optimization model for designing the lane clearing time Section 7. Conclusions are given in Section 8. and the delay of the downstream intersection [20]. Mao et al. investigated the efect of adopting two high- occupancy vehicle (HOV) schemes on the reversible lane 2. Literature Review under a connected vehicle environment, which can elim- 2.1. Traditional Reversible Lane Control. Lane reversal has inatethe trafc tidalphenomenon[21]. Maoet al. proposed a real-time dynamic reversible lane scheme based on the been used for several decades and much has been in- vestigated regarding its efectiveness, feasibility, and safety. real-time service level and Bureau of Public Road (BRP) Journal of Advanced Transportation 3 spatiotemporal resource optimization at intersections. When functions in the cooperative vehicle infrastructure system (CVIS) [22]. For two-way quantity allocation of reversible changing the lane functions in reversible lane sections, drivers and vehicles need a certain amount of time to adjust due to lanes, Zhang and Ioannou developed a coordinated vari- able speed limit, ramp metering, and lane change control vehicle performance, driver characteristics, and other factors. which guarantees stability of the trafc fow and improves From the perspective of trafc safety, the reasonable setting of trafc mobility, safety, and the environment [23]. Yao et al. the reversible lane presignal control can efectively improve the putforwardanoptimizationmodelthatminimizesthetotal driver’s adaptability to the lane variation, reduce the rate of delay and a control method that coordinates a variable sign trafc accident, and ensure the vehicles’ efcient operation. and the corresponding signal group [24]. Ampountolas Schmied et al. presented a presignal control method of re- et al. proposed a simple and practical real-time strategy for versible lane sharing through the entrance straight and left turn efcient motorway tidal fow lane control [25]. Conceicao at the intersection [33]. Zhao and Zhou presented a dynamic exclusive bus lane (DBL) design during the various periods of et al. introduced the reversible lane network design problem, formulated in mixed-integer nonlinear mathe- a signal cycle [34]. Shu et al. presented a variable bus approach lanedesignwithabusguidanceandprioritycontrolmodel[35]. matical programming for both the trafc assignment and the reversible lane decisions [26]. Hu et al. established Intersections in the urban road network are interacting. Te a bilateral six-lane motorway model with the tidal lane signal cycle of the reversible lane is reasonably optimized. Te model based on the well-known Kerner-Klenov-Schreck- functionofreversiblelanechangetimeandsignaltimingshould eneberg-Wolf (KKSW) Cellular Automaton (CA) model be matched cooperatively, which can efectively reduce the [27]. Zhou et al. proposed a dynamic allocation model for vehicledelayatintersections.Liuetal.proposedaprocedurefor reversible lanes for road sections and intersections in the estimating the left-turn queue length at signalized intersections with contrafow left-turn lane (CLL) design [36]. Wu et al. intelligent vehicle-infrastructure cooperative system (IVICS) [28]. Te safety control models are the basis and proposed control strategy introducing an extra stage between the presignal and the main signal at the signalized intersection guarantee for the efcient operation of the real-time dy- namic reversible lane. In the safe evacuation model of the with the CLL design [37]. An et al. proposed a new type of intersection that utilizes the bus lane for the left turn based on reversible lane, the microsimulation technology is used to compare and analyze the safety and its impact before and relationship between the main signal and the presignal [38]. In after the setting of variable guide lanes at intersections terms of coordinated optimization control of urban reversible [29, 30]. Mo et al. presented a modifed algorithm for lane intersection group signals, the change of lane attributes at fnding such critical edges on the basis of the maximal singleintersectionwilldirectlyafecttheoperationstateoftrafc capacity path algorithm for the classical maximum fow fow and the surrounding signal cycle. Tus, it is necessary to problem [31]. Liu and Shi used a back-propagate (BP) efectively coordinate and control the signal phase of the in- tersection group. Levin et al. developed a decentralized max- neural network to obtain the lane changing rules for the microscopic lane changing decision model [32]. pressure policy that controls both autonomous intersection management and dynamic lane reversal [39]. Chen et al. In summary, reversible lane dynamic control is still a popular subject among researchers. In terms of the proposed a novel multilane cell transmission model for dy- opening time of reversible lanes, the research objectives namic lane reversal. A logit model is used to characterize the require manual opening operation depending on the trafc lane-changing behaviours under uncontrolled cases [40]. Azadi fow, queue length, or expert experience. In the two-way et al. proposed a combining fexible lane assignment and quantity allocation of reversible lanes, many existing studies reservation-based intersection control [41]. Zhang et al. pro- have presented diferent control models for reversible lanes, posed a single-step method that directly outputs lane shape which take efcient utilization of lane space and trafc modelparameters[42].Wangetal.presentedamethodofearly capacity as the optimization goal. In the safe evacuation warningbyusingthefuzzycomprehensiveevaluationtechnique [43].LiuandHustudiedthecollaborativecontrolmethodofthe model of the reversible lane, several studies take the max- imum trafc capacity at intersections in extreme weather tidal lane intersection group based on Internet of Tings [44]. As demonstrated in the literature review, many existing conditions as the optimization objective to analyse. Al- though the above-mentioned studies fully considered the studies have proposed reversible lane and signal control dynamic control optimization model for reversible lane optimization models, which try to maximum trafc capacity switching, the switching of reversible lane function is mostly at single intersection or multiple related intersections. controlled by manual switching or timing switching. And Moreover, the previous studies have certain limitations there is a lack of research on the trafc states under complex which are as follows: First, although the models of reversible conditions and reversible lane switching durations so as to lane and signal control optimization make sense, the in- reasonablyallocateroadresourcesbasedonthebidirectional teraction between the two has not actually been adequately real-time trafc supply and demand. studied. Second, although there are some studies on signal control optimization (including fxed signal timing, etc.) basedonthedelayandqueuelengthmodel,theoptimization of signal timing by combining with available phase green 2.3.Model ofReversible Lane and SignalControl Optimization. Presignal control, single intersection signal control, and mul- time, available phase red time, reversible lane function tiple intersection signal collaborative control are important switching control, and other factors has not been fully foundations for realizing real-time dynamic reversible lane considered. Meanwhile, the sensitivity and efectiveness of 4 Journal of Advanced Transportation feedback after applying the optimization models have not 3.1.1. Te Reversible Lane Switching Conditions. been investigated [1]. According to the reversible lane implementation conditions recommended by the American Society of Transportation Up to now, there are two aspects that need to be addressedinabove-mentionedstudies:(1)thereversiblelane Engineers, the road condition, road capacity, and trafc functionswitchingrarelyconcentratesonthediferenttrafc volume are generally considered [22]. In this paper, the road statesanddurations;and(2)thereversiblelaneclearingtime conditions and trafc conditions for opening the reversible is afected by both the lane switching time and the signal lane scenario are studied. control of upstream and downstream intersections. Most of Te road conditions are described as follows: the studies are on reversible lanes of single intersection or ① Lane setting conditions: for the introduction of re- arterial roads, which ignore the correlation relationship versible lanes, there must be at least three original between the upstream and downstream intersections. And roads in both directions [22]. there is a lack of the collaborative control of lane clearing ② Trafcfacilityconditions:urbanroadswithreversible timeandsignaltimingofassociatedintersection,whichdoes lanes should generally not be equipped with central not take the attribute variation of the reversible lanes under barrier or trolley tracks and other immovable diferent conditions into consideration and fails to make full facilities [22]. use of spatiotemporal resources. To address the above- mentioned shortcomings, this paper presents a collabora- Te trafc conditions are described as follows: tive control model of reversible lane clearing time and signal ① Trafc directions: In a continuous period, the fow timing of associated intersections, including the following ratio of opposite lanes is greater than 3:1, and the three steps: First, the operating characteristics of relevant lane fow with trafc volume of 3 is more than 80%. intersections under dynamic reversible lanes are analysed in Telanefowwithtrafcvolumeof1islessthan80%. terms of capacity. Next, a reversible lane function switching Te reversible lane should be set [45]. controlmodelisconstructedbasedonshort-termtrafcfow prediction. Finally, the collaborative control model of re- ② Signal cycles: According to existing studies, it is versible lane clearing time and signal timing of associated found that 80% of road congestion occurs in 2 to 3 intersections is established to obtain the optimal time for cycles during the transitional stage from fat peak to reversible lane function switching under complex peak [46]. In order to avoid trafc congestion as conditions. much as possible, this paper stipulates that the time threshold for triggering the reversible lane function switching is 3 cycles. 3. The Reversible Lane Function ③ Trafc capacity: After the introduction of reversible Switching Control lanes, the capacity of the road should still satisfy the When the unbalanced bidirectional trafc fow is caused by original trafc demand [22]. the trafc tidal phenomenon during a day, a management strategy of reversible (tidal) lane control is usually adopted. 3.1.2. Te Switching Control Model. In the real road net- At present, the most common practice of switching re- work,thespatialdistributionoftrafcfowisheterogeneous. versible lane function is manual operation (through em- Te complexity, tendency, and periodicity of trafc fow pirical observation by closed circuit television (CCTV) distributionintheroadnetworkarenotperfectlyrevealedby surveillancecameras)ortimingcontrol,whichcannotsatisfy defning the associated road links only through spatial ad- the real-time trafc demands timely and accurately. To jacent. Terefore, the DCNN-LSTM method is adopted to address these problems, this section determines the ap- analyze the computational results of dynamic time warping propriate switching timing based on the trafc fow pre- (DTW) so as to identify more relevant road links from the diction with the fast clearing of the reversible lane as the linkset.Tesensitivitytotheimpactofthepredictionresults optimization objective to realize the reversible lane has been taken as the fundamental index to achieve the switching control. closed-loop feedback in the selection process of road links andefcientlyselecttheassociatedroadlinks.Toaddressthe 3.1. Te Reversible Lane Switching Control Based on Trafc problem that the traditional two-dimensional convolutional neural network (CNN) lacks the ability of characteristic Flow Prediction. Te trafc demand degree of the reversible lane is an essential factor to change its functional attributes, compression and temporal characteristic expression, this andthedynamic trafcfow prediction of reversiblelanecan paper adopts a hybrid model of the one-dimensional CNN realize the intelligent function switching control so that the (1DDCNN) and the long short-term memory network reversible lane functional switching can respond to the (LSTM).Tehistoricaltrafcfowofeachroadsectioninthe dynamic variation of trafc fow in real time. Terefore, road link set for the past several time intervals (i.e., ten- based on the analysis of the characteristics of trafc fow in dency) and the trafc fow at the same time in the past few days (i.e., periodicity) are used as inputs to the 1DDCNN reversible lane, this section constructs the reversible lane switching control model based on the dynamic time layer, respectively. Ten, the extracted spatial characteristics arefedintotheLSTMmodelseparatelytolearnthetendency warping-convolutional neural network-long short-term memory network (DCNN-LSTM). and periodicity of trafc fow. Finally, these two types of Journal of Advanced Transportation 5 characteristics are fused and input to the fully connected Step 2: select the target road links for the trafc fow layer, thus gradually improving the prediction accuracy. to be predicted. In this section, the CNN model and the LSTM model are Step 3: Select spatiotemporal associated road link frstly introduced as follows: sets. Te tendency correlation and periodicity cor- relation of the primary associated links in the road ① CNN model network are calculated by the DTW algorithm of CNN is an artifcial neural network that requires con- trafc fow correlation so as to obtain the matching volutional layers, but it can also have other types of tendency correlation R , P ∈ (1, η), j ∈ (i + 1, i + h) layers,includingnonlinear,pooling,andfullyconnected j and periodicity correlation D , P ∈ (1, η), j ∈ (i+ layers [47–49]. In a convolutional layer, multiple flters 1, i + h) of the target road links and the associated are slid over the layer for given input data. Each con- road links in diferent time periods. volution operation is specifed by stride, flter size, and Step 4: calculate the variance (defned as δ ) corre- zero padding [48, 50, 51]. Te sum of the element-by- j sponding to the tendency correlation and periodicity element multiplication of the flters and the perceptual correlation of each associated link, as shown in the feld of the input is then calculated as the output of this following equation: layer.Teweightedsumisusedasanelementofthenext layer by calculating several nonlinear functions [52–54]. j j j j R − R D − D 2 P P P P (1) δ � η + ϑ , ② LSTM model j j j P P LSTM is a recurrent neural network after improve- j j where R is the tendency correlation, R is the av- ment, which can solve the problem that the recurrent P P neural network (RNN) cannot handle regarding long erage value of the tendency correlation, D is the distance dependence [55]. Te main goal of LSTM is periodicitycorrelation,and D istheaveragevalue of toobtainthetemporalsimilaritycharacteristicsofthe the periodicity correlation. trafc fow time series. Te basic principles of the Step 5: select the N road links with stronger corre- LSTM model are described as follows: Firstly, the lation by classifying the variance δ of each LSTM model makes the decision to drop some ir- associated links. relevantinformationinthecellstateintheforgetgate layer. Next, the LSTM model will decide the new Step 6: calculate the spatiotemporal correlation information that needs to be kept in the cell state weights of each link according to the previous Steps through the input gate layer. Te update is based on 3–5 and form a spatiotemporal correlation weight the principle of forgetting some information of the matrix of the associated links. old cell state in the forget gate and adding some Step 7: Te trafc fow spatiotemporal correlation information of the candidate cells in the input gate to sequence sets are constructed based on the time obtain the new cell information. Finally, the input to interval (defned as τ), which are used as the input of thehiddenlayeratthecurrentmomentisobtainedby the prediction model. For example, the trafc fow the sigmoid layer, while the output is determined by during time interval t can be predicted based on the the output gate layer. historical trafc fow sequence of [t − nτ, t − τ]. Te asynchronous spatiotemporal correlation eigenma- Next, the learning model framework of the proposed trices of target trafc fow are established by equa- method is shown in Figure 1. Te specifc implementation tions (2)∼(3): steps of the learning model are described as follows: Step 1: Data processing: the trafc fow data are divided into training and test sets. d d d x (t − nτ) · · · x (t − nτ) · · · x (t − nτ) 1 O N ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ d d d ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ x (t − nτ + τ) · · · x (t − nτ + τ) · · · x (t − nτ + τ) ⎥ ⎢ ⎥ trend d ⎢ ⎥ d d ⎢ 1 O N ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ X � · · · x � ⎢ ⎥, (2) x · · · x ⎢ ⎥ ⎢ ⎥ t N ⎢ ⎥ 1 O ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⋮ ⋮ ⋮ ⋮ ⋮ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ d d d x (t − τ) · · · x (t − τ) · · · x (t − τ) 1 O N d− m d− m d− m x (t − τ) · · · x (t − τ) · · · x (t − τ) 1 O N ⎡ ⎢ ⎤ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ T ⎢ ⋮ ⋮ ⋮ ⋮ ⋮ ⎥ ⎢ ⎥ period ⎢ ⎥ ⎢ ⎥ d− m d− 2 d− 1 ⎢ ⎥ ⎢ ⎥ X � , x � ⎢ , (3) x · · · x ⎢ ⎥ ⎢ ⎥ t ⎢ d− 2 d− 2 d− 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ x (t − τ) · · · x (t − τ) · · · x (t − τ) ⎥ ⎢ ⎥ ⎢ 1 O N ⎥ ⎢ ⎥ ⎣ ⎦ d− 1 d− 1 d− 1 x (t − τ) · · · x (t − τ) · · · x (t − τ) 1 O N 6 Journal of Advanced Transportation Input spatial Input Sv , Sv , Sv , … 1 2 3 eigenvectors Input Layer Traffic flow data Traffic flow data temporal eigenvectors Convolution1 ReLU 1DDCNN Spatial characteristics 1DDCNN Layer Extraction Convolution2 ReLU LSTM Tendency and LSTM LSTM Layer Periodicity Extraction ReLU Convolution3 Fusion ReLU Fully Connected … Output the results C C C C C C FCL 1 2 3 4 5 n Layer (FCL) S S S Spatial 1 2 3 … FCL characteristic C C C C C C 1 2 3 4 5 n Training Stage T T T 1 2 3 Temporal Spatial Convo Convo Convo characteristic FCL eigenvectors lution1 lution2 lution3 Input Traffic Data Output all extracted Fusion flow data preprocessing characteristics Temporal LSTM FCL eigenvectors ReLU Figure 1: Te learning model framework. trend d d where x is the trafc fow time correlation sequence Y � LSTMh (t − nτ), h of target associated road link O in the [t − nτ, t − τ] (5) on day d. x (t − nτ) is the trafc fow of road link N ·(t − nτ + τ), · · · , h (t − τ), trend at the time t − nτ on day d. X represents the trafc fow data matrix of the spatiotemporal asso- period d− m d− 2 Y � LSTM h (t − τ), · · · h period t ciated road links for the past n time intervals. X (6) d− 1 ·(t − τ), h (t − τ) , refers to the trafc fow data matrix of the spatio- temporal associated road links for the same time in the past mdays. where h (t − τ)istheoutputofthe1DDCNN attime trend t − nτ on day d. Y represents the tendency spa- Step 8: Input the asynchronous spatiotemporal t tiotemporal characteristics extracted from the LSTM correlation eigenmatrix into the 1DDCNN network. period model. Y represents the periodicity spatiotem- Tree convolutionlayersareused.Teoutput ofeach t poralcharacteristicsextractedfromtheLSTMmodel. convolution layer is activated by nonlinear function ReLU, which is used as the input of the next con- Te memory cells are able to save the historical in- volution layer. To avoid the loss of key information, formation that is controlled by three gates, namely, no pooling layer is added between the convolution the input gate, the forget gate and the output gate. In layers. Finally, a fully connected layer is added for time correlation sequence t, the outputs of the input classifcation. Te current spatial eigenvector is gates are calculated by the following equation: output as follows: I L t t t t− 1 t− 1 A � ω T + ω S + ω Bd + ω sm , τ iτ i iSτ i hτ cτ j c S � S , S , S , · · · , S . (4) j�1 1 2 3 N i�1 c�1 (7) Step 9: determine the 1DDCNN-LSTM model. where A is input to the memory cell after being period trend ① Step 9.1: Take X and X as input to the activated by the activation function (defned as 1DDCNN-LSTM model. Te associated road links Bd � f(A )). ω is the connection weight for the τ τ are captured by the 1DDCNN to obtain spatial memorycell.Teinputgates,theforgetgates,andthe characteristics. Ten, the obtained time correlation outputgatesarerepresentedbysubscripts i, h,and c. I sequences with spatial characteristics are put into the and L are the sizes of the input layers and the LSTM LSTM model. Te dynamic changes are obtained by layers, respectively. C is the number of memory cells. the information transmission between cells, and the As shown in Figure 1, the value received by the input temporal characteristics are captured. Te trafc fow gate is afected by the previous LSTM output value t− 1 spatiotemporal tendency characteristics and peri- and the state values of all memory cells. Bd rep- odicity characteristics are calculated by equations resents the outputs of all diferent memory cells at t− 1 (5)∼(6): previous time. sm represents the states of all c Journal of Advanced Transportation 7 memory cells in the same module. ST refers to the Te memory cell serves as the output of the whole input of the LSTM model, which forms the eigen- memory module and is controlled by the output gate. vector of each acquisition time sequences in a certain Tis output will also serve as the input of the whole trajectory. Te calculation results are shown as memory module at the next time. Te activation follows: function (defned as H(·)) is calculated by equation (14) [56]. T S 1 1 ⎡ ⎢ ⎤ ⎥ t t t ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ Bd � Bd Hs . (14) ⎢ ⎥ ⎢ ⎥ ⎢ T S ⎥ c ω c ⎢ ⎥ ⎢ ⎥ ⎢ 2 2 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ST � ⎢ ⎥, (8) ⎢ ⎥ i ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⋮ ⋮ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ Te goal of the model in the training process is to T S minimizethelossfunction.Asthetrafcfowdataare n n continuous values, the loss function of the model is where T is the temporal eigenvector of each acqui- selected as the mean square error (MSE). Te MSE is sition time sequences. S is the spatial eigenvector of calculated by equation (15) as follows: eachacquisitiontimesequences. nisthetotalnumber N t X − X of trajectories. 2 t�1 O O (15) σ � , Te forget gate of the memory module of the LSTM model is used to control the hidden layer state where N is the number of training samples. X is the (defned as s ) at the previous time, which is similar t− 1 real value of the predicted trafc fow on the target to the input gate. Te output is shown in equation (9) associated road link O. X is the predicted value of [56], which is as follows: the trafc fow output from the model. I L C ② Step 9.2: Te proportion of the tendency spatio- t t t t− 1 t− 1 A � ω T + ω S + ω Bd + ω s , temporal prediction value and the periodicity spa- iφ iSφ hφ cφ φ i i j c i�1 j�1 c�1 tiotemporal prediction value in all prediction values will fuctuate with time. Terefore, in order to in- (9) tegrate the two prediction values to obtain the op- Similarly, A is activated by the activation function timalpredictionresults,thecorrespondingweightsof t t (defned as Bd � f(A )). Tis characteristic con- the tendency and periodicity predictions can be φ φ t− 1 trolled by the input gate and Bd constitutes the calculatedbasedonthehistoricalpredictionresultsto input to the memory cell, as calculated in equation achieve the optimal fusion efect. Te fusion function (10) [56], which is as follows: is shown as follows: t t X � υ X + υ X , (16) I L 1 2 O O,trend O,period t t t t− 1 A � ω T + ω S + ω Bd . (10) c ic i iSc i hc j i�1 j�1 where X is the short-term trafc fow fusion pre- diction value. X is the trafc fow tendency O,trend Te output of the memory cell is controlled by the spatiotemporalpredictionvalue. X isthetrafc O,period forget gate. If there is a state of the previous time that fow periodicity spatiotemporal prediction value. υ is not forgotten, this output of the memory cell at and υ are the weights of spatiotemporal prediction t− 1 time t − 1 (defned as s ) is received and used for c values of tendency and periodicity, respectively. calculation at the same time. Tus, the output of the υ + υ � 1. 1 2 memory cell is calculated by equation (11) [56], In order to make the fusion efect time sensitive, this which is as follows: paper takes the minimum total MSE of historical t t t− 1 t t prediction results as the goal to calculate the weights s � Bd s + Bd gA , (11) c φ c τ c of tendency and periodicity spatiotemporal pre- diction values. Te total MSE is calculated as follows: where g (·) is the activation function. Finally, the input of the output gate is calculated by equation (12) 2 2 J � υ σ , (17) [56], which is as follows: i i i�1 I L C t t t t− 1 t A � ω T + ω S + ω Bd + ω s . 2 ω iω i iSω i hω j cω c where σ is the MSE of historical prediction values of i�1 j�1 c�1 tendency (periodicity) sequences, which is calculated (12) by equation (15). Under the condition of λ � 1, the weights can be i�1 i Te activation function corresponding to the output calculated by solving the minimum value of J gate is shown in equation (13) [56]. according to the multivariate extreme value function t t theory: Bd � fA . (13) ω ω 8 Journal of Advanced Transportation 1 Step 2: determine the target associated road link to be λ � , (18) 2 n 2 predicted. σ 1/σ i i�1 i Step 3: construct the input matrix of the trafc fow sequence with spatiotemporal characteristics. where i �1, 2. Step 4: use the 1DDCNN model to predict the trafc ③ Step 9.3: as shown in equation (19), the trafc fow fow in the upstream and downstream directions of the prediction values are obtained by using the fully target associated road link at the next moment. connected layer. Step 5: Constraints: the switching conditions of re- versible lanes need to be satisfed in Section 3.1.1 to t t (19) X � tanhW ∘ X + b , O FC O FC change the travel direction of the reversible lane. Otherwise, make t � t+1, and return to Step 4. where W is a learnable parameter. ∘ represents an FC Te fow chart of the reversible lane switching control element-by-element multiplication operator. b is FC model based on the 1DDCNN is shown in Figure 3. an ofset in the fully connected layer. Tanh represents According to set mobile sensor detectors at exit and an activation function that ensures that the output entrance of each intersection (See in Figure 2), the number valuesarehyperbolictangentbetween − 1and1. X is of queuing vehicles at each associated road link is calculated the predictive output of the fully connected layer. as follows: ④ Step 9.4: According to equation (16), the w (k + 1) � w (k) + T · D (k) − q (k), (20) i i i r,i 1DDCNN-LSTM model is trained by minimizing the loss function. Te optimization algorithm named where w is the number of queuing vehicles. D(k) represents i i root mean square propagation (RMSProps) [57] is the trafc volume entering associated road link i. q (k) r,i selected to update the weights and ofsets of each represents the trafc volume leaving the associated road link layer in the model to achieve the purpose of mini- i. T is model sampling time. mizing the loss function. Step 10: Use the test set to detect the prediction efect of the proposed model. If the model satisfes the end 4. The Analysis of Reversible Lane conditions and the switching constraints, go to Step Clearing Time 11. Otherwise, return to Step 7. Step 11: Te prediction results corresponding to the Inordertoobtaintheoptimalreversiblelaneclearingtime,it is necessary to model and analyze the infuences of lane smallest error are inverse normalized to obtain the fnal short-term trafc fow prediction. Ten, the switching time and upstream and downstream intersection signalcontrol onreversiblelaneclearingtime.Terefore,the driving direction of the reversible lane is changed based on the above steps. switching model for fast reversible lane clearance is estab- lished based on the analysis of reversible lane clearing time and signal control in this section. 3.2. Te Reversible Lane Segment Clearing Control. Te re- versible lane function switching is guided by the reversible information signs that are usually arranged at the start and 4.1. Te Reversible Lane Clearing Pattern end of the lane to guide drivers to drive correctly. When the 4.1.1. Te Reversible Lane Segment Clearing Strategy. In this reversiblelane function is about to switch and thelane needs paper, the reversible lanes are divided into three equal to be cleared, the whole lane will be closed, which will have segments for segment clearing. Te clearing times of road a serious impact on the trafc capacity of the associated road links, l , l , and l (i.e., l), are calculated in turn. As shown in 1 2 3 link. In order to reduce average vehicle delay in the re- Figure4,thereversiblelanefunctionfromwesttoeasttoeast versible lane, closing the whole reversible lane immediately to west is taken as an example for segment clearing. For is not recommended, but instead, the reversible lane seg- instance, when the road link l is cleared, vehicles on the ment clearing control is applied to implement a strategy of 1 adjacent lane (traveling from east to west) can drive into switching while clearing as a way to improve the utilization road link l to continue driving so as to improve the uti- of the reversible lane. Terefore, as shown in Figure 2, the 1 lization of road resources. reversibleinformation signswillbe evenly distributed on the According to the distribution of queue length on the reversible lane and gradually changed. reversible lane, it is divided into four cases to discuss the In order to grasp the real-time trafc fow variation of clearing time of the reversible lane segment (i.e., l). each reversible lane link, the support of trafc detectors is required. In this paper, the trafc fow prediction in Section ① Case I: when the reversible lane entrance indicator 3.1 is input into the reversible lane simulation model. Te switches, there is no queue for the whole specifc steps of the reversible lane switching control model reversible lane. based on the 1DDCNN are given as follows: ② Case II: when the reversible lane entrance indicator Step 1: data preprocessing. switches, the queue length reaches the road link l . 3 Journal of Advanced Transportation 9 Road Link i Road Link i+1 Road Link i+2 Mobile sensor detector Figure 2: Te reversible lane segment diagrammatic sketch. Start Data pre-processing Select the target associated road link to be predicted Construct input spatiotemporal matrix Use 1DDCNN model to predict traffic flow in the target associated road link t=t+1 Whether satisfy road and trafc conditions? Change the travel direction of reversible lane End Figure 3: Te fow chart of the reversible lane switching control model. ③ Case III: when the reversible lane entrance indicator lane is selected, i.e., the reversible lane switches the lane di- switches, the queue length reaches the road link l . rection when the last vehicle traveling from intersection 1 to intersection 2 passes the downstream intersection, the lane ④ Case IV: when the reversible lane entrance indicator utilization range at this time is the B region. When the switches, the queue length reaches the road link l . reversible lane segment clearing strategy is used, the lane In order to analyse the impact of diferent clearing pat- change is implemented for the road link l once the vehicle terns for reversible lanes, the clearing patterns for reversible leaves the road link l and so on, so the lane utilization range lanes are divided into two parts, including the segment for this method is the regions of B , B , and B . Terefore, the 1 2 3 clearing and overall clearing of reversible lanes. As shown in diference in the lane utilization range between the two Figure 5, when the overall clearing strategy of the reversible measures is ∆B � B + B , indicating that the lane utilization 1 2 10 Journal of Advanced Transportation Road Link l Road Link l Road Link l 1 2 3 Intersection 1 Intersection 2 Figure 4: Te reversible lane segment clearing diagrammatic sketch. t t S 2redS 2redE g r 2 2 Intersection 2 Intersection 2 l B 2 2 l B Intersection 1 Intersection 1 t t t t t 1 2 3 4 5 Green time Green time Red time Red time Figure 5: Te impact of diferent clearing patterns for reversible lanes. Figure 6: Te four clearing states of the reversible lane. efciency will be higher with the implementation of the As shown in Figure 5, in the case of the original signal segment clearing strategy, but the corresponding reversible timing, the vehicles departing from intersection 1 at time t can only leave the road link at time t , that is, the re- lane control requirements will be higher. 2redE versible lane clearing starts at time t and needs to clear the lane at time t , whose reversible lane clearing time is 2redE 4.1.2. Aiming Clearing State for the Infuence of Lane ∆t � t − t . However, if the green light extension redU 2redE 1 Switching Time and Upstream and Downstream Intersection strategy is adopted, the road link clearing time becomes Signal Control. In order to improve the trafc efciency t + g , where g is the green light extension time. Te 2redS gle gle duringreversiblelanefunctionswitchingandreduceaverage corresponding reversible lane clearing time is ∆t � redY vehicle delay, it is necessary to reduce the reversible lane t + g − t . Tus, it is found that ∆t >∆t and the 2redS gle 1 redU redY clearing time. Since the clearing time is related to the re- signal timing of intersection adjustment afects the clearing versible lane function switching time and the signal control time of the reversible lane, but because its signal adjustment of upstream and downstream intersections. Te infuence of also afects the average delay at the intersection and even on the reversible lane switching time and the signal control of the entire arterial. upstream and downstream adjacent intersections on the Due to the infuence of the reversible lane function clearing time can be analysed by the graphic method and the switching time and the signal control of the upstream and gather-disperse wave theory. downstream intersections on the clearing time, it is found As shown in Figure 6, t , t represent the critical time of 1 5 thatuptofvereversiblelaneclearingstateswillbegenerated passing the road link without stops. Vehicles entering the based on the graphic method and the gather-disperse wave interval [t , t ] need to queue up at the intersection. t 1 5 2redS theory [58], which are shown as follows: and t representthestartandendtimeof theredphaseat 2redE the downstream intersection 2, respectively. t and t are the ① When the reversible lane switching time is within 3 4 start and end time of the red phase at the upstream in- interval [t , t ], the upstream intersection 1 queue is 1 2 tersection 1, respectively. completely dissipated. Journal of Advanced Transportation 11 ② When the reversible lane switching time is within 4.2. Te Reversible Lane Clearing Time Model. Te critical interval [t , t ], the upstream intersection 1 is at the times t and t of passing through the reversible lane without 1 5 2 3 green phase. Te downstream intersection 2 is at the stopping are determined. Ten, according to the queue red-light queue state. length distribution of the reversible lane, the functional relationship between the clearing time of its corresponding ③ When the reversible lane switching time is within reversible lane and the reversible lane function switching interval [t , t ], the upstream intersection 1 is at the 3 4 time is studied based on the gather-disperse wave theory red phase, and no vehicles enter. Te downstream [58]. Te specifc steps are described as follows: intersection 2 is at red-light queue state. ④ When the reversible lane switching time is within Step 1. etermine the critical times t and t of passing 1 5 interval [t , t ], the upstream intersection 1 is at the 4 5 through the reversible lane without stopping. green phase. Te downstream intersection 2 is at the If the queue on the reversible lane is completely dissi- queue dissipation state. pated before t , the critical time t � t − l/v for 2redS 1 2redS j ⑤ When the reversible lane switching time is within passing through the reversible lane without stopping. interval [t , t + C ], the vehicle entering the re- 5 1 2 Otherwise, there is no such critical situation. versible lane can stop and pass through the down- According to the gather-disperse wave theory, it is ob- stream intersection 2. tained as follows: C and C represent the signal cycles of upstream in- 1 2 tersection 1 and downstream intersection 2, respectively. ω ω ji ji t − t + t − t ω + t − t � ω t + − t , (21) 2 1 4 3 ji 5 4 li 5 2redE k k v where l is the reversible lane segment length. v is free fow k � q /q . Similarly, ω � kω , where ω is ag- j straight left ji leftji ji speed. k is the ratio of the straight incoming fow (defned as gregated wave speed. ω is dissipated wave speed. Terefore, li q ) to the left incoming fow (defned as q ), i.e., the clearing critical time is calculated by as follows: straight left kω 1 1 k − 1 kω l ji li t � t − t + t − t + t − . (22) 5 2 1 4 3 2redE kω − ω k k k kω − ω v li ji li ji j Tecriticaltime t needstosatisfy t ≤ t ≤ t + C . ② If t ≤ t ≤ t , then T � t − t + (t − t )ω /kω . 2redE 5 2redS 2 2 3 2redE 1 ji li If not, there is no such critical situation. ③ If t ≤ t ≤ t , then T � t − t + (t − t )ω / kω + 3 4 2redE 2 1 ji li (t − t )ω /ω . 3 ji li Step 2. Analyze clearing time in the fve states based on the ④ If t ≤ t ≤ t , then T � t − t + (t − t + t − t )ω / 4 5 2redE 2 1 4 ji gather-disperse wave theory. kω + (t − t )ω /ω . li 4 3 ji li Te number of queuing vehicles in each reversible lane ⑤ If it satisfes other situations, then T � l/v . segment canbe calculated by equation(20) soasto judge the j range of reversible lane queue length. Ten, the relationship t is the reversible lane function switching time. T is the between the reversible lane clearing time and the reversible reversible lane clearing time. lane function switching time is analysed. In summary, the clearing time function is calculated as follows: ① If t ≤ t ≤ t , then T � t − t + (t − t )ω /kω . 1 2 2redE 1 ji li 12 Journal of Advanced Transportation t − t ω ⎧ ⎪ 1 ji ⎪ t − t + , if t ≤ t ≤ t , ⎪ 2redE 1 2 kω li t − t ω ⎪ 1 ji t − t + , if t ≤ t ≤ t , ⎪ 2redE 2 3 kω li t − t ω t − t ω 2 1 ji 3 ji T � f(t) � (23) t − t + + , if t ≤ t ≤ t , ⎪ 2redE 3 4 kω ω li li t − t + t − t ω t − t ω 2 1 4 ji 4 3 ji ⎪ t − t + + , if t ≤ t ≤ t , ⎪ 2redE 4 5 kω ω ⎪ li li ⎪ l , if othersituations. the maximum green and minimum green. Te minimum 5. The Reversible Lane Signal green time of intersection 1 is defned as g . Te max- 1min Control Optimization imum green time is defned as g . Te green light early 1max break time of upstream intersection is defned as t , and To reduce the impact on the signal timing scheme of upstream szd and downstream intersections, according to the idea of the g − t − ∆t ≥ g 1 szd transition 1min this condition needs to be literature [58], but unlike the literature [58], it is known from r + t +∆t ≤ g 1 szd transition 1max Section4thatbothcriticaltimesanddiferentstatesofreversible satisfed, where ∆t is the transition time of the phase. transition lane clearing times are related to the signal timing of the up- Terefore, the value range of t is calculated as follows: szd streamanddownstreamintersections.Tedynamicadjustment t ∈ 0, g − g +∆t of the signal timing scheme at upstream and downstream in- szd 1 1min transition (24) tersections afects the reversible lane clearing time. In order to ∩ 0, g − r − ∆t . 1max 1 transition shortenthereversiblelaneclearingtimeasmuchaspossible,the signal timing scheme at the upstream intersection can be ad- justed to reduce the number of vehicles entering the reversible 5.1.2. Green Light Extension Time of Downstream lane. Meanwhile, the signal timing scheme at the downstream Intersection. Since the green light at the upstream in- intersection can be adjusted to make the vehicles that have tersection is broken early, t and t will be changed. Te 2 3 entered the reversible lane pass it as soon as possible. In this criticaltimeofthenewnonstoppassingthroughintersection section, the clearing time is dynamically optimized by using the 2 is defned as t . Te start time of the red-light phase at the strategy of compressing the green time at the upstream in- new intersection 1 is defned as t . In order to make vehicles tersection and extending the green time at the downstream entering the reversible lane at moment of t pass through intersection without changing the signal cycle and based on the intersection 2 smoothly, it is necessary to extend the green vehicle arrival state and satisfying the conditions of maximum light duration of downstream intersection 2 under the and minimum green lights at each phase. condition of satisfying the maximum green and minimum green. Meanwhile, the green light extension time of ′ ′ downstream intersectionisdefnedas t − t .∆t isthe 3 2 transition 5.1. Te Strategy of the Upstream Green Light Early Break and transition time of the phase. Downstream Green Light Extension. Green light early break Te green light extension time under diferent condi- at the upstream intersection and green light extension at the tions is described as follows: downstream intersection are shown in Figure 7. In Figure 7, g and r represent the red time and green ′ ′ ′ (1) If r − (t − t ) − ∆t ≥ g &g + (t − 1 1 2 3 2 transition 2min 2 3 time of intersection 1, respectively. g and r represent the t ) +∆t ≤ g , that is, if green light exten- 2 2 2 transition 2max red time and green time of intersection 2, respectively. sion time not only satisfes the maximum green but Te green light early break time of upstream intersection also satisfes the minimum green of the next phase. is calculated. Ten, the green light extension time at the Te green light extension time of downstream in- downstream intersection is calculated. tersection is calculated by the following equation: ′ ′ t � t − t +∆t . (25) yc 3 2 transition 5.1.1. Green Light Early Break Time of Upstream Intersection. ′ ′ ′ ′ Te degree of vehicle release at upstream intersections will (2) If r − (t − t ) − ∆t ≤ g &g + (t − t ) 2 3 2 transition 2min 2 3 2 afect the clearing efciency of the reversible lane. Tus, the +∆t ≤ g , that is, if green light extension transition 2max greenlightphasetimeoftheupstreamintersectionshouldbe time satisfes the maximum green, however, it does appropriately compressed under the premise of satisfying notsatisfytheminimumgreenofthenextphase.Te Journal of Advanced Transportation 13 r g 2 2 Intersection 2 Intersection 2 Intersection 1 r g 1 1 Intersection 1 1 t t t t t 1 2 3 4 5 t t t t t 1 2 3 4 5 Green time Green time Red time Red time Green-light extension Green-light extension Green-light early break Green-light early break Figure8:Tediagramofupstreamredlightdelayanddownstream red light early break. Figure 7: Te diagram of upstream green light early break and downstream green light extension. reversible lane. Tus, if the reversible lane switching time is green light extension time of downstream in- within the interval [t , t ], the red light phase time at the 3 4 tersection is calculated by the following equation: upstream intersection can be appropriately extended while t � r − g − ∆t . satisfying the premise of maximum green and minimum (26) yc 2 2min transition green. If the red light delay time at the upstream intersection ′ ′ ′ ′ is defned as t , it needs to be satisfed (3) If r − (t − t ) − ∆t ≥ g &g +(t − t ) syc 2 3 2 transition 2min 2 3 2 +∆t ≥ g , that is, if green light extension r + t +∆t ≤ g transition 2max 1 syc transition 1max , where ∆t is the tran- transition time does not satisfy the maximum green, however, g − t − ∆t ≥ g 1 syc transition 1min it satisfes the minimum green of the next phase. Te sition time of the phase. Te value range of t is calculated syc green light extension time of downstream in- by the following equation: tersection is calculated by the following equation: t ∈ 0, g − g − ∆t syc 1 1min transition t � g − g − ∆t . (27) yc 2max 2 transition (29) ∩ 0, g − r − ∆t . 1max transition ′ ′ ′ ′ (4) If r − (t − t ) − ∆t ≤ g &g +(t − t )+ 2 3 2 transition 2min 2 3 2 ∆t ≥ g , that is, if green light extension transition 2max time neither satisfes the maximum green nor sat- 5.2.2. Te Red Light Early Break Time of Downstream isfes the minimum green of the next phase. Te Intersection. t will be changed when the red light delay green light extension time of downstream in- occurs at the upstream intersection. At this time, the end tersection t is calculated by the following equation: yc time of the red light phase at the upstream intersection 1 r − t − ∆t � g , ⎧ ⎨ ′ becomes t . After the red light delay strategy is implemented 2 yc transition 2min (28) ⎩ at the upstream intersection, there will be no more vehicles g + t +∆t � g 2 yc transition 2max . drive into the reversible lane. However, in order to make the vehicles that have entered the reversible lane and waiting in If this equation has a unique solution, the green light the queue to leave the downstream intersection 2 as soon as extension time is defned as t . Otherwise, the green light yc possible, so as to achieve the purpose of reversible lane fast extension strategy at the downstream intersection cannot be clearing. Terefore, the red light early break strategy can be carried out. implemented at the downstream. At the same time, the red light early break strategy needs to satisfy maximum green and minimum green of downstream intersection 2, i.e., 5.2. Te Strategy of the Upstream Red Light Delay and r − t − ∆t ≥ g 2 zd transition 2min Downstream Red Light Early Break. Red light delay at the , where ∆t is the tran- transition g + t +∆t ≤ g 2 zd transition 2max upstream intersection and red light early break at the sition time of the phase. downstream intersection are shown in Figure 8. In order to minimize the clearing time, it is necessary to ensure that the vehicle entering at moment of t can just pass 5.2.1. Te Red Light Delay Time of Upstream Intersection. throughthedownstreamintersection2withoutstopping.Tus, Te red light delay strategy is implemented at the upstream the red light early break time at the downstream intersection intersection to reduce the number of vehicles entering the (defned as t ) is calculated by the following equation: zd0 14 Journal of Advanced Transportation t t t − t ω 2redS 2redE 2 1 ji t � t + − . (30) zd0 3 v kω j li Intersection 2 Te diagram of downstream red light early break is shown in Figure 9. Te red light early break time at the downstream in- tersection under diferent conditions is described as follows: (1) r − t − ∆t ≥ g &g + t +∆t ≤ 2 zd0 transition 2min 2 zd0 transition g , where ∆t is the transition time of the 2max transition phase. Te red light early break phase satisfes the Intersection 1 minimum green of downstream intersection 1 and the maximum green of its next phase. Te red light early break time is calculated by the following t t t t t T 1 2 3 4 5 equation: Green time Red time t � t − ∆t . (31) zd zd0 transition Red-light early break (2) r − t − ∆t ≤ g &g + t +∆t ≤ Figure 9: Te diagram of downstream red light early break. 2 zd0 transition 2min 2 zd0 transition g , where ∆t is the transition time of the 2max transition phase.Teredlightearlybreakphasedoesnotsatisfy Inordertoachieveamoreaccurateevaluation,thesignal the minimum green of downstream intersection 1 timing scheme of upstream and downstream intersections is but satisfy the maximum green of its next phase. taken as the input of the VISSIM platform. Te average Tus, the red light early break time is calculated by vehicle delay is selected as the evaluation index of trafc the following equation: simulationtomeasurethecontrol efectofsignaladjustment variation at upstream and downstream intersections, which t � r − g − ∆t . (32) zd 2 2min transition is calculated by the following equation: (3) r − t − ∆t ≥ g &g + t +∆t ≥ Y � Ht , t , t , t , (35) 2 zd0 transition 2min 2 zd0 transition yc zd syc szd g , where ∆t is the transition time of the 2max transition where Y represents the average vehicle delay of upstream phase. Te red light early break phase satisfes the minimum green of downstream intersection 1 but (downstream) intersection. t , t , t , t are the signal yc zd syc szd adjustment strategy of upstream and downstream in- doesnotsatisfythemaximumgreenofitsnextphase. tersections, respectively. Te red light early break time is calculated by the following equation: 6. The Reversible Lane Cooperative t � g − g − ∆t . (33) zd 2max 2 transition Control Model 6.1. Establish a Cooperative Optimization Model of Reversible (4) r − t − ∆t ≤ g &g + t +∆t ≥ 2 zd0 transition 2min 2 zd0 transition Lane Clearing and Signal Control. In this paper, the re- g , where ∆t is the transition time of the 2max transition versible lane clearing time and the signal timing scheme of phase.Teredlightearlybreakphasedoesnotsatisfy upstream and downstream intersections are coordinated the minimum green of downstream intersection 1 and the maximum green of its next phase. Whether and optimized. Combined with the equations of the re- versible lane clearing time and the average vehicle delay in there is a unique solution to equation (34) needs to Section 4.2, through signal control to speed up the road bedetermined.Ifso,theredlightearlybreakstrategy clearing at the same time, reduce the impact of vehicles’ at the downstream intersection can be implemented. operation, taking into account the reversible lane function Otherwise, the red light early break cannot be exe- switching in the environment contains undersaturated, cuted, as shown in the following equation: critical saturation, oversaturation three trafc conditions. t − t − ∆t � g , 2r zd transition 2min Tus, a double objective optimization function is con- (34) g + t +∆t � g . structed as follows: 2 zd transition 2max Journal of Advanced Transportation 15 J � α F ∆t + α Ht , t , t , t , 1 factors 2 yc zd syc szd ⎧ ⎪ ∆T � f ∆t ,∆t ∈ ∆t,∆t ⎪ factors factors signal − v ⎪ 1 − e l F ∆t � · − v factors ⎪ 1 + e v T ⎪ − Y 1 − e Y − Y min ⎪ ∆Ht , t , t , t � ∆Y � · yc zd syc szd ⎪ − Y Y − Y 1 + e ⎪ max min r − t − ∆t ≥ g 2 yc transition 2min (36) g + t +∆t ≤ g 2 yc transition 2max s.t. ⎪ t − t − ∆t ≥ g ⎪ 2r zd transition 2min g + t +∆t ≤ g 2 zd transition 2max t ≥0 yc t ≥0 ⎪ zd ⎪ t ∈ 0, g − g +∆t ∩ 0, g − r − ∆t szd 1 1min transition 1max 1 transition t ∈ 0, g − g − ∆t ∩ 0, g − r − ∆t , syc 1 1min transition 1max transition where α and α are weight coefcients, respectively, i.e., the complexity of the objective function and the large 1 2 α + α � 1. To standardize the magnitudes, Tand Y need to number of constraints and parameters, the model is slow to 1 2 be normalized to obtain f(t) and H(t , t , t , t ), re- solve using the traditional optimization algorithms. At yc zd syc szd spectively. ∆T is variation amount of the reversible lane present, the adaptive sampling algorithm performs linear clearing time. ∆t is variation amount of the reversible lane ftting of the complex environmental parameters, which can function switching time. ∆t is adjustment amount of adaptively reduce the input parameter dimension of the signal signal timing at the intersection. Te ideal minimum cooperative control model. Meanwhile, the frefy algorithm clearing time of the reversible lane is defned as has good global searching ability and robustness, which is − v − v − v − v T � 1 − e /1 + e · l/v . Let 1 − e /1 + e be the nor- suitable for solving complex nonlinear optimization prob- best j malized fow-speed ratio coefcient of the vehicles. Tere- lems. Inordertospeedup themodelsolutionandensurethe fore, the shorter the clearing time, the closer f(∆t,∆t ) is real-time performance, this paper introduces the adaptive signal to 1. Te amount of normal vehicle delay variation at the sampling-frefy algorithm (ASFA) method to solve the upstream and downstream intersections is obtained through cooperative control model. − Y − Y the min-max normalization, i.e., ∆Y � 1 − e /1 + e · Step 1: Initialize parameters based on the proposed Y − Y /Y − Y . When the smaller the ∆Y is, the min max min model. Te mobile sensor data are handled to obtain ∆H(t , t , t , t ) is closer to 1. yc zd syc szd multiple information of the reversible lanes. In order to obtain the shortest clearing time and the Step 2: Perform linear ftting on the above multiple optimal signal control strategy of upstream and down- information to judge whether its wave momentum is stream,itisnecessarytoselecttheappropriate t, t , t ,and yc syc greater than the threshold x . If it is greater, set the t , which can maximize the value of objective function J. It szd number of information samples to 6N. Otherwise, is worth noting that the reversible lane function switching is set 3N. based on ∆J � J − J , where J is the objective after after before functionvalue afterswitching. J istheobjectivefunction Step 3: Perform scan matching. Te information before value before switching. Terefore, if ∆J >0, the reversible samples are from the optimized proposed distribution lane function switching is performed. Otherwise, no [59]. Calculate the weights of the current particles. switching is performed. Step 4: Judge the number of sampled particles. If it is 6N, proceed to the next step. If it is 3N, go to Step 11. 6.2. Model Solution Method. Te solving process of the re- Step 5: Accordingto the particle weights, determine the versible lane cooperative control model is actually the variables including the reversible lane function solving process of the nonlinear optimization model. Due to switching time t and the signal control strategy of 16 Journal of Advanced Transportation upstream and downstream intersections. Set constraint model prediction. In the GCN convolution layer, the size of conditions as detailed in Sections 4 and 5. the flter receiver feld K is varied from 1 to 5. In the LSTM layer,thenumberofrecenttrendintervals n variesfrom1to Step 6: divide the current particles and variables into (i) 12 (5min to 1hour). Te size of daily cycle interval m varies a high similarity area (defned as Hsa st ) and a low (i) from 1 to 14days. In the 1DCNN layer, the convolution similarity area (defned as Lsa st ). kernel size is 3, which remains the same in each layer. In the Step 7: to prevent the frefy algorithm from reducing 1DCNN-LSTMlayer,thebatchsizeofeachmodeltrainingis the diversity of particles and multiple variables due to 128.Adamisselectedastheoptimizer.Telossfunctionuses itshigh optimization performance,athreshold N isset. categorical crossentrogy. Te early stopping criterion sets Step 8: Judge whether the number of particles n and the training batches (epoch). Training is stopped when there variables in the high similarity area is greater than the isnoimprovementinaccuracy.Te trainingtimeofthefnal threshold value N . If it is less than N , proceed to the f f accuracyrateforthefrsttimeissetasthemaximumtraining next optimization operation. Otherwise, go to Step 10. times (max_epochs). Step 9: Calculate the global optimal value p . Cal- best culate the attractiveness between each particle and the 7.2.1. Parameter Sensitivity Analysis. Four parameters are optimal particle at the same time. Ten, the optimi- zation is performed. If the number of iterations or selected to analyze the spatiotemporal infuence factors in the 1DDCNN-LSTM model on prediction performance, accuracy or ftness function J is reached, stop opti- mization. Otherwise, continue to Step 9. including the size of the flter receiver feld K, the number of recent trend intervals n , the size of daily cycle interval m, i j Step 10: Output global extreme points and optimal and the convolution kernel size. For example, when K �3, individual values. Recalculate the particle weights and the adjacent road links within the third stage (including the normalize the results. third stage) of the target road link are fed into convolution Step 11: Carry out selective resampling based on the operation to capture the local spatial correlation. When number of efective particles, that is, set the threshold a parameter is changed, the other three parameters are set to N 2 (1) N � exp(1/ [w ] ). When the number of ef- eff i�1 remain unchanged from the previously defned default fective particles is less than the threshold value B, parameters to observe the separate infuence of this resampling is performed. Otherwise, this operation will parameter. not be performed. As shown in Figure 11, Figure 11(a) demonstrates that Step 12: update the various parameters until the ftness the best prediction performance is K �3. Tis may be the function J converges and the algorithm ends. case when K is large; the model can capture the spatial correlation between the predicted and adjacent road links. 7. Numerical Case Analysis However, when the road links involved in the receiver feld are far away from the predicted road links, the spatial 7.1. Case Study. A section of reversible lane on Chaoyang correlation becomes weaker. It indicates that the trafc fow RoadinBeijingisselected forthecasestudy. Tetotallength data of the adjacent road links with higher degree cannot of this section which is located between Jingguang Bridge improve the prediction performance of the model. In and Zhenzhi Road is about 740m. Te trafc organization Figure 11(b), when trafc fow data of the current six-time diagram is shown in Figure 10. Taking the evening peak intervals (30min) are fed into the recursive layer, the model hours as an example, the reversible lane changing direction achieves better performance. Especially, when n �2, the can be switched from the direction of entering the city to the model has got the best performance. Ten, RMSE rises with leaving direction. Te trafc fow data of the reversible lane the increase in historical trafc fow data. Tese results show are presented in Table 1. that trafc fows have a strong short-term temporal corre- lation, which is concentrated in the past for a shorter time 7.2. Te Trafc Flow Prediction Verifcation. Te trafc fow period. datasets are selected during working days from November 1 As shown in Figure 12(a), the prediction accuracy is to 29, 2016. Te datasets from November 1 to 28 are used as improved by adding periodic data to the recursive layer. the training samples, and the data on November 29 are used When m is greater than 9, the RMSE reaches a relatively low as the test samples. In order to verify the efectiveness of the level. It shows that trafc fow at future moments can be proposedtrafcfowpredictionmodel,thepredictionresults predicted more accurately using trafc fow sequences of the are compared with the following models: LSTM, graph same time interval for more than 9days in the past. Tis is convolutional networks (GCNs), GCN-LSTM, because the larger the number of trained samples, the more 1DCNN-LSTM [60], and 1DCNN- GCN. Te root mean accurate the spatiotemporal characteristics trained by the square error (RMSE) and the mean absolute error (MAE) prediction model is. As shown in Figure 12(b), when the [61] are chosen to measure the accuracy of the number of channels remains unchanged, the recognition prediction model. ability of the network generally tends to decrease as the size Before model training, the min-max normalization of the convolution kernel increases. When the convolution method is used to scale the input data to the range [− 1, 1]. kernelincreases,thenumberofweightsinthenetworkis too Te predicted values are rescaled back to normal values after large, and the time spent on the training network will also Journal of Advanced Transportation 17 From 17:00 to 20:00, this lane is changed from North The direction of the direction of entering the city entering the city to leaving the city. BRT BRT BRT Reversible lane Reversible lane Reversible lane BRT BRT BRT After the evening peak, the lane function will be The direction of restored in the leaving the city direction of entering the city. Figure 10: Te trafc organization diagram. Table 1: Te reversible lane volume entering and leaving the city. Entering Leaving the city direction the city direction Hourly trafc volume (pcu/h) 2540 4320 4.8 4.8 4.75 4.75 4.7 4.7 4.65 4.65 4.6 4.6 1 23456789 10 11 12 1 2345 Te number of recent trend intervals n Te size of flter receiving feld K (a) (b) Figure 11: Te frst two parameters’ sensitivity analysis. (a) Change the value of K. (b) Change the value of n . RMSE RMSE 18 Journal of Advanced Transportation 4.9 100 4.85 4.8 4.75 90 4.7 4.65 4.6 80 1 2 3 4 5 6 7 8 9 10 11 12 13 14 3 4567 The size of daily cycle interval m j Convolution kernel size (a) (b) Figure 12: Te last two parameters’ sensitivity analysis. (a) Change the value of m. (b) Change the value of the convolution kernel size. associated road links. In addition, compared with the increase. Terefore, when the convolution kernel size is 5 (i.e., the value is 90.08), the recognition ability of the 1DCNN-GCN and GCN model, the measurement results of 1DDCNN performs best. the 1DDCNN-LSTM model show the importance of spatial correlation modelling. Te GCN can accurately capture the topological correlation of the road network and has higher 7.2.2. Prediction Results. To verify the model efects, the prediction accuracy. Compared with LSTM, GCN-LSTM, prediction results of the above-mentioned six models are and 1DCNN-LSTM, the measurement results of the presented in Figure 13. As shown in Figure 13, several 1DDCNN-LSTM model present the importance of temporal results are presented as follows: Firstly, the LSTM model correlation modelling. Te LSTM can obtain the temporal clearly shows the periodic fuctuations and local upward correlation of trafc fow. or downward trends of trafc fow evolution, indicating In summary, the 1DDCNN-LSTM model fully considers that the LSTM model can efectively capture the temporal the spatiotemporal correlation of trafc fow. As a result, it correlation of trafc fow. Secondly, the prediction results can better learn the spatiotemporal characteristics of trafc of GCN-LSTM, 1DCNN-LSTM, and 1DCNN-GCN are fow and improve the prediction accuracy. closer to the real values of trafc fow than the LSTM model, which indicates that trafc fow not only evolves 7.3. Determine Signal Coordinated Control Scheme Based on over time variation but also is afected by surrounding road links. Te spatial correlation can be obtained by the ASFA. As shown in Table 4, the signal control scheme for graph convolution model. Finally, the 1DDCNN-LSTM reversiblelanesatupstreamanddownstreamintersectionsis predicted trafc fow has the highest overlap with the presented, including the name of intersection, phase, green actual trafc fow, which indicates that the light time, and cycle. Te cycle length is the same for both 1DDCNN-LSTM model can predict trafc fow more upstream and downstream intersections, and the value is accurately than other models. 195s. Te phases contain the release sequence for four According to characteristics of trafc fow in diferent diferent directions of the intersection. Te green light times periods, the trafc fow during whole day is divided into are shown in Table 4. According to the actual investigation, the free fow speed three parts: the peak period (7:00–10:00 and 17:00–20:00), the fat peak period (6:00-7:00, 10:00–17:00, and 20:00-21: of the reversible lane is 50km/h. Te ideal minimum 00), and the low peak period (21:00–6:00). Tables 2∼3 show clearing time of the reversible lane is T �53.24s. A bset thepredictionperformanceresultsofthesixmodels foreach simulation road network is built through VISSIM. Te time period and throughout the day, respectively. original state of associated road link is simulated and ob- As shown in Table 3, the 1DDCNN-LSTM model sig- tained the normal average vehicle delay at the upstream and nifcantly improves the trafc fow prediction performance. downstream intersections, taking its average value as Te RMSE value of the 1DDCNN-LSTM model is the lowest Y �67.57s. among the other fve models at 2.4027, which verifes the Let the time when the reversible lane function switching efectiveness and superiority of the method in short-term is just satisfed be 0. Te switching time starts from 0 and trafc fow prediction. Meanwhile, the prediction perfor- traverses a cycle in 1s. Each switching time should traverse mance of the proposed model is better than other models, all possible signal control schemes for upstream and which presents the importance of selecting spatiotemporal downstream intersections. At the beginning of the RMSE 1DDCNN accuracy Journal of Advanced Transportation 19 0 5 10152025 Time (h) Original value 1DDCNN-LSTM 0 5 10152025 Time (h) Original value GCN 0 5 10 152025 Time (h) Original value LSTM 0 5 10 15 20 25 Time (h) Original value GCN-LSTM 0 5 10 152025 Time (h) Original value 1DCNN-LSTM 0 5 10 15 20 25 Time (h) Original value 1DCNN-GCN Figure 13: Te six models’ prediction results. Table 2: Te prediction performance results of the six models in each time period. Peak period Flat peak period Low peak period Predicted models MAE RMSE MAE RMSE MAE RMSE LSTM 3.1680 6.7780 5.0010 8.1030 3.2140 4.6450 GCN 3.0050 5.9010 4.9840 7.3040 3.1090 3.9940 GCN-LSTM 2.6920 5.3380 4.6370 7.0980 2.5170 2.7490 1DCNN-LSTM 2.5290 4.8540 4.0220 5.4170 2.3380 2.2010 1DCNN- GCN 2.2530 3.1170 3.9910 4.6610 1.8710 1.7360 1DDCNN-LSTM 1.7190 2.5370 3.0180 3.1150 1.0090 1.5560 simulation, the initial timing parameters of the upstream In order to ensure the rapidity of solution, the param- and downstream intersections are shown in Figure 14. Since eters of the ASFA Algorithm are described as follows: the t > t + C , there is no such critical situation. number of frefy population is 30. Te number of iterations 4 2redS 2 Trafc volume (pcu/h) 20 Journal of Advanced Transportation Table 3: Te prediction performance results of the six models throughout the day. Predicted models MAE RMSE LSTM 3.7943 6.5087 GCN 3.6993 5.7330 GCN-LSTM 3.2820 5.0617 1DCNN-LSTM 2.9630 4.1573 1DCNN- GCN 2.7050 3.1713 1DDCNN-LSTM 1.9153 2.4027 Table 4: Te signal control scheme. Intersection Phase Green light time Cycle East-west straight 70 East-west left 40 Te upstream intersection 195 North group release 45 South group release 20 East-west straight 70 East-west left 40 Te downstream intersection 195 North group release 40 South group release 25 t =64 t =168 2redS 2redE g r 2 2 Jingguang Bridge Zhenzhi Road 2.7 29 135 197 259 T t t t t t 1 2 3 4 5 Green time Red time Figure 14: Te initial timing parameters of upstream and downstream intersections. is 200. Te update parameters of the algorithm are set as the signal training and ftting degree of ASFA is better than follows: maximum attraction factor β � 1, step factor the GA. As shown in Figure 16, the MAE and the RMSE of α � [0,1], and light absorption coefcient c � 1. Te ASFA regression training are 35.6266 and 44.7238, re- threshold value B is 0.002. spectively. At the same time, the mean error and the Te parameters of the genetic algorithm (GA) are set as standard deviation (STD) error of ASFA regression training follows:thepopulationsizeis25.Tecrossoverprobabilityis are 2.6670 and 44.7242, respectively. In the lower part of 0.65. Te mutation probability is 0.05. Te number of it- Figure 16, the MAE and the RMSE of ASFA regression erations is 250. Learning factors are selected as fxed weight training are 34.1530 and 42.1885, respectively. Te mean α � β � 0.5. Compared with the GA, the evolution process error and the STD error of ASFA regression training are and the results are shown in Figure 15. Te results show that 9.9440 and 41.1717, respectively. Journal of Advanced Transportation 21 GA and ASFA Signal Trained 0.06 0.04 0.02 0 20 40 60 80 100 120 140 160 180 200 220 240 Iteration Number GA Model ASFA Model ASFA Train Error = 0.0018278 -6 -4 -2 0 246 Standard Deviation -3 ×10 ASFA Parameters Fitting value -2 0 20 40 60 80 100 120 140 160 180 200 220 240 Iteration Number Energy Entropy Short Time Energy Spectral Centroid ASFA Spectral Flux Figure 15: Comparison results of the evolutionary process of the ASFA and GA. Figure 17 demonstrates the comparison of objective reversible lane segment l (i.e., the lane indicator switching function (ftness) convergence for the GA and ASFA. When time) is 189s. Te signal control strategy for the upstream the iteration number is 120, the ftness function J has and downstream intersections remains unchanged; the converged. Te overall curve tends to be stable, where the maximum objective function is 0.4734. Under this control optimal cost is stable at around 0.002. However, when the strategy, the changes in lane number from east to west and iteration number of the GA is 200, the curve shows a sta- the speed-density variation of reversible lanes are shown in tionary point of convergence. Tus, the ftness function J has Figure 20. converged. Te results show that the ASFA converges faster Figure 20 shows that the density of the reversible lane and more stable than the GA. increases rapidly and the average speed decreases rapidly during the opening transient process of l , which is because the speed of vehicles driving from west to east into the 7.4. Simulation Results. As shown in Figure 18, VISSIM reversible lane segment l decreases in the process, and the simulation software is used to build a simulation platform. number of vehicles entering the reversible lane is larger than Diferent control methods are used to evaluate the simu- the leaving vehicles. Tus, the density increases. When the lation efects. Te VISSIM COM interface with MATLAB is reversible lane segment l opens, the average speed of the used to connect VISSIM with diferent control modes based reversible lane decreases slowly and the density increases on reversible lanes. slightly, which is because the vehicles in the reversible lane Data in Section 7.3 are input into VISSIM. Te simu- segment l have been speeded up to drive normally, and the lation results of each switching time and its corresponding reversible lanequeue is dissipating.Whenthe reversiblelane optimal signal control scheme are visualized in Figure 19. segment l opens, the reversible lane function is completely As shown in Figure 19, when the opening time of the switched.Telanenumberinthedirectionofleavingthecity reversible lane segment l is 148s, the opening time of the is switched from 5 to 6. Te speed and density of reversible reversible lane segment l is 165s and the opening time of lanes are gradually stabilized. Fittest Cost Results Fitting Deviation Value Probability Density 22 Journal of Advanced Transportation ASFA Train - R = -37.2463 ASFA Test - R = -36.2579 2000 2000 1500 1500 1000 1000 500 500 0 0 -500 -500 -500 0 500 1000 1500 2000 -500 0 500 1000 1500 2000 Train Target Test Target Fitted curve Fitted curve Prediction bounds Prediction bounds ASFA Train - R = -18.5668 ASFA Test - R = -17.2252 2000 2000 1500 1500 1000 1000 500 500 0 0 -500 -500 -500 0 500 1000 1500 2000 -500 0 500 1000 1500 2000 Train Target Test Target Fitted curve Fitted curve Prediction bounds Prediction bounds Figure 16: Te results of regression training process for ASFA. To verify the efectiveness of the cooperative optimiza- than the nonsegmented clearing result. Tus, the reversible tion model, the average vehicle delay, clearing time, and lane switching time selection not only shortens the clearing model output are simulated by VISSIM, respectively. Te time but also helps to implement the reversible lane seg- simulation results are shown in Table 5. mented clearing strategy. As shown in Table 5, the clearing time of the reversible According to the reversible lane segment clearing lane is not only afected by the reversible lane function strategy, the minimum clearing time is the best solution. switchingtimebutalsobythesignalcontrolofupstreamand Although the requirement of the shortest clearing time is satisfed, the average vehicle delay at the upstream and downstream intersections. Comparing the segmented clearing model with the nonsegmented clearing model, we downstream intersections is large, 78.03 and 73.54s, re- can see that the segmented clearing of the reversible lane spectively, which afects the operational efciency of the mainly afects average vehicle delays at its upstream in- upstream and downstream intersections. If the minimiza- tersection. When the fxed time switching model is adopted, tion of the average vehicle delay is the best solution, the the efect of the nonsegmented clearing model is better than clearing time will become longer, reaching 57.22s, which is that of segmented clearing. Tis is because when some lane not conducive to the reversible lane function switching functions on the reversible lane are switched, the delay is in time. caused by the red light when vehicles entering the upstream In terms of vehicle delays at the upstream and down- intersection of the reversible lane. Terefore, the reversible streamintersectionsinTable5,comparedwiththefxedtime lane segment clearing model needs to be coordinated with switching model, the cooperative optimization model re- the signal control at the upstream and downstream in- duces 10.47s. Te index increases by 26.38%. Compared tersections to achieve the best control result. Among them, with the shortest clearing time model, the model reduces the segmented clearing efect of minimum average vehicle 2.27s, and the index improves by 2.98%. In terms of clearing delay and cooperative optimization is signifcantly better time, compared with the fxed time switching model, the Train Output Train Output Test Output Test Output Journal of Advanced Transportation 23 -3 GA Algorithm Training ASFA Algorithm Training ×10 11 0.012 0.01 0.008 7 0.006 0.004 0.002 3 0 0 50 100 150 200 250 0 50 100 150 200 Iteration Number Iteration Number GA Train ASFA Train Figure 17: Te GA and ASFA method training result. Figure 18: Te simulation platform. 0.6 (189,0.4734) t t t 1 2 3 0.4 0.2 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Switching Time (s) Figure 19: Te simulation results. GA Best Cost Result Vehicle Delay (s) Clearing Time (s) Objective Function ASFA Best Cost Result 24 Journal of Advanced Transportation 2.5 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Simulation Time (s) Figure 20: Te parameters of reversible lane simulation results. Table 5: Comparison result. Average vehicle delay Average vehicle delay at upstream intersection at downstream intersection Clearing time (s) J (s) (s) Fixed time switching (no segmentation) 79.88 78.61 64.37 0.3473 Fixed time switching (segment clearing) 83.07 78.92 64.45 0.3411 Minimum average vehicle delay (no segmentation) 73.18 67.04 57.22 0.4215 Minimum average vehicle delay (segment clearing) 70.01 66.85 57.22 0.4360 Minimum clearing time (no segmentation) 76.54 73.63 51.71 0.4507 Minimum clearing time (segmentation) 78.03 73.54 51.71 0.4499 Cooperative optimization (no segmentation) 74.61 70.05 53.98 0.4517 Cooperative optimization (segmentation) 71.57 67.39 53.98 0.4633 Table 6: Random 5-day simulation results. Fixed time switching Cooperative optimization Switching time Objective Clearing efciency Time Average vehicle Clearing Average vehicle Clearing state function (%) delay (s) time (s) delay (s) time (s) April 5th [0, t1] 85.63 71.38 71.53 58.42 0.4385 18.16 April 11th [t , t ] 82.56 65.59 68.93 54.21 0.4830 17.35 3 4 April 14th [t , t ] 79.83 64.62 69.28 54.08 0.4829 16.31 3 4 April 19th [t , t ] 83.74 69.31 69.85 53.95 0.4820 22.16 1 2 April 26th [t , t ] 81.75 68.76 70.37 57.03 0.4536 17.06 3 4 cooperative optimization model reduces 10.39s. Te optimization model can search for the optimal control clearing efciency improves by 25.04%. Compared with the strategy that balances the requirements of the shortest minimum average vehicle delay model, it reduces 3.24s. Te clearing time and the minimum vehicle delay. Meanwhile, clearing efciency improves by 9.02%. the reversible lane function switching control model can To avoid the simulation contingency, the evening peak make full use of the spatiotemporal resources in the road hours of 5days in a month are randomly selected for ver- network to adjust the trafc demand of the associated road ifcation based on the above-mentioned process. Te sim- links in real time, improve the global trafc efciency of ulation results are presented in Table 6. main arterial roads, and efectively alleviate trafc conges- tion caused by imbalance of bidirectional trafc fow. As shown in Table 6, the clearing efciency optimization is improved by more than 15%. Te average vehicle delay is reduced by more than 10%. Te optimal switching time will vary based on the reversiblelane function switching demand 7.5. Sensitivity Analysis. In order to evaluate the sensitivity time and the control strategy of upstream and downstream of varying the main parameters to the proposed model, the intersections. Te results show that the cooperative infuences of diferent main parameters on average vehicle Density (veh/km) Speed (km/h) Lane number Journal of Advanced Transportation 25 100 110 60 50 0 50 100 150 200 0 50 100 150 200 Switching Time (s) Switching Time (s) Before optimization Before optimization After optimization After optimization (a) (b) Figure 21: Te impact of changingthe mainparameters on averagevehicle delayand clearing time. (a)Te impact on average vehicle delay. (b) Te impact on clearing time. 0.5 19 1.5 0.48 18 0.46 17 0.5 0.44 16 0.42 15 50 100 150 200 250 300 0 100 200 300 400 Simulation Time (s) Simulation Time (s) Objective function Before Control Clearing efficiency After Control (a) (b) Figure 22: Te impact of changing the main parameters on optimal solution and saturation. (a) Te impact on optimal solution. (b) Te impact on saturation. delay, clearing time, saturation, objective optimization average vehicle delay and clearing time for diferent function, and clearing efciency are analysed in this section. switching time cases are evaluated by VISSIM. First, the diferent switching times of reversible lane Figure 21(a) shows that when the opening time of the function increases depending on the diferent states of the reversible lane segment l is 148s, the opening time of the trafc fow. As shown in Figure 21, the comparison results of reversible lane segment l is 165s, and the opening time of Vehicle Delay (s) Saturation Clearing Time (s) 26 Journal of Advanced Transportation the reversible lane segment l is 189s. Te signal control found that the optimal control efect can be achieved by strategy of upstream and downstream intersections remains considering the two objective conditions of the shortest clearing time and the minimum average vehicle delay. Tis unchanged, and the optimal average vehicle delay is mini- mum. Meanwhile, compared with the results of diferent proposed approach can efectively utilize road spatiotem- average vehicle delays, the proposed model is found to be poral resources and fexibly and dynamically handle the efcient in reducing the average vehicle delay. Te con- trafc capacity at diferent time periods to alleviate trafc clusion further demonstrates the more obvious improve- congestion. ment efectiveness of the proposed model in implementing In addition to the above-mentioned studies, there are the reversible lane segmented clearing strategy. Figure 21(b) many research components that deserve further in- shows that if the optimal clearing time for the reversible lane vestigation: the complex setting variations of signal phases is used as an optimization solution, it can satisfy the min- have an impact on the performance of reversible lane op- imum clearing time requirement and reduce the average timization solution, and the infuence between diferent vehicle delay at the upstream and downstream intersections. types of trafc fow disturbances and trafc fow on various lane distribution types could also be incorporated into our Next, for comparison, Figure 22(a) illustrates that the proposed model can fnd the optimal control strategy that proposed model. balances the two requirements of the shortest clearing time and the smallest average vehicle delay. As shown in Data Availability Figure 22(b), before the reversible lane function switching All the data used to support the fndings of this study are control,thereisamismatchbetweentrafcdemandandlane included within the article. functionsettings,resultinginanimbalanceintrafccapacity and service level for the associated road links. After the reversible lane function switching control, the saturation of Conflicts of Interest each associated road link is stable within the range of Te authors declare that there are no conficts of interest. 0.55–0.71. At the same time, all associated road links are at service level B or C, which means that the spatial and Acknowledgments temporal resources of the road network are efectively uti- lized and the associated road links are not congested. Tis article is partially supported by the National Natural ScienceFoundationofChina(no.62262011)andtheNatural 8. Conclusions Science Foundation of Guangxi (no. 2021JJA170130). 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Journal
Journal of Advanced Transportation – Hindawi Publishing Corporation
Published: May 5, 2023