Traffic Flow Characteristics and Lane Use Strategies for Connected and Automated Vehicle in Mixed Traffic Conditions

T raffic Flo w Characteristics and Lane Use Strategies for Connected and Automated V ehicle in Mixed T raffic Conditions Zijia Zhong a, ∗ , Jo young Lee a , Liuh ui Zhao b a John A. R eif, Jr. Dep artment of Civil and Envir onmental Engine ering, New Jersey Institute of T e chnolo gy, Unite d States b Col le ge of Engine ering, Ge or gia Institute of T e chnolo gy, A tlanta, GA 30332 Abstract Managed lanes, s uc h as a dedicated lane for connected and automated v ehicles (CA Vs), can provide not only technological accommo dation but also desired market incentiv es for road users to adopt CA Vs in the near future. In this pap er, we inv estigate traffic flow characteristics with t w o configurations of the managed lane across different market p enetration rates and quantify the b enefits from the p ersp ec- tiv es of lane-level headwa y distribution, fuel consumption, communication density , and ov erall net work p erformance. The results highlight the b enefits of implemen ting managed lane strategies for CA Vs: 1) a dedicated CA V lane significantly extends the stable region of the speed-flow diagram and yields a greater road capacity . As the result shows, the highest flow rate is 3,400 v ehicles p er hour p er lane at 90% market p enetration rate with one CA V lane; 2) the concentration of CA Vs in one lane results in a narro wer headwa y distribution (with smaller standard deviation) even with partial market p enetration; 3) a dedicated CA V lane is also able to eliminate duel-b ell-shape distribution that is caused by the heterogeneous traffic flow; and 4) a dedicated CA V lane creates a more consistent CA V density , which facilitates comm unication activity and decreases the probability of pack et dropping. 1. In tro duction The mobilit y landscape is experiencing a paradigm shift due to rapid adv ancements of the information and vehicular technologies. Among them, the connected and automated vehicle (CA V) technologies ha ve b een contributing to the adoption of next-generation vehicles that are equipp ed w ith connectivity (i.e., connected vehicles) and/or automation (i.e. automated v ehicles). In spite of CA V’s immense b enefits and p otentials in reshaping the mobility landscap e, the adoption of CA Vs by consumers is still uncertain [ 1 ], although some low er-level v ehicle automation in the form of driver-assistance system has b een commercially av ailable. The near-term deploymen t of CA Vs is characterized b y mixed traffic conditions, where h uman-driven v ehicles (HVs) and CA Vs constantly in teract with each other. The p oten tial b enefits from CA Vs may b e offset by the interactions among differen t t yp es of v ehicles. F or example, the short following time gap (e.g., 0.6 s ) is only feasible when a CA V follows another CA V. T o ov ercome suc h shortcoming in near- term CA V deploymen t, managed lane strategies, suc h as CA V dedicated lane, is one of the promising solutions in order to facilitate the formation of the CA V strings. Practically , managed lane strategies are freew ay lanes that are set aside and op erated under v arious fixed and/or real-time strategies in resp onse to certain ob jectives, suc h as improving traffic op eration [ 2 ]. It is also an ticipated that managed lane strategies incentivize the adoption of CA V, just as they did for encouraging car-p o oling or lo w emission v ehicles. The goal of this study is to inv estigate the impact of different lane use strategies under mixed traffic conditions at v ehicle tra jectory- as well as lane-level. F or clarity , we refer mixed traffic condition to the condition that CA Vs and HVs op erate on the same roadwa y net work in the following discussions. The con tributions of the pap er include: 1. the analysis of CA V-enhanced traffic flow characteristics at the lane- and vehicle-lev el, ∗ Corresponding author: Zijia Zhong, zijia.zhong@njit.edu Please cite this article: Z. Zhong, J. Lee, and L. Zhao “T raffic flow characteristics and lane use strategies for connected and automated v ehicles in mixed traffic conditions”, J. Adv anced T ransp., vol 2021, doi: 10.1155/2021/8816540 Zhong et al. F ebruary 9, 2021 2. the in vestigation of traffic performance with gradual in tro duction of CA V plato ons under difference managed lane strategies, and 3. the implications of managed lane strategies from a dedicated short-range communication (DSRC) comm unication p erspective. The remainder of the pap er is organized as follows. Related work regarding the research of CA Vs in mixed traffic and managed lanes is review ed in Section 2 , follo w ed b y the ev aluation metho dology , includ- ing customized CA V mo dule and defined scenarios, in Section 3 . The sim ulation results are presented and discussed in Section 4 . Lastly , findings and recommendations are discussed in Section 5 . 2. Literature Review There hav e b een numerous studies on the implemen tation and ev aluation of CA Vs in v arious traffic settings. Aligning with our research topic, we fo cused our literature searc h on tw o key asp ects of CA V studies: 1) CA V ev aluation in mixed traffic conditions at netw ork level and 2) managed lane strategies for CA V. 2.1. CA V Evaluation in Mixe d T r affic Conditions Three main approaches hav e b een used to assess the b enefits of CA Vs: 1) analytical study , 2) simula- tion ev aluation, and 3) field test with equipp ed vehicles. On-road testing provides the utmost degree of realism with equipp ed automated driving systems (ADS) and real-world traffic environmen t. Ho wev er, the safety and efficiency issues for testing CA V on public roads ha ve b een the ma jor concern, esp ecially after several severe CA V-inv olv ed accidents in recent years. Due to safety , technological, and budgetary limitations, the scale of a CA V field test at curren t stage tends to be small (e.g., with a handful of CA Vs). As a result, the conclusions from these small-scale field te sts ma y not b e reliably generalized to a traffic flo w level. F urthermore, it was estimated by Kalra and Paddock that billions of kilometers of road test w ould b e required to ac hieve the desired lev el of confidence in terms of safet y of an ADS [ 3 ]. Th us, analytical and sim ulation approaches serve as tw o primary metho ds for ev aluating traffic flow impact of CA Vs. The ma jority of the analytical mo dels is based on macroscopic traffic flo w models and ma y exp erience difficult y in faithfully capturing the complex phenomena in transp ortation netw orks, such as lane drop. Smith et al. prop osed an analytical framew ork for assessing the benefits of CA V op erations [ 4 ]. The results indicated that CA Vs impro ved net work mobility performance, even with lo w MRP and no managed lane p olicies. Throughput without managed lanes increased by 4%, 10%, and 16% at the MPR of 10%, 20%, and 30%, resp ectiv ely . It w as also disco v ered that the managed lane p olicy facilitated homogeneous CA V traffic flow leading to more consistent and stable netw ork outputs. An analytical mo del for determining the optimal managed lane strategy w as prop osed in [ 5 ], where the maximum system throughput in a mixed traffic condition could b e calculated under the assumption of random vehicle distribution on a freew ay facility . Three types of headwa ys (i.e., conserv ative, neutral, and aggressive) were used in the mo del. W ang et al. prop osed a second-order traffic flow mo del for mixed traffic streams with HVs and A Vs. The authors found that the second-order model consistently outp erformed the first-order one in terms of the accuracy of traffic densit y when the v ariabilit y of the p enetration rate increases [ 6 ] . A t the corridor lev el, a capacity of 4,250 vphpl (v ehicle per hour p er lane) was observed in [ 7 ] on a 6-km high wa y segment with uniformly distributed ramps under full market p enetration of CA Vs. The study b y Shladov er et al. observed a pip eline capacit y of 3,600 at 90% MPR of CA Vs [ 8 ], where the pip eline capacit y refers to the throughput observ ed on a single-lane roadwa y without any in terference of lateral mo vemen ts [ 9 ]. Arnaout and Arnaout ev aluated CA Vs under mo derate, saturated, and ov er-saturated demand levels on a hypothetical 4-lane high wa y under different market p enetrations. They found that 9,400 v ehicles could b e served within an hour when the CA V MPR reached 40% [ 10 ]. Songchitruksa et al. assessed the net work p erformance with CA Vs on the 26-mile I-30 freewa y in Dallas, TX and found the highest throughput b eing 4,400 vph at 50% MPR [ 11 ] among four MPR scenarios (i.e., 10%, 30%, 50%, and 70%). Another study [ 12 ] also rev ealed that the mobility b enefits of CA V emerged at 30% MPR. Liu et al. inv estigated the b enefits of alleviating freewa y merge b ottlenec k and compared the p erfor- mance of CA CC with ACC under full mark et p enetration. The results show ed that CACC yielded a 50% reduction in fuel consumption (as estimated with the EP A MOVES mo del) while increasing corridor capacit y b y 49%, compared to the A CC scenario [ 13 ]. With a subsequent test on an 18-km segmen t of SR-99, the research team found that deploying v ehicle a wareness device (V AD)-equipp ed vehicles 2 along with managed lane strategies w as helpful in improving corridor-level traffic flo w under lo w and medium CA V mark et p enetrations [ 14 ]. Besides MO VES, comprehensiv e modal emission mo del (CMEM) [ 15 ], VT-Micro [ 16 ], the F uture Automotive Systems T echnology Simulator (F ASTSim)[ 17 ] are among the commonly used v ehicle emission mo dels in quantifying p otential en vironmental impact of deploying CA Vs. The p oten tial impact of the short follo wing time headw ay of CA Vs on HVs has also b een studied in previous studies. Among them, the K ONV OI pro ject found that the carry-o v er effect for CA CC driv ers in man ual driving after the disengagement of the CACC system [ 18 ]. In recent years, driving simulator has b een employ ed to study the b eha vioral adaptation of human drivers op erating in the vicinity of CA Vs. No wak o wski et al. found that test participan ts are lik ely to driv e under a shorter following distance in the presence of CACC plato ons in the adjacent lane [ 19 ]. A similar study w as conducted by Gouy et al. to inv estigate the b eha vioral adaptation of human drivers along a CACC plato on, in which t wo CACC plato on configurations were tested: 1) a 10-truc k plato on with 0.3-s intra-platoon headwa y and 2) a 3-truc k plato on with 1.4-s intra-platoon headw ay . It was found that a smaller av erage HV headwa y was observ ed in the first scenario, under whic h participants sp en t more time under a 1-s headwa y . Although suc h short headwa y was generally deemed unsafe in previous studies (e.g., [ 21 ]). 2.2. CA Vs and Manage d L anes Managed lanes ha ve b een in practice ov er the years to improv e target op eration ob jectives, suc h as 1) promoting the adaptation of environmen tally-friendly vehicles by offering priorit y usage to sp ecific tra vel lanes (e.g., the California Clean Air V ehicle Decal [ 22 ]), 2) encouraging car-p o oling by adopting high-o ccupancy v ehicle (HO V) lanes [ 23 ], and 3) p erforming active traffic management with the aid of high-occupancy toll (HOT) lanes [ 24 ]. a CA V lane is one v ariant of managed lane strategies that pro vides exclusive lane use privilege to CA Vs. Although managed lane strategies hav e b een widely applied to highw a y operation with successful cases, due to distinctiv e op erational characteristics of CA Vs, kno wledge learned from a conv en tional managed lane may not be directly transferable to the implemen tation of a CA V lane. The provision of a CA V-managed lane has t wo primary reasons. First, CA V-managed lanes can incen tivize the adaptation of CA Vs by offering priorit y usage to managed lanes, which typically provides b etter and more reliable trav el b ecause of activ e traffic management. More imp ortan tly and unique to CA Vs, CA V-managed lanes can pro vide accommodations for the underlying operational c haracteristics of CA Vs. A CA V is able to operate at a m uch closer headwa y than a human driver with the assistance of V2V wireless communication and the automated driving system (ADS) [ 25 , 26 ]. Hence, the necessary condition for realizing suc h a short follo wing headw a y is the a v ailabilit y of the v ehicle driving information of at least one of the predecessors on the same lane, i.e., through a CA V follo wing another CA V. Otherwise, the string stability of CA Vs cannot b e guaran teed [ 27 ], and the lack of thereof is termed as CA V degradation [ 28 ], whic h could potentially be a ma jor h urdle for CA Vs op erating in mixed traffic. A n umerical example b y W ang et al. has sho wed that the current technological maturity of CACC contributed negatively to the stabilit y of heterogeneous flow [ 28 ]. T o mitigate CA V degradation, ad ho c co ordination, lo cal coordination, and global co ordination are the three ma jor strategies that outline the organization of CA V plato ons [ 29 ]. Ad ho c coordination assumes that CA Vs arrive in random sequence and do not actively seek clustering opp ortunities in a traffic stream. By extension, the probability of driving around other C A Vs is highly correlated to MPR. On the contrary , CA Vs activ ely iden tify and approac h an existing CA V cluster (or other free- agen t CA Vs) to form a new cluster through lo cal co ordination, regardless of CA V MPRs. Finally , global coordination (a.k.a. end-to-end platooning) requires a high-lev el route planning and extensive comm unication to coordinate vehicles trav eling with the same origin-destination pair ev en before the CA Vs entering highw a y sections [ 30 ]. T o successfully form and main tain platoons, accurate and cost-effectiv e lo calization of CA Vs in a dynamic traffic environmen t remains one of the biggest c hallenges, esp ecially for lo cal co ordination [ 29 , 31 ]. In the presence of a CA V-managed lane, a higher concen tration of CA Vs facilitates lo cal coordination with muc h less stringent requirements on the accuracy of vehicle lo calization. In addition, the CA V- managed lane strategy aligns w ell with the three-stage deplo ymen t roadmap considering mark et diffusion and technological maturation for CA Vs [ 32 ]. In the first stage, the adoption of CA Vs is incentivized by allo wing the use of the managed lane free of charge. At this stage, the following headwa y of CA Vs on the managed lane may b e comparable to that has b een observ ed from HVs for safety reasons in a mixed traffic condition. In the second stage, a shorter following headwa y for CA Vs could b e implemented to further increase the carrying capacit y of the managed lane when the demand of CA Vs along with the 3 familiarit y of road users to CA Vs increases. In the third stage, when the CA Vs reach a critical level of MPR, high-p erformance driving enabled by the CA Vs can b e achiev ed due to homogeneous CA V traffic flo w on the managed lane. T o assess the impact of CA V-managed lane strategies, Zhang et al. compared the p erformance of a managed lane and general propose lanes (GPL) based on av erage sp eed, throughput, and tra vel time [ 33 ]. The results indicated that the sp eed impro vemen t in the managed lane was significant compared to that of GPLs. With 20% MPR, the laten t demand (the demand that cannot en ter the sim ulation net work due to congestion) decreased to zero. Inspired b y the fluid appro ximation of traffic, W right et al. prop osed an algorithm for sim ulating the wea ving activity at the interface of a managed lane and the adjacen t GPL at a macroscopic scale [ 34 ]. Chen et al. prop osed a time-dependent deplo ymen t framework that was formulated with a netw ork equilibrium mo del and a diffusion mo del. With the constraint of a giv en set of candidate lanes which corresp onds to the field condition, the so cial cost was minimized with the consideration of different MPR levels [ 35 ]. Zhong and Lee studied four managed lane strategies and compared the benefits for GPL and managed lane users in terms of mobility , safety , emission, and equity [ 36 ]. In freewa y settings, the authors recommended a 30% minimal MRP for deploying a CA V-managed lane to a void lane use imbalance that could degrade the p erformance [ 37 , 38 ]. Qom et al. prop osed a multi-resolution framew ork to study the mobility impact of CA V lanes. T raffic flo w-based static traffic assignment and the meso-scopic sim ulation-based dynamic traffic assignment w ere adapted in the bi-level framework. The former yielded the MPR-based trends, whereas the latter refined the trend based on traffic congestion. The results indicated that it was not b eneficial to provide toll incen tiv e for CA Vs at low er MPR due to the marginal increase in high wa y capacit y [ 39 ]. Ghiasi et al. proposed an analytical capacit y model for mixed traffic [ 40 ]. The mo del relied on the Marko v c hain representation of the spatial distribution of heterogeneous and sto c hastic headwa y . With the sufficien t and necessary condition of capacit y increase pro ven, the authors emphasized the imp ortance of quan titative analysis of the actual headwa y stetting. The introduction of a CA V lane to a signalized corridor was rep orted in [ 41 ]. Tw o configurations of a CA V lane, along with other managed lanes, w ere ev aluated. Due to the turning nature of an arterial, buffer zones were implemen ted where HVs are allow ed to temp orarily use the CA V lane for turning mov emen ts. P apadoulis et al. ev aluated the safet y impact of CA Vs using the Surrogate Safet y Assessmen t Mo del (SSAM) [ 42 ]. The time to collision (TTC) and the p ost encroachmen t time (PET) w ere adapted with safety thresholds of 1.5 s and 5 s, resp ectively . They observed substan tial safety b enefits in terms of reduction in traffic conflicts: 12-47% at 25% MPR to 90-94 % at 100% MPR. In [ 43 ], TTC w as also used to assess the safety conditions for HVs when CA V lo cal clustering strategy was emplo yed. Ali et al. found that drivers with adv anced traffic information enabled b y connectivity tend to wait longer and maintained a larger space on mandatory lane change (the communication dela y for lane merging assistance was unnoticeable when it was less than 1.5 s). Post-encroac hmen t time (PET) analysis also indicated impro ved trav el safety from CA V implementation [ 44 ]. 2.3. Summary The v ast ma jority of previous studies ev aluated the b enefits of CA Vs at an aggregated level with the emphasis of ov erall traffic improv emen t. Analytic mo dels are in macroscopic nature under ov erly ideal conditions, and they hav e difficulty in factoring in the stochastic nature of h uman driv ers in a mixed traffic environmen t. CA V-managed lane strategy could b e instrumental in the near-term deploymen t of CA Vs, but it is still an under-explored area, despite its increasing recognition. 3. Ev aluation F ramew ork and Exp erimen t Design This study fo cuses on analyzing mixed traffic flow c haracteristics at a corridor level considering differen t CA V MRPs and managed lane strategies. In this section, the integrated sim ulation test b ed, transp ortation netw ork, and simulation scenarios are discussed in detail. 3.1. CA V Behavior Mo del The PTV Vissim [ 45 ], a commercial-off-the-shelf microscopic simulation pack age, is chosen for the ev aluation. Vissim has b een widely adapted b y transp ortation practitioners and researchers, owing to its high-fidelit y simulation mec hanism and flexible mo dules. Although compared to other op en-source traffic simulators (e.g., SUMO), one reserv ation for Vissim b eing a commercial softw are is its close- sourced nature. As shown in T able 1 , a calibrated Wiedemann car-following model and the Enhanced In telligent Driver Mo del (E-IDM) [ 46 ] w ere used to mo del HVs and CA Vs, resp ectively . The intelligen t 4 driv er mo del (IDM) and its v ariants ha ve b een used to design the ACC/CA CC con troller that resem bles h uman-like car-following b eha viors [ 47 – 51 ]. As an improv ed iteration of the collision-free IDM [ 52 ], the E-IDM deals with CA V longitudinal maneuv er. The b eha vior mo del of the E-IDM is expressed in Eq. 1 , 2 , and 3 . T able 1: Differences b et ween HVs and CA Vs in the simulation model V ehicle Type Longitudinal Con trol DTG Sto c hasticit y HV W eidemann 99 1.4 s Y CA V E-IDM 0.6, 1.2 s N ¨ x = ( a [1 − ( ˙ x ˙ x des ) δ − ( s ∗ ( ˙ x, ˙ x lead ) s 0 )] if ¨ x I D M ≥ ¨ x C AH (1 − c ) ¨ x I D M + c [ ¨ x C AH + b · tanh ( ¨ x I DM − ¨ x C AH b )] otherwise (1) s ∗ ( ˙ x, ˙ x lead ) = s 0 + ˙ xT + ˙ x ( ˙ x − ˙ x lead ) 2 √ ab (2) ¨ x C AH = ( ˙ x 2 · min { ¨ x lead , ¨ x } ˙ x 2 lead − 2 x · min { ¨ x lead , ¨ x } if ˙ x lead ( ˙ x − ˙ x lead ) ≤ − 2 x · min { ¨ x lead , ¨ x } min { ¨ x lead , ¨ x } − ( ˙ x − ˙ x lead ) 2 Θ( ˙ x − ˙ x lead ) 2 x otherwise (3) where, a is the maximum acceleration; b is the desired deceleration; c is the co olness factor; δ is the free acceleration exp onen t; ˙ x is the current speed of the sub ject vehicle; ˙ x des is the desired sp eed, ˙ x lead is the sp eed of the lead vehicle; s 0 is the minimal distance; ¨ x is the acceleration of the sub ject v ehicle; ¨ x lead is the acceleration of the lead vehicle; ¨ x I D M is the acceleration calculated by the original IDM mo del [ 52 ]. The minimal distance can b e calculated as s ∗ ( ˙ x, ˙ x lead ) where T is the desired time gap; and ¨ x C AH is the acceleration calculated by the constant-acceleration heuristic (CAH) comp onen t, where Θ is the Hea viside step function that is used to eliminate the negative approaching rate of sub ject vehicle [ 46 ]. In this study , the E-IDM model is selected as the longitudinal con trol for the CA Vs. Although without built-in multi-an ticipative car-following function, as the literature shows, E-IDM is still a go od simple car-follo wing mo del for CA Vs, as the sto c hastic nature of human driving is remov ed (i.e., automation prop ert y), and the acceleration of the preceding vehicle is taken into account in the driving mo del (i.e., connectivit y prop ert y). As shown in T able 2 , all the parameters remain the same as those originally sp ecified in [ 46 ], with the exception of the desired time gap (DTG), which is defined with t wo v alues: 0.6 s and 1.2 s. The former DTG is used when the communication b etw een a preceding CA V and the sub ject CA V is successful, whereas the latter one is in effect when the communication failure occurs. The up dating frequency for the E-IDM mo del in Vissim is 10 Hz. The densit y of CA Vs whic h is used to calculate the communication activity is up dated at a 2-Hz frequency to reflect the traffic dynamic. Eac h transmission is assumed to hav e up to five attempts (four re-transmission). A t least one successful attempt is required for a transmission to b e considered successful, up on which the DTG is determined. T able 2: E-IDM V ehicle Control Parameters P arameter T intra T inter s 0 a b c θ ˙ x des v alue 0.6 s 1.2 s 1 m 2 m/s 2 2 m/s 2 0.99 4 105 k m/h T o implement these tw o car following mo dels in Vissim, the subset of the human driving b eha vior is realized by adjusting car-follo wing parameters of the Wiedemann car-following model, which is relativ ely straigh tforward. The E-IDM, on the other hand, is implemen ted via the external driv er model application programming in terface (API) and connected with Vissim through a dynamic link library (DLL). The DLL is inv ok ed in each simulation time step such that the default car-following b eha vior will b e ov erwritten for a sp ecified vehicle type. The DSR C wireless communication mo dule, discussed later in Section 3.2 , is also implemen ted in the API to achiev e a dynamic resp onse based on prev ailing traffic conditions. One of the most prominent features in CA V b ehavior modeling is the short time headwa y during car- follo wing, whic h is manifested b y sev eral k ey differences b etw een a CA V and a HV. First, the sto c hasticity of the CA Vs is significantly low er than that of h uman drivers. This is enabled b y the on-b oard sensors that are able to con tinuously and accurately perceive the surrounding en vironmen t. Ho wev er, the stochaticit y cannot be completely eliminated due to sensor noise and comm unication dela y/error. Second, a CA V has minimal reaction time due to its algorithmic decision making pro cess and computational p o wer. P ast 5 studies hav e already iden tified that the impact of the reaction time of human driv ers in v arious traffic phenomena, including capacit y drop [ 53 ] and flo w stabilit y [ 49 ], whereas driving sim ulation tests revealed that the information augmen ted by connectivity could decrease the reaction time for drivers [ 54 ]. In addition, h uman factor plays a crucial role in the resumption of control of a CA V when an ADS exits its op erational domain (e.g., high risk of collision, sensor failure, communication interference). Quan titative evidence regarding the transition of control from traffic psychology or human-mac hine in teractions is still limited [ 55 ], though few frameworks hav e b een prop osed to sim ulate human b eha vior endogenously [ 56 , 57 ]. F or example, the prosp ect theory w as used to mo del the risk and human p erception [ 58 , 59 ]. The Risk Allostasis Theory [ 60 ] was adopted for mo deling relationship b etw een cognitive pro cessing of information and physical p erformance. The T ask C apacit y Interface [ 61 ] w as employ ed by Saifuzzaman et al. for quan tifying situational aw areness of a driv er. Calv ert and v an Arem developed a framework that encompasses the driving task demand and driver task saturation [ 55 ]. The framew ork’s main goal is to assess the p erformance impact during the tran- sition of control for A Vs. The total task demand, situational aw areness, and reaction time during the transition of con trol from A Vs was explored. The framework show ed promising capability in capturing the interactiv e effects of h umans with lo wer level A Vs. How ev er, empirical evidence is still needed to relax the assumptions used in the framew ork from not only the cognitiv e p oin t of view, but also from v ehicle dynamics and inter-v ehicle interactions. Another human factor is driver compliance to the ADS. Since in lo wer or medium lev el of automa- tion, the driver is ultimately resp onsible for his or her vehicle, whic h means ov erwriting, when deemed necessary , is p ossible b y the human driv er. This control authorit y , in extreme cases, could cancel out the b enefits promised by the CA V tec hnologies. In a recen t study [ 59 ], Sharma et al. employ ed the prosp ect theory to mo del driver decision-making mechanisms including irrational ones, and captured the negative relationship b et w een headwa y and compliance decision by a driver. In this study , w e represen t the differences of a CA V and a HV with different desired time headw ays through separate car following mo dels, with the following assumptions made for CA Vs: 1) no error for the on-b oard sensors and the vehicle controller, i.e., perfect perception; 2) no h uman factor mo deling p ertaining to the transition of authority; and 3) no b ehavior adaptation for CA Vs for non-CA V drivers. 3.2. Wir eless Communic ation Mo del In an early study , we implemen ted a pack et-lev el comm unication mo dule through Vissim API [ 38 ]. Similar adaptations for the mo del were also found in previous studies [ 11 , 38 , 62 ]. The analytical mo del [ 63 ] was developed from ns-2, an empirical pac ket-lev el netw ork simulator that returns the probability of one-hop broadcast reception of basic safet y message (BSM) under IEEE 802.11p, an approv ed amend- men t tailored to wireless access in vehicular environmen t (W A VE) in the 802.11 family proto col. The mo del uses the concept of communication densit y lev el, a metric repres en ting channel load in vehicular comm unication in the form of the sensible transmission p er unit of time and p er unit of the road [ 64 ]. The data reception rate is determined jointly by comm unication density level and transmission p o w er. An illustration for the reception probability is sho wn in App endix B . Note that this comm unication mo del only p ertains to the physical lay er of the DSRC communication (e.g., no MA C lay er dela y). P r ( x, δ , ϕ, f ) = e − 3( x/ϕ ) 2  1 + 4 X i =1 h i ( ξ , ϕ )( x ϕ ) i  ξ = δ · ϕ · f (4) where, h i ( ξ , ϕ ) is the tw o-dimensional p olynomial of fourth-degree for all curving fitting parameters [ 65 ], which is also shown in App endix B ; ξ is comm unication density , even ts/s/km; and ϕ is the transmission p o w er, m; δ is vehicle p er kilometer that p eriodically broadcast messages, veh/km; and f is transmission rate, Hz. 3.3. T r ansp ortation Network A 9.3-km 4-lane h yp othetical netw ork was constructed in Vissim with t wo in terchanges lo cated at mile mark er 2 (km) and 6 (km) resp ectiv ely . An abstract geometry of the netw ork along with vehicle demand of the origins and destination is shown in Figure 1 . The primary reason for using a simply syn thetic netw ork is to limit v ariables for the simulation. Note that the driving b eha vior parameters for the Wiedemann car-following mo del (for HVs) is the same as in previous studies [ 37 , 43 , 66 , 67 ], which represen ts a subset of the calibrated driving behavior in the I-66 segmen t in northern Virginia. The demand originated on the mainline is delib erately set higher than usual to create a congested netw ork. 6 The sp eed limit for the mainline of the netw ork is set as 120 k m/h . Three data collectors are placed at “C1”, “C2”, and “C3” lo cations. Figure 1: Network geometry and demand 3.4. Manage d L ane Sc enarios Three cases of CA V lanes, as shown in T able 3 , are implemented in the net work: • No managed lane (NML) : This scenario serves as the base condition of the study . There is no priorit y lane use for CA Vs, and they are mixed with HVs throughout the netw ork; • One CA V lane (CA V-1) : In this strategy , one CA V lane is implemented in the left-most lane (the fourth lane from the righ t); • Tw o CA V lanes (CA V-2) : An additional CA V lane is added to the CA V-1 case, making tw o CA V lanes av ailable at the leftmost and the second leftmost lane in the roadw ay segmen t. It aims to in vestigate the duel managed lane configuration. As revealed in previous studies [ 32 , 33 , 68 , 69 ], a managed lane ma y ha v e a detrimental effect on traffic p erformance if implemented prematurely , i.e., usually with an MPR less than 30%. Therefore in this study , we set CA V MPRs for “CA V-1” to start from 30%. With the same logic, the “CA V-2” cases start with 40% to co ver certain transition MPR, since the linear extrap olation may not hold. T able 3: Managed Lane Ev aluation Plan P olicy No Managed Lane Managed Lane #1 Managed Lane #2 ID NML CA V-1 CA V-2 1st Lane HV + CA V HV + CA V HV + CA V 2nd Lane HV + CA V HV + CA V HV + CA V 3rd Lane HV + CA V HV + CA V CA V 4th Lane HV + CA V CA V CA V MPR 0% - 100% 30% - 100% 40% - 100% 4. Results and Analysis Fiv e replications are run for eac h combination of managed lane polic ies and MPRs. Aggregated data are collected at 5-min in terv als, and the ra w data are collected at eac h sim ulation time step. The analysis is performed on four aspects: 1) traffic flo w c haracteristics, 2) headw ay distribution, 3) fuel consumption, 4) wireless comm unication, and 5) ov erall net work p erformance. 4.1. T r affic Flow Char acteristic Figure 2 exhibits the speed-flow c haracteristics of the sim ulation scenarios ha ving 40% MPR and ab o v e. The plot is color-coded by trav el lanes with index “1” representing the rightmost lane, and “4” the leftmost. The sp eed-flo w diagram is comprised of a stable region and a unstable (congested) region, separated by the optimum (maximum) flo w. Several distinctive patterns can b e observed. First, regardless of the managed lane strategy , the sample p oin ts b ecome more concentrated as the MPR 7 Figure 2: Sp eed-flow curves increases, with the disapp earance of the congested region typically found in the low er speed region. Second, the CA V lane has a distinct pattern compared to the GPLs. Such pattern is most apparent in CA V-1, where the traffic samples on the leftmost lane (CA V lane) shift to the right along the flo w axis. The congested region disapp ears when MPR reaches 70% in the CA V-1 case for all of the lanes. The impro vemen t for the GPs is due to a higher carrying capacit y of the CA V lane, whic h results in less traffic on the GPLs. The homogeneity of the CA V traffic is the primary factor in realizing the mobilit y b enefit of CA Vs: in NML cases, the sample p oin ts from difference lanes are evenly distributed, in contrast to managed lane cases. F or the CA V-2 case, the separation of the CA V lanes (leftmost and the second leftmost) started to show at 70% MPR. At full p enetration (100%), the traffic patterns are very similar, as the managed lane b ecomes irrelev an t. 4.2. He adway Distribution The simulation collects raw data from the data collector, an equiv alen t of real-world detectors (e.g., lo op detectors, video cameras, microw a ve sensors). By analyzing the high-resolution raw data (collected ev ery 0.1 s), the headwa y distribution in CA V lanes can b e obtained. Recall that the collectors are placed in three sections of the roadw ay segment, as shown in Figure 1 . The cumulativ e probabilit y function (CDF) curves are display ed in Figure 3 . The v ertical lines in the figure are the headwa ys when 100% cumulativ e probability is reac hed. The slop e of the CDF indicates the lev el of concentration of the samples within a distribution. In NML cases, t w o types of tipping p oin ts exist: the one at lo wer headwa y resulted from a high MPR and the one with higher headwa y observed at a lo w MPR (b elo w 40%). F or CA V-1, the pattern for CDF at 30% and 40% is transformed to the pattern observed at high MPRs. With 2 CA V lanes, the CDF increases gradually in the mid-range MPR (40% to 60%) b ecause of under-saturation on the CA V lanes, as illustrated in the CDF on the 3rd and 4th lanes. Such under-saturation situation is alleviated when the MPR reac hes 70%. A similar pattern in CDFs is observed at a high MPR range (i.e., 80% to 90%) regardless of the managed lane strategies, indicating a high concen tration of samples with headwa y ab o v e 1 s. Tw o-sample Kolmogorov-Smirno v (K-S) test is adopted to analyze the CDFs to chec k whether tw o random samples are from the same p opulation [ 70 ]. It is a non-parametric test where no assumption is made regarding the distribution of the v ariables [ 71 ]. The null h yp othesis ( H 0 ) of the tw o-sample K-S test is that the tw o sample sets are from the same contin uous distribution. Nearly all the CDFs in the pairwise comparison rejects the null h yp othesis with a low p-v alue at the 0.05 significance level, with the exception of the comparison of 40% and 50% in NML. Figure 4 is a heatmap that shows the pairwise K-S statistic that represen ts the supremum of the tw o tested empirical CDFs. The denser the color, the higher the difference in cum ulative probability b et ween tw o comparing scenarios. The a v erage headwa y for HVs and CA Vs in ev ery tra vel lane is sho wn in Figure 5 . The row represen ts the v ehicle types, whereas the column represents the trav el lane. Recall that the 4th lane is the le ftmost lane. F or HVs, their av eraged headwa y decreases as the MPR increases in CA V-1 and CA V-2 cases. While the headwa y also decreases in the NML case, it is at a lesser rate. When it comes to CA Vs, the decreasing rate in CA V-2 is greater than that in CA V-1 or NML. The mean headwa y is around 4 s in CA V-2 case when the MPR is low or in mid-range due to low lane utilization in the CA V lanes. The 8 Figure 3: CDF for headwa y distribution among tra vel lanes Figure 4: K-S statistics for CDF comparison a verage headwa y in CA V-2 case reaches a comparable level to its counterparts at 70% MPR, which is the deflection p oin t. The low est mean headwa y achiev ed among all scenarios is observed at 70% MPR in CA V-1 case for CA Vs, which corresp onds to the maxim um capacity with all other factors being equal. Lastly , the headwa y trend for CA Vs remains a similar pattern across four trav el lanes in the NML case, since CA Vs are uniformly distributed across all lanes. Figure 6 shows the comparison of headw ay distributions in the leftmost lane among three managed lane scenarios under different MPRs. In the 40% to 70% MPR range, it is shown that implementing a managed lane for CA Vs clearly shifts the distribution to the left-hand side, which represents smaller headw ays. The distributions of headwa y collected for either CA V-1 or CA V-2 b ecome “narrow er” (with less standard deviation), as the MPR increases from 40% to 70%. The highest bin of the histogram for b oth CA V-1 and CA V-2 cases is 1 s - 1.2 s when the MPR is b elo w 50%. When the MPR is higher than 50%, the highest bin of the histogram shifts to 0.8 s - 1 s. In comparison, the NML case do es not exhibit 9 Figure 5: Average headwa y suc h a concentration pattern as the MPR increases. The result indicates that a homogeneous traffic flo w comprised of only CA Vs is able to realize the short-headwa y b enefits from deploying CA Vs. (a) 40% MPR (b) 50% MPR (c) 60% MPR (d) 70% MPR Figure 6: Headway distributions in the leftmost lane 4.3. F uel Consumption The VT-Micro mo del [ 16 ], an individual v ehicle and op eration-lev el emission mo del, is adopted to calculate the instan taneous fuel consumption rate. The inputs for the VT-Micro model are instan taneous v ehicle sp eed and acceleration, and the output is the second-by-second fuel consumption rate, as shown in Equation 5 , where ˙ x is the instantaneous sp eed, ¨ x is instantaneous acceleration, L e i,j and M e i,j are regression co efficien ts for emission and fuel consumption at sp eed p o wer i and acceleration pow er j , resp ectiv ely . f ( ˙ x, ¨ x ) =    exp  P 3 i =0 P 3 j =0 ( L e i,j · ˙ x i · ¨ x j )  for ¨ x ≥ 0 exp  P 3 i =0 P 3 j =0 ( M e i,j · ˙ x i · ¨ x j )  for ¨ x < 0 (5) The v ehicle data was derived from the raw data from the detectors in three lo cations (mark ed in Figure 1 ). The result for the fuel consumption is plotted in Figure 7 , which shows t wo distinctive patterns for the GPLs and the managed lane. The concentration of fuel consumption is within 5 ml /s 10 to 10 ml/s for lanes that allows HV op eration (i.e., mixed traffic), when the MPR for CA Vs is equal or less than 60%. When the MPR rises to ab ov e 60%, the instantaneous fuel consumption shifts to a low er v alues with a “narrow er” slop e: higher concentration b etw een 5 ml /s and 7 ml /s . Figure 7: Instantaneous F uel Consumption for All V ehicles W e then isolate the CDF curv e for both CA Vs and HVs, when they op erate on the leftmost lane under homogeneous flow condition. More sp ecifically , the separated CDF curves represent the observ ations of HVs from the 0% MPR in NML case and the observ ations for CA Vs from the 100% MPR for CA V-1 case. The CDF curves in Figure 7 exhibit tw o different patterns for CA Vs and HVs. The former with 60% of the observ ations fall b elo w 4 ml/s , whereas the latter with 60% of the observ ations b elo w 12 ml/s with a wider spread. The wider spread for HVs is probably caused by the sto c hastic nature of h uman driv ers (which is simulated by the Wiedemann model). Hence the mixed traffic condition is comprised of t wo comp eting flows that excreting their influence. In the GPLs, the MPR pla ys as an indicator for the dominance of each traffic flo w. The higher the MPR, the closer the CDF curves approac h the pattern of managed lane that is used b y CA V exclusively . In the managed lane, the CA V traffic is the sole dominating traffic. Therefore, the fuel consumption curv e exhibits only CA V traffic characteristics, regardless of the MPR. W e include the fuel consumption rate CDF curves for HVs and CA Vs in App endix I I (Figures C.2 and C.3 ) - both figures demonstrate the shift to wards CA V fuel consumption CDF pattern as the MPR grows. (a) vehicle density (b) pack et reception rate Figure 8: V2V communication p erformance measure 4.4. Wir eless Communic ation Figure 8 (a) sho ws the maximum and the av erage density for instances of V2V comm unication among three managed lane p olicies. Recall the DSRC communication mo del only deals with the physical la yer. While the transmission density increases as the MPR increases, the maximum density in NML is higher 11 than CA V-1 and CA V-2, b ecause the CA V plato ons were brok en do wn by certain HVs which are suscep- tible to sho c kwa v es. As such, the traffic flo w is compressed, pro ducing a higher traffic density and th us higher transmission density . With the aid of CA V lane, the communication densit y is thus main tained at a low er level. In a CA V lane, the CA Vs distribute longitudinally on the managed lane. The NML, in comparison with tw o managed lane cases, is more likely to generated p ock ets of traffic with CA Vs across m ultiple lanes, which could result in lo calized higher transmission activity . The probability of successful reception of BSM from a leading vehicle to a sub ject vehicle is shown in Figure 8 (b). The probability curves under CA V-1 and CA V-2 scenarios are in close proximit y to each other and they are sho wing the same trend. The maximum difference b et w een these tw o curv es is 0.04 at 90% MPR. The probability of successful communication of NML at high MPR range (60% to 90%) is consisten tly lo wer than those of CA V-1 and CA V-2. This is caused by the compression of traffic flow b y lo calized sho c kwa v es. There is an ov erall decreasing trend of the probability as the MPR increases, but still remains a successful rate of 94% and ab o v e. 4.5. Network Performanc e The measures used in this section gauges the ov erall p erformance of the simulation netw ork at an aggregated level. The throughput represents the total num ber of v ehicles that ha ve arriv ed at their destinations, sho wn in Figure 9 . As men tioned before, the netw ork was configured with a higher than usual demand. With a 10,000-vph demand for a four-lane highw a y , the netw ork was only able to pro cess 6,500 vph in the absence of CA Vs. Under the NML scenario, as the MPR of CA Vs increases, so do es the netw ork throughput. The throughput reaches approximately 8,000 vph with 40% and 50% MPRs. Ho wev er, at 60% MPR, the net w ork throughput is bo osted again and maintains at the same level at 9,600 vph when the MPR is ab o v e 70%. The throughput in CA V-1 case b egins to outp erform the NML case at MPR 50% and keeps increasing to 9700 vph at 70% MPR, where the throughput starts leveling in spite of the increase in MPR. F or the CA V-2 policy , the system throughput only reaches the same lev el of the tw o counterparts at 70% MPR due to under-utilization of CA V lanes with low MRPs. Figure 9: Network throughput The av erage delay experienced by vehicles (plotted in Figure B.1 (a)) within the netw ork is calculated b y dividing the total delay b y the sum of the v ehicles within the netw ork and the vehicles that ha ve exited the netw ork. F or three strategies, the av erage delay starts to decrease as the throughput levels off: at 60% for NML and CA V-1, and at 70 % for CA V-2. Such seemingly counter-in tuitiv e phenomena could b e explained by taking into accoun t the av erage sp eed, whic h is sho wn in Figure B.1 (b): when the throughput is in a graduate increase as the MPR go es un til 60%, the av erage sp eed exhibits a decreasing trend, which is in an inv erse relationship with vehicle delay . This trend is in agreement with the sp eed-flo w fundamental diagram. 12 (a) av erage delay (b) av erage sp eed Figure 10: Average Sp eed and Delay 5. Discussion and Conclusions In this section, we highlight the findings from the previous section and discuss the study in a b oarder con text. 5.1. Summary The analysis results indicate that the introduction of CA V could increase the throughput of the ov erall system, even when no managed lane p olicy is in place. The congestion region in the sp eed-flo w diagram disapp ears as the MPR of the CA Vs increases. This is an indication of the improv ement of roadw a y capacit y owing to CA Vs, whic h is consistent with the findings of previous studies. More imp ortan tly , the congestion region first disapp ears in the CA V lane in CA V-1 case, illustrating that the homogeneity of CA V traffic results in a more stable traffic flow with a high throughput. A CA V lane, with an MPR of as low as 40%, is able to accommo date more traffic compared to a GP lane and it helps to alleviate the ov erall congestion of the netw ork. The a verage vehicle delay exhibits a decreasing trend, even after the netw ork throughput levels after 70% MPR. This is an indicator that the netw ork is able to carry additional traffic than the high demand sp ecified in Fig. 1 . The individual headwa ys among consecutiv e vehicles are measured for each lane. F rom the headwa y distribution, one can not only measure the compactness of the traffic but also the stability of the traffic flo w. Both HVs and CA Vs ha ve a predominate headwa y as sho wn in T able 1 . In a heterogeneous traffic flow, tw o spikes with different tipping p oin ts can b e observ ed in the headw ay CDF curve. Each segmen ts indicates a high concen tration for the headw ay samples. One is for the following headw a y samples observed on HVs, and the other is for the headw ay samples for CA Vs. With traffic homogeneit y on the CA V lane, there is only one spike on the CDF curves. The magnitude of the spike also dep ends on the lane o ccupancy , as evidenced b y the comparison of CA V-1 and CA V-2 at the same MPR. The t wo-spik e pattern remains even at high-range MPR (i.e., 60-80%) in the absence of CA V lane (the NML case). The VT-Micro model, which pro duces instan taneous fuel consumption for individual v ehicles, w as emplo yed to estimate the en vironmental impact of the CA V lane. The vehicle speed and acceleration w as collected as inputs and the relativ e fuel consumption, instead of the absolute one, is examined. Again, distinct patterns for a GPL and a CA V lane were observ ed. The av erage instantaneous fuel consumption for CA V lane has a narrow er distribution. Lastly , the DSRC communication was measured using an analytical comm unication mo del that is deriv ed from a pac k age-lev el netw ork simulator. It simulates the physical la y er of the DSR C communica- tion that is an integral element of CA Vs. W e found a low er communication density in CA V lane, as the CA Vs were more ev enly distributed longitudinally . A low er communication density indicates a less con- gested communication channel, whic h increases the p erformance of the V2V communication. Compared to CA V-1 and CA V-2 scenarios, it is more likely under NML scenario to generate p o c kets of traffic with CA Vs across m ultiple lanes, whic h could introduce higher lo calized transmission activit y and increase the loss of BSM pac kets. The ov erall results show that a single CA V lane in a four-lane high wa y netw ork is able to pro vide the necessary technical accommo dation efficiently in the mixed traffic conditions with a wide range of MPR. A CA V dedicated lane is helpful to guarantee the b enefits of CA Vs, as it creates a homogeneous CA V flo w. Implementing t w o CA V lanes, how ever, ma y adversely affect the o verall traffic, esp ecially when the MPR of CA V do es not warran t an additional CA V lane. 13 5.2. Limitations While the paper demonstrates the b enefits of managed lane for CA V at lane- and vehicle- lev els, w e should note that there are limitations in this study and the b enefits are realized in a con trolled en vironment under certain assumptions. First of all, although the Wiedemann mo del is b ehaviorally sound and has b een adopted by numerous researchers for simulating human drivers, the complexit y of a h uman driv ers under dynamic traffic conditions is difficult, if p ossible at all, to be captured b y sim ulation mo dels. In addition, the b eha vioral adaption for human driv ers in the presence of CA V is not kno wn yet, due to the lack of empirical evidence in the public domain. Preliminary results revealed that a smaller time headwa y w as adopted by a HV when driving along side with closed plato oned CA Vs [ 20 ]. Note that the Wiedemann driv er b eha vior parameters were calibrated using field data where CA Vs hav e not b een deplo yed on the roadwa y yet. The calibrated parameters represents a subset of the driving p opulation, and they may not directly transferable to other driving conditions or demographics. The E-IDM, while b eing widely adopted, do es not contain the multi-an ticipativ e car-following feature, which has b een promoted as one of the crucial feature enabled by V2V communication. Therefore, the p erformance of the CA Vs are exp ected to b e more conserv ativ e. Like many existing CA V car-following mo dels, the E-IDM do es not factor in the asp ects of human factor that is an ticipated to b e more pronounced in the lo wer levels of automation. In addition, there are several salien t issues regarding the lo w level automation and its mo deling as w ell. F or a CA V, the drivers’ acceptance of short following headwa y (e.g., 0.6 s) is still an op en question [ 25 ], given that the short following headwa y is technologically attainable. It is reasonable to exp ect that the acceptance of extremely short headwa y would b e low initially , although it will gradually increase as CA V penetration increases. The pace of adaption, though, is largely dep ending of the level of confidence to the ADS from human driv ers. The level of compliance from drivers (in the absence of automation) is also an imp ortan t factor in harnessing rich information brough t b y the connectivity . The lay er of driv er sto catistcit y in reacting to traffic information remains. In the extreme case, a complete disregard of useful information could negate the b enefits of connectivity . Another crucial issue is the transition of control from the ADS back to the human driver. As p er the definition of vehicle automation by the SAE, the Level 3 automation (and b elo w) requires a fallback receptiv e driv er when the ADS exits its designed op erational domain. As studies ha ve sho wn, such fallbac k pro cess is wa y more complicated than merely re-taking the steering wheel. First, a driver needs to regain situational aw areness of the traffic environmen t from the disengagement of driving. The surge in cognitive demand during the initial p eriod of re-engaging in driving tasks could result in deterioration in driv er’s p erformance (e.g, increased reaction time, inadequate situational aw areness). This asp ect rarely exists in curren t CA V mo dels, and muc h likely it will require an endogenous cognitive models that is able to take in to account the driving task demand and the cognitive capacity of human drivers [ 55 ]. Therefore, the human-mac hine interfacing is seldom captured in current simulation mo del, including the one used in this study . 5.3. F utur e R ese ar ch The future research would fo cus on relaxing the assumptions in this study . The first direction is the CA V b eha vior mo deling. Researchers hav e recently started the incorp oration of human factor aspect, suc h as an extension module in IDM to model driver’s resp onses to adv anced traffic information [ 59 ], an endogenous model of human cognitive for the transition of control [ 55 ]. Such developmen ts offer a great opportunity to in tro duce human factor in a mixed traffic flow in the future. Second, the inner most lane is generally assigned as the managed lane in current practices, which requires eligible users to merge to access the managed lane, and induces additional demand of lane changing. The access plan (e.g., ingress and egress p oin ts of the managed lane, eligibility) requires further study to minimize the negativ e impacts caused by induced wea ving activity . A cost-b enefit analysis may also b e warran ted for comparing managed lane strategies with other emerging technologies, such as vehicle a wareness device (V AD), for the near-term deploymen t of CA V. Some researc hers ha ve started the exploration of right- most managed lane in U.S. [ 72 ]. Lastly , the characteristics of mixed traffic flow that is anticipated in the near-term deplo yment of CA V needs further exploration. Esp ecially , the impact of CA Vs at individual tra jectory level by analyzing high-resolution vehicle tra jectory data desires further exploration. 14 App endix A. List of Abbreviations T able A.1: List of Abbreviations Abbreviation Definition AD AS adv anced driver-assistance systems ADS automated driving systems A CC adaptiv e cruise control A V automated v ehicles API application programming in terface BSM basic safet y message CV connected v ehicles CA V connected and automated v ehicles CA CC co operative adaptive cruise control CAH constant-acceleration heuristic CDF cumulativ e probabilit y function CHEM comprehensiv e mo dal emission model DSR C dedicated short-range comm unication DLL dynamic-link library DTG desired time gap E-IDM enhanced intelligen t driver mo del GPL general purp ose lane HV h uman-driven vehicle HO V high-o ccupancy vehicles IEEE Institute of Electrical and Electronics Engineers MPR mark et p enetration rate MO VES motor v ehicle emission simulator PET p ost encroachmen t time SSAM surrogate safet y assessment mo del SAE So ciet y of Automotiv e Engineers International SUMO sim ulation of urban mobility TTC time to collision V AD vehicle aw areness device W A VE wireless ac ¬ cess in vehicular environmen t App endix B. Co efficien ts for Wireless Communication Mo del The co efficien ts obtained from the p olynomial function h i ( ξ , ϕ ) is sho wn in T able B.1a . It is w orth stressed that even seemingly negligible v alues, if omitted, could result deviation in the probability of reception from 8% to 100% [ 65 ]. ( j, k ) (0,0) (1,0) (2,0) (3,0) (4,0) h ( j,k ) 1 0.0209865 -9.66304 e -07 -1.72786 e -11 5.09506 e -17 -7.91921 e -23 h ( j,k ) 2 2.24743 7.84884 e -07 2.28533 e -10 -5.89802 e -16 3.55262 e -22 h ( j,k ) 3 2.56426 2.82287 e -05 -7.09939 e -10 1.34371 e -15 -3.01956 e -22 h ( j,k ) 4 2.41146 -9.32859 e 05 6.77403 e -10 -9.64188 e -16 3.69652 e -23 (3,1) (2,1) (2,2) (1,1) (1,2) h ( j,k ) 1 3.16577 e -20 2.13587 e -14 -5.05716 e -17 4.00928 e -09 -1.88707 e -11 h ( j,k ) 2 4.07120 e -19 -2.66510 e -13 8.64273 e -17 -7.31274 e -08 2.98549 e -10 h ( j,k ) 3 -1.85451 e -18 1.02847 e -12 1.80250 e -16 1.56259 e -07 -8.50944 e -10 h ( j,k ) 4 1.85043 e -18 -1.13894 e -16 -4.05333 e -16 -2.56738 e -08 6.24415 e -10 (1,3) (0,1) (0,2) (0,3) (0,4) h ( j,k ) 1 3.25406 e -14 0.000418109 -4.30875 e -06 1.00775 e -08 -7.32254 e -12 h ( j,k ) 2 -3.24982 e -13 0.00498750 -7.22232 e -06 1.69755 e -08 -2.94381 e -11 h ( j,k ) 3 7.59094 e -13 -0.0227008 7.50391 e -05 -1.81469 e -07 2.02182 e -10 h ( j,k ) 4 -3.57571 e -13 0.0191490 -6.92678 e -07 1.79917 e -07 -2.07263 e -10 (a) Co efficien t h ( j,k ) i in Eq. 4 (b) PDF of successfully reception (300-m p o wer range) Figure B.1: DSRC Mo del Co efficients & PDF 15 App endix C. 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