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Purpose – Freeway work zones have been trafﬁc bottlenecks that lead to a series of problems, including long travel time, high-speed variation, driver’s dissatisfaction and trafﬁc congestion. This research aims to develop a collaborative component of connected and automated vehicles (CAVs) to alleviate negative effects caused by work zones. Design/methodology/approach – The proposed cooperative component is incorporated in a cellular automata model to examine how and to what scale CAVs can help in improving trafﬁc operations. Findings – Simulation results show that, with the proposed component and penetration of CAVs, the average performances (travel time, safety and emission) can all be improved and the stochasticity of performances will be minimized too. Originality/value – To the best of the authors’ knowledge, this is the ﬁrst research that develops a cooperative mechanism of CAVs to improve work zone performance. Keywords Connected and automated vehicles, Cooperative cellular automata model, Microscopic trafﬁc ﬂow models, Work zone Paper type Research paper f = The trafﬁc ﬂow volume of light vehicles; Nomenclature f = The trafﬁc ﬂow volume of heavy vehicles; G = The front gap of vehicle n at time t; n,t L = The length of activity area; x = The longitudinal location of work zone; wz G = The front gap of vehicle n with front n,f,t x = The longitudinal location of left front n,t neighboring vehicle at time t; point on vehicle n at time t; P = The possibility of merging maneuver; merge y = The lateral location of left front point on n,t d = Maximum allowable deceleration of n,t vehicle n at time t; vehicle n at time t; L = The length of transition area; TTC = The time left to collision; and l = The length of vehicle n; D = The comfortable deceleration rate. comfort t = The headway of vehicle n at time t; n,t t = The interaction headway; acc a(V ) = The acceleration rate of vehicle n at time t; n,t 1. Introduction B = The brake status of vehicle n at time t; n,t A work zone is a partially closed road section due to periodic V = The velocity of vehicle n at time t; n,t maintenance, rehabilitation and reconstruction, bringing V = The speed limitation of vehicle n at time t; limit,n,t negative impacts on trafﬁc performance, such as, accident, G = The effective front gap of vehicle n at time t; eff,n,t congestion, long travel time and dissatisfaction among road G = The distance from the front bumper of wz,n,t vehicle n to work zone at time t; G = The safety distance; security © Yun Zou and Xiaobo Qu. Published in Journal of Intelligent and Connected p(f , f , L , L ) = The randomization probability within L H a t Vehicles. Published by Emerald Publishing Limited. This article is published work zone; under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen The current issue and full text archive of this journal is available on at http://creativecommons.org/licences/by/4.0/legalcode Emerald Insight at: www.emeraldinsight.com/2399-9802.htm The authors would like to thank University of Technology Sydney (UTS) for providing the scholarship. Journal of Intelligent and Connected Vehicles Received 20 November 2017 1/1 (2018) 1–14 Revised 18 February 2018 Emerald Publishing Limited [ISSN 2399-9802] [DOI 10.1108/JICV-11-2017-0001] Accepted 3 April 2018 1 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 users (Meng and Weng, 2011). The number of the through the penetration rate of CAVs goes up if a proper collaborative lanes declines; as a result, the trafﬁc capacity is signiﬁcantly mechanism is well designed. In this research, to bridge this reduced because of not only lane closure but also lane-changing void, we propose a cooperative cellular automata model activities (Laval and Daganzo, 2006; Qu et al.,2015). Vehicles (CCAM) based on the ICA model developed by Meng and on non-through lanes have to merge into through lanes; Weng (2011). otherwise, vehicles need to decelerate or even stop due to the The paper is organized as follows. In Section 2, the existence of the work zone; in other words, lane-changing conﬁguration of work zone from cellular automata model and a maneuvers become compulsory for those vehicles on non- study area on Paciﬁc Highway are demonstrated, followed by a through lanes. It makes the situation even worse when a large review of ICA model with an amendment at the end. Section 3 number of vehicles merge into a same target lane without describes the proposed microscopic trafﬁc ﬂow model for cooperation. Indeed, the presence of a work zone can increase CAVs with the cooperative component among vehicle not only the possibility of trafﬁc accidents happening but also illustrated in detail. Section 4 presents the performance the travel time due to the boost of density (Wang et al., 1996; indicators, including trafﬁc delay, safety and vehicle emission, Rouphail et al., 1988; Khattak et al.,2002; Garber and Zhao, under various penetration rates of CAVs. The last section 2002; Meng and Weng, 2011). concludes the paper. With the continuous increase of the travel demand, trafﬁc ﬂow becomes more unstable and vulnerable. During peak hours, even 2. Model development to simulate the movement a slight disturbance imposes high possibility of causing severe of the manually driven vehicle trafﬁc interruptions, as human drivers are more likely to make heterogeneous responses under these conditions (Qu et al., 2.1 Site description 2017). It has been well recognized that these human driver’s limit This research is established on the basis of a two-lane (in one and heterogeneity are essentially non-controllable in trafﬁc direction) freeway with a work zone at the Lane 1 starting from operations. Macadam (2003) proposed that human drivers show longitudinal location x to x as shown in Figure 1(a). The speed 1 4 obvious reaction delay in reacting to different indications, such as limit on this freeway is 110 km/h before vehicle entering advance merge indications and brake indications; moreover, the intensity warning zone that is from longitudinal location x to x .The 0 1 of an indication has to reach a threshold to be sensed by human speed limit turns to 80 km/h after reaching the advance warning drivers. In this regard, transportation researchers develop models sign which is located at x , and it then reduces to 60 km/h when and applications that are very robust to accommodate these limit vehicles enter the work zone. Figure 1(b) shows a photo of a work and heterogeneity, which lead to low capacity of our transport zone located on Paciﬁc Highway around Coolangatta airport, systems. With the advent of the connected and automated where the number of lanes drops from two to one because of a vehicles (CAV), the cooperation among vehicles becomes large scale of construction tasks as indicated by the circle. possible and, as a result, the limit and the heterogeneity can be controlled through developing a cooperative vehicle motion 2.2 Modiﬁed ICA model controlling system that is able to smooth our trafﬁc ﬂow To simulate the trafﬁc ﬂow dynamics of MVs, the ICA model is dynamics (Zhou et al., 2017a, 2017b). used with modiﬁcations to incentive and safety criteria. There are a few studies analyzing the inﬂuences caused by According to the ICA model, lanes are divided into cells of 0.5 work zones. Adeli and Jiang (2003) used a neuro-fuzzy logic m in length and 0.7 m in width. G denotes the front gap n,t model to estimate the work zone capacity on the freeway. Jiang between vehicle n and its leading vehicle n 1 or a work zone at and Adeli (2004a, b) used clustering-neural network models to time t; thus, for any two sequential vehicles: estimate the work zone capacity on the freeway with less than 10 per cent error and applied object-oriented model to estimate G ¼ x x l (1) n;t n1;t n;t n1 the freeway work zone capacity, as well as queue delay. Meng and Weng (2011) proposed an improved cellular automata Similarly, G denotes the front gap between vehicle n and wz,n,t (ICA) model to simulate the work zone trafﬁc ﬂow dynamics. the work zone ahead; thus: Weng and Meng (2014) proposed a methodology to estimate the rear-end crash possibility on the work zone merging area, G ¼ x x 1 y L =5 (2) wz;n;t wz n;t n;t t and it is found that this possibility increases as a result of late merging which is an instant merging maneuver with short front 2.2.1 Acceleration gap to the activity area in a work zone. Weng and Yan (2016) If time headway t is greater than interaction headway t or established a truncated lognormal distribution method to n,t acc neither vehicle n nor its leading vehicle n 1 has braked (B = 0 estimate the trafﬁc capacity due to the presence of work zone. To the best of our knowledge, there is no research that applies otherwise B = 1) during the previous simulation interval t 1, CAVs’ smoothing work zone trafﬁc ﬂow dynamics. CAVs are vehicle n accelerates with acceleration rate of a(V ). Namely, if n,t V W able to make immediate reaction to the deceleration of the (B =0 B =0) t > t : n,t–1 n–1,t–1 n,t acc leading vehicle; therefore, shorter headways are required. V ¼ min V 1aV ; V (3) ðÞ n;t n;t1 n;t limit;n;t Moreover, an embedded computer is able to compute the optimal safe speed as well as sliding distance to narrow the front Here, a(V ) is a function of current speed V , and the values gap, which is almost impossible for human drivers to calculate. n,t n,t As such, the average travel time to go through the work under different speeds are demonstrated in Table II. V limit,n,t zone and the speed oscillation are anticipated to be reduced as denotes the current speed limitation. 2 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 Figure 1 A plan view of freeway section around a work zone and a work zone on paciﬁc highway 2.2.2 Deceleration Table I Comparison between ICA and modiﬁed ICA Compared with the original CA model, the ICA model proposed a new concept that is effective front gap, taking the Variable ICA model Modifications in CCAM movement of vehicle n 1 into account: Randomization Both are determined by function that is illustrated in probability equation (6), and the parameters are demonstrated in G ¼ G 1 max 0; minðÞ V ; G G eff;n;t n;t n1;t1 n1;t security Table II. (4) Allowed 45 cell/s within a work Illustrated in Table III maximum zone 60 cell/s where the component min(V , G ) denotes the n–1,t–1 n–1,t speed elsewhere anticipated velocity of the leading vehicle. Acceleration Both are determined by brake status and headway If Geff < V , vehicle n decelerates to avoid rear-end crash n,t n,t Deceleration Determined by effective The effective front gap is with its leading vehicle or the merging vehicle. The target front gap modiﬁed as shown in velocity for the deceleration period is Geff instead of G , n,t n,t equation 14 which is too conservative, namely: Incentive Encouraged by a larger Encouraged by the criterion front gap distance to the work zone V ¼ minðÞ V ; G (5) n;t n;t eff;n;t Safety criterion Exclude the inﬂuence of Include the inﬂuence of the front gap with the the front gap with the If V < V , vehicle n decelerated with brake status n,t n,t–1 ALV ALV activated, namely, B =1. n,t 2.2.3 Randomization probability 0; if G > 8 V wz;n;t limit;n;t Randomization probability was ﬁrst proposed in Nagel– P ¼ (7) merge 1; if G 8 V wz;n;t limit;n;t Schrechenberg’s CA model to simulate the excessive brake and acceleration delay, which simulates the human limit as trafﬁc ﬂow forward (Nagel and Schreckenberg, 1992). Meng and 2.2.5 Safety criterion Weng (2010) pointed out that the randomization probability is As mentioned in the ICA model, the value of the gap between a function of trafﬁc ﬂow of light vehicles, trafﬁc ﬂow of heavy vehicle n and its back neighboring vehicle in the target lane vehicles, the length of activity area and the length of transition needs to be greater than the value of the maximum speed, area: namely, G > V (Meng and Weng, 2011). However, n,b,t limit,n,t this safety criterion excludes the gap between subject vehicle PfðÞ ; f ; L ; L¼ af 1 bf 1 cL 1 dL 1 e (6) L H a t L H a t and its anticipated leading vehicle (ALV), which is unrealistic. To avoid rear-end crash during merging period, a merging Parameters in equation (6) were calibrated by Meng and Weng vehicle has to maintain enough gap with its ALV; therefore, this (2010) using a trial-and-error method as demonstrated in gap needs to start from a reasonable value to accommodate the Table I. speed difference. 2.2.4 Incentive criterion We propose a new safety criterion in CCAM, that is, the front gap with the ALV from through lane has to be greater than In the ICA model, two incentive criteria are proposed, which R (V – V )1 G to accommodate the speed difference. are V > G ^ V > V and G < G . However, the n,t n,t n,t n–1,t n,t n,f,t c n,t alv,t security dominating incentive ahead of a work zone is the distance to the Here, R denotes the reaction time, and it is assumed to be 1 s. transition area. In that case, vehicles are encouraged to merge With regard to lateral speed, it is limited to be less than two cells into the through lane as G reaches a critical value. Hidas per second according ICA (Meng and Weng, 2011). However, wz,n,t (2002) proposed that lane-changing action becomes essential merging maneuver is assumed to be completed within 1 s in when the headway to a lane blockage is less than 8 s. Based on CCAM, which means vehicles are able to merge into the target this, we propose equation (7) to calculate the possibility of lane- lane during the next simulation interval as long as conditions changing action in this research: are fulﬁlled. To better compare the performances of ICA and 3 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 n1 1;t CCAM, MVs are assumed to be able to ﬁnish merging d ¼ V V 1 (10) ðÞ n;t n;t n1 1;t maneuver with 1 s as well, and the main differences between the ICA model and the CCAM are compared in Table I. Then d , the maximum disturbance that a car following n,t scenario can accommodate, can be calculated. This 3. Model development to simulate movements of disturbance can be used to determine the optimal speeds as connected and automated vehicles depicted in the following section. 3.1 Following model 3.1.2 Optimal speed increment 3.1.1 Maximum allowable deceleration As CAV n narrows the front gap with its leading vehicle n – 1, a In this model, we propose a concept named the maximum speed difference between these two successive vehicles are allowable deceleration. The maximum allowable deceleration computed as optimal speed increments; With these d is deﬁned as the maximum disturbance that a trafﬁc state n,t computations, the following vehicles are able to not only reduce could accommodate, and d denotes the disturbance that n,t the headway at highest efﬁciency but also avoid rear-end crash vehicle n suffers at time t.If V > V – d , there is a risk n11,t n,t n,t even when the leading vehicle brakes immediately. The worst that rear-end crash occurs between vehicle n and its following condition results from the leading CAV’s maximum vehicle; otherwise, a rear-end crash is able to be avoided. In that deceleration rate that is the lesser of aforementioned case, the maximum allowable deceleration needs to be disturbance d and the comfortable deceleration rate; thus, n–1,t considered only if V > V – d . n11,t n,t n,t the minimum possible stopping distance for vehicle n at the If both vehicles maintain the same speed for the following current simulation interval is G 1 V – min(d , n,t n–1,t n–1,t simulation intervals, the time to collision (TTC) under such D ). Here, V – min(d , D ) denotes the comfort n–1,t n–1,t comfort disturbance d is calculated as: n,t minimum possible velocity of the leading vehicle and the target nþ1;t velocity of vehicle n. The maximum velocity for vehicle n TTC ¼ (8) V ðÞ V d nþ1;t n;t n;t narrowing the gap is V 1 D , where D denotes the n–1,t n,t n,t optimal speed increment; thus, the equation can be written as: Let t be the threshold of time to collision. Only if nþ1;t 2 2 t, can a crash be avoided. To rearrange the V ðÞ V d ðÞ D V ðÞ V minðÞ d ; D nþ1;t n;t n;t n;t1 n1;t n1;t n1;t comfort equation: ¼ 2 G 1 V min d ; D D (11) ðÞ ðÞ n;t n1;t n1;t comfort comfort nþ1;t d ðÞ V V 1 (9) n;t n;t nþ1;t That is: Thus: qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ D ¼ 2 G 1 V min d ; D D 1 V min d ; D V (12) ðÞ ðÞ ðÞ ðÞ n;t n;t n1;t n1;t comfort comfort n1;t n1;t comfort n1;t 3.1.3 Effective gap the speed with its surrounding CAVs accurately with negligible Case 1: if leading vehicle is an MV delay. In addition, an updated effective gap is sent from the If the leading vehicle n 1 is an MV rather than a CAV, the leading CAV n 1 to the subject CAV n for the effective gap subject CAV n will not expect more information from its calculation, which enables two sequential CAVs to travel with a leading vehicle. Thus, a same equation from ICA model is used shorter gap so as to increase the trafﬁc capacity. to calculate the effective gap, namely: 3.1.4 Deceleration The velocity of a CAV is mainly determined by both the front G ¼ G 1 max 0; minðÞ V ; G G eff;n;t n;t n1;t1 n1;t security gap and the relative speed to its leading vehicle. CAVs will (13) brake if its leading vehicle decelerates and the current front gap is relatively small, namely, if B =1 ^ G < = aV , n–1,t n,t n,t –1 Case 2: if leading vehicle is a CAV B =1. Here a is calibrated to be 2 s. The assumption is that n,t If two successive vehicles are both CAVs, the effective gap of CAVs regard two sequential brakes that can potentially indicate the leading vehicle can be sent to its following vehicle; the congestion downstream. In that case, if G > 2 V , n,t n,t–1 therefore, we modiﬁed the effective gap as follow: there will be two possible scenarios depending the brake status. G ¼ G 1 maxf0; min V ; G G g ðÞ Scenario 1: if the leading vehicle’s brake status during next eff;n;t n;t n1;t eff;n1;t security simulation interval is not activated, G is deﬁnitely (14) n,t11 acceptable for the subject vehicle to keep its following action. Scenario 2: if the leading vehicle’s brake status during next In this equation (14), V is used to calculate the anticipated n–1,t simulation interval is activated, the front gap which is more speed of leading vehicle instead of V which is applied in n–1,t–1 equation (13), because the leading CAV n 1 is able to share than the value of V (thus the effective gap is deﬁnitely n,t–1 4 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 greater than the current velocity) is enough for a CAV maneuver is indicated by this CAV. Both ALV and AFV receive decelerate or even stop. the message of this merging maneuver. When CAV starts Trajectories extracted from simulations have proved that merging, ALV updates its maximum allowable deceleration by rear-end crash can be avoided when a is equal to two. taking G and V into account. At the meanwhile, AFL n,alv,t n,t If G < V , vehicle n decelerates to G avoid rear-end also updates its front gap to G , and the front gap of the n,afv,t eff,n,t n,t eff,n,t crash with its leading vehicle n 1, namely, V =min(V , CAV is equal to the lesser of G and G ; thus, maximum n,alv,t n,t n,t n,t allowable deceleration, optimal speed increments and effective G ); moreover, a CAV will decelerate if its surrounding eff,n,t gaps of these three vehicles are updated. vehicles need cooperation as illustrated in the lane-changing model. If V < V , vehicle n decelerates with brake status n,t n,t– 1 activated: (B = 1). n,t Table II Parameters in randomization probability equation 3.1.5 Narrowing the front gap Coefficient p p in out G is introduced into CCAM from the ICA model to security –4 –5 ensure that CAVs can decelerate to a safe speed before rear-end a –1.24 10 –6.80 10 –4 –4 crash happens with a relatively small deceleration rate for b –1.30 10 –1.28 10 –5 comfort consideration. If vehicle n has a greater velocity than its c –3.00 10 0 leading vehicle when the front gap is greater than the safety d 00 distance, the velocity of vehicle n is allowed to be greater than e 0.425 0.541 that of its leading vehicle by one speed increment; however, the Source: Meng and Weng (2011) velocity should be less than the effective gap to avoid a rear-end crash. Namely, If G > G ^ V > V ,: n,t security n,t – 1 n – 1,t V ¼ minðÞ V 1D ; G (15) n;t n1;t n;t eff ;n;t Table III General coefﬁcients At the same time, vehicle n can avoid the necessity of excessive Variable Condition MV CAV brakes. Acceleration V 11cell/s 44 n,t–1 If the velocity of vehicle n is less or equal to that of vehicle n-1 rate (cell/s ) when the front gap is greater than the safety distance, there are 11cell/s < V 33 n,t–1 two scenarios: 22cell/s 1 Scenario 1: when the brake status of vehicle n is not V > 22cell/s 22 n,t–1 activated, vehicle n accelerates by acceleration rate Deceleration 66 proposed in the ICA model; however, the speed difference rate (cell/s ) should not be greater than one speed increment, namely, Comfortable 6.8 6.8 If G > G ^ B = 1 ^ V V : n,t security n,t n,t – 1 n – 1,t deceleration V ¼ min V 1aVðÞ; V 1D (16) rate (cell/s ) n;t n;t1 n;t1 n1;t n;t Interaction 66 2 Scenario 2: when the brake status is activated, vehicle n headway (s) keeps a lesser speed of V and V , that is, if n,t–1 n–1,t–1 Safety distance 99 G > G ^ B =1 ^ V V : n,t security n,t n,t–1 n–1,t (cell) Maximum speed freeway Based on 60 (cell/s) equation (24) V ¼ min V ; V (17) ðÞ n;t n;t1 n1;t1 freeway work zone Based on 45 equation (24) 3.2 Lane-changing model Case 1: The ALV and the anticipated following vehicle (AFV) are both CAVs, where the ALV and AFV are the leading vehicle and the following vehicle after the subject vehicle merging into Table IV Coefﬁcients of VT-micro model the through lane. 2 3 Coefficients Constant Speed Speed Speed If G G ^ G G , vehicle n is able to n,alv,t security n,afv,t security start merging. Positive acceleration Otherwise, if G < G : Constant 0.87605 0.03627 0.00045 2.55E-06 n,alv,t security Acceleration 0.081221 0.009246 0.00046 4.00E-06 V ¼ V minðÞ D ; D ; d (18) n;t n;t1 n comfort n;t Acceleration 0.037039 0.00618 2.96E-04 1.86E-06 Acceleration 0.00255 0.000468 1.79E-05 3.86E-08 and if G < G : n,afv,t security Negative acceleration V ¼ V min D ; D ; d (19) ðÞ afv;t afv;t1 afv comfort afv;t Constant 0.75584 0.021283 0.00013 7.39E-07 Acceleration 0.00921 0.011364 0.0002 8.45E-07 Here, G and G indicate the gap with ALV and AFV, n,alv,t n,afv,t Acceleration 0.036223 0.000226 4.03E-08 3.5E-08 respectively. If a CAV receives a message of an oncoming work 3 Acceleration 0.003968 -9E-05 2.42E-06 1.6E-08 zone from the leading vehicles of its platoon, a merging 5 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 Figure 2 Deterministic indicators over penetration rate 6 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 Case 2: The AFV is a CAV; however, ALV is an MV. ALV may interrupt the merging maneuver of CAV, which If G G ^ G G , vehicle n is able to makes the waiting period longer. n,alv,t security n,afv,t security start merging. Case 3: The AFV is an MV, and the ALV is either an MV or a Otherwise, if G < G : CAV: n,alv,t security Scenario 1:If G G ^ G G 1 n,alv,t security n,afv,t security V ¼ V minðÞ D ; D ; d (20) n;t n;t1 n comfort n;t R (V – V ), vehicle n is able to start merging. c afv,t n,t and if G < G : n,afv,t security Scenario 2: If G < G , but the gap between ALV n,alv,t security and AFV can accommodate the merging vehicle, namely, V ¼ V min D ; D ; d (21) ðÞ afv;t afv;t1 afv comfort afv;t G 1 G 2 G 1R (V – V ), the n,alv,t n,afvt,t security c afv,t n,t A difference from Case 1 is that the ALVs are not indicated velocity of merging vehicle will be adjusted according to about this merging maneuver; thus, the deceleration of the an updated front gap that is G = min(G , G ). The n,t n,alv,t n,t Figure 3 Following front gap comparison based on trajectories Figure 4 Following model performance analysis based on trajectories 7 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 subject vehicle n will be able to merge whenever the velocity of the following vehicle of ALV, and D denotes the afvf condition mentioned in scenario is reached. deceleration rate (which is illustrated in the ICA model) of the Scenario 3: If G < G , and the gap between ALV and following vehicle of ALV. n,afv,t security AFV cannot accommodate the merging vehicle, namely, if To summarize, when all of these three vehicles are CAVs, a G 1 G < 2 G 1 R (V – V ), the subject well-developed collaborative strategy can guarantee a smooth n,alv,t n,afvt,t security c afv,r n,t vehicle n will have to expect to merge into a following gap, and: merging maneuver. While the ALV is the only MV among these three vehicles, the other two vehicles’ collaborations can still V ¼ V min D ; D ; d (22) ðÞ n;t n;t1 n comfort n;t perform well without the participation of the ALV. If the AFV In addition, if the AFV is followed by another CAV, this CAV is an MV, only a certain condition can encourage the subject will decelerate to prepare a gap for the subject vehicle n: V = CAV merge into the gap no matter ALV being CAV or not; afvf,t V – min(D , D , d ). Here, V denotes the otherwise, the collaboration will be currently terminated while afvf,t–1 afvf comfort afvf,t afvf,t Figure 5 Priority analysis during lane-changing period Figure 6 Cooperation between CAVs and MVs during lane-changing period 8 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 the subject CAV decelerates to look for collaborations with f V ¼ V K (23) following vehicles. K where V denotes the free ﬂow speed which is same as the 4. Case study maximum speed of CAVs, K denotes the jam density which is 4.1 Model calibration assumed to be 60 vehicles per kilometer and V and K denote According to trafﬁc fundamental diagram, the speed is limited the actual speed and actual density, respectively. With the by the current density which can be transferred into current decrease of the headway, drivers of MVs are encouraged to headway for individual vehicle. Greenshield’s model is applied drive slower than the actual speed limit to avoid rear-end to simulate the speed limit of MVs: crashes (Table II). Figure 7 Trajectories without CAV’s participation Figure 8 Trajectories with penetration rate being 100 per cent 9 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 4.2 Deterministic indicators by CAV can reduce the speed variation. In Figure 2(e), the time To precisely illustrate the relationship between deterministic period of stops shows a concave decrease trend as penetration indicators and penetration rate, data are collected from 14 increases, and there will not be any vehicle stopping as a result of simulations while the headways are initially 3 s. The merging maneuver when the penetration rate reach 98.5 per distributions of CAVs and MVs in both lanes are different cent. As shown in Figure 2(e),the y-axis denotes the total among these 14 simulations to cover all scenarios of emission during the whole time span, and emission continues cooperation; moreover, curve ﬁttings are done to demonstrate decreasing with the increase of percentage of CAVs involved. the relationship with equations. The trend is relatively steep when penetration rate rises from 50 These deterministic indicators are illustrated as followed: to 80 per cent, which means CAVs can contribute more to Travel time is an essential criterion to evaluate trafﬁc reduce emission if they are the majority of vehicles. When the performance according to trafﬁc jam economic cost (Zhou MV is the major part, CAVs have to give priorities to MVs et al., 2017a). The average travel time is the average frequently; thus, the collaboration that CAVs provided is duration when one vehicle travels from the 8,000th cells to relatively limited. the 10,000th cells. 4.2.1 Disaggregated trajectory analysis The excessive brake represents a disturbance caused by As shown in Figure 3, CAVs are able to tolerate much shorter aggressive merging maneuver downstream. We regarded headways than MVs, and the increase of density will not reduce comfortable deceleration rate that was suggested by the average speed as illustrated in Figure 2(a); in addition, American Association of State Highway and trajectories of CAVs demonstrate a better performance than Transportation Ofﬁcials (AASHTO) (2004) to be 6.8 cell/ those of MVs when reacting the leading vehicle’s deceleration, s as the threshold of excessive brake; thus, the number of excessive brake is the total number of times when the Figure 9 Massive illustration of average travel time over penetration deceleration rate is greater than 6.8 cell/s . rate Merge delay represents the time span that starts from when the merging indication is activated to whenever the merging maneuver is ﬁnished. Speed standard deviation is an indicator for speed variation which may cause passengers’ dissatisfaction, and the speed standard deviation for vehicle n is calculated within the equation: sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ V V n;t t¼1 SD ¼ (24) The time period of stops represents the cumulative time span when one vehicles stops (f). The quantity of emission is gained from VT-micro model that was proposed by Ahn et al. (2002), and has been widely used in trafﬁc studies (Xu et al., 2018; Meng et al., 2010): 3 3 > XX > e i j > L s a for a 0 i;j Figure 10 Massive illustration of emission over penetration rate i¼0 i¼0 lnðÞ MOE ¼ (25) 3 3 XX > e i j K s a for a < 0 i;j i¼0 i¼0 e e where L and K represent the coefﬁcients in this two i;j i;j scenarios, whereas a and s denote acceleration and speed, respectively, as shown in Table III (Table IV). As shown in Figure 2(a), a concave descending trend can be witnessed when penetration rate keeps increasing. The average travel time is reduced by 25 per cent when penetration rate reaches 34.1 per cent, and only half of the original travel time is needed if penetration rate reaches 62.25 per cent. In Figure 2(b), the number of excessive brake concavely decreases from 3,103 to 271 when penetration rate rises from 0 to 100 per cent. In Figure 2(c), the cumulative merge delay for all vehicles shows a non-monotonic decrease from around 3,561 s to 9 s. In Figure 2(d), the standard deviation decreases with the increase of penetration rate, and it proves that the collaboration provided 10 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 Figure 11 Velocities over locations around the work zone 11 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 Figure 11 12 Connected automated vehicles Journal of Intelligent and Connected Vehicles Yun Zou and Xiaobo Qu Volume 1 · Number 1 · 2018 · 1–14 and there is less acceleration delay when the leading vehicle zone, but this problem can be alleviated when there are more accelerates. This advantage is even clearer when CAVs are in a CAVs in the platoon, as shown in Figure 11(c). With the platoon as shown in Figure 4. While MVs suffer from the speed collaboration provided by CAVs, MVs suffer less disturbances, variations and over-braking, CAVs are able to keep a very stable as shown in sub-ﬁgure 1. Sub-ﬁgures 2 and 3 illustrate the trajectory, thus the speed variations due to headway variations velocities of two successive vehicles that consist of a leading are avoided. Consequently, not only is the average travel time CAV and a following MV, and the main differences are circled reduced, but also road users’ comfort is enhanced. in the ﬁgure. CAV has higher peak speed than MV at same As shown in Figures 5 and 6, dashed lines represent the condition because CAVs can handle shorter front gap after trajectories when vehicles are on Lane 1, whereas solid lines precise calculations. In that case, vehicles can narrow the front represent the trajectories when vehicles are on Lane 2, and the gaps effectively. When penetration rate reaches a relatively high green circles represent the moments when vehicles on Lane 1 level, most of disturbances are able to be avoided at high level merge into Lane 2. In Figure 5, a CAV is able to determine (80 per cent) of penetration rate. In Figure 11(d), sub-ﬁgures 1 whether to merge in front of or behind its adjacent vehicle and 2 and sub-ﬁgures 3 and 4 illustrate two pairs of successive according to their relative position; however, if an MV sends a vehicles both consisting of a leading MV and a following CAV. lane-changing indication to the anticipated following CAV, this The circled areas in sub-ﬁgures 3 and 4 illustrate the advantage CAV will give priority to the MV encouraging the MV to that CAVs can decelerate with a relatively small deceleration merge, which is clearly shown in Figure 6. rate to avoid passengers’ dissatisfaction while avoiding the rear- Figures 7 and 8 illustrate the trajectories when penetration end crash at the same time. Hence, disturbances cumulated rate are 0 and 100 per cent, respectively. When there is no CAV along the platoon can be effectively avoided; moreover, most of participates in the simulation, the merging maneuvers bring vehicles can accelerate to its original speed after leaving the severe disturbance to the following vhicles leading to wide work zone. moving jam; nevertheless, the cooperation among CAVs can to a large extent solve this probem, and it is shown in Figure 8. 5. Conclusion Work zones bring negative impact on freeway trafﬁc, and a 4.3 Probabilistic indicators number of problems emerge, such as long travel time, high Figure 9 shows the average travel time collected from more speed variation, driver’s dissatisfaction and trafﬁc congestion. than 2,000 simulations, and the average travel time variation In this research, for the ﬁrst time, we develop a CCAM decreases with the penetration rate, which means that the trafﬁc introducing a collaborative component of CAVs to simulate a condition can be predicted in a more deterministic manner with highway work zone system. Results are collected from different the increase of CAVs’ penetration rate. Similarly, a same trend penetration rates for comparison purposes, and positive effects appears on emission prediction as shown in Figure 10. The are demonstrated. The average travel time decreases by 25 and decreasing trend is similar with the one shown in Figure 8. 50 per cent when penetration rate reaches 34.1 and 62.25 per However, the variation keeps decreasing, and it is positively cent, respectively. The variability of these indicators also has related to penetration rate. It should be mentioned that both signiﬁcant decrease as the penetration rate of CAVs goes up. ﬁgures are depicted when initial headway is 3 s. We also extract some of the trajectories to analyze the reason for these improvements, and it clearly reveals how CAVs 4.4 Trafﬁc phase analysis harmonize trafﬁc ﬂow dynamics. Figure 11 demonstrates the velocities at different longitudinal positions around the work zone under CAVs’ penetration rates of (a) 0, (b) 30, (c) 50 and (d) 80 per cent, respectively. Their References sub-ﬁgures illustrate the velocities of the 50th vehicle and the Adeli, H. and Jiang, X. 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Journal of Intelligent and Connected Vehicles – Emerald Publishing
Published: Oct 2, 2018
Keywords: Connected and automated vehicles; Cooperative cellular automata model; Microscopic traffic flow models; Work zone
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