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Abstract DVDA eil-ovhceadvehicle-to- to referred and commonly communication, vehicle-to-vehicle infrastructure NDIVIDUAL uoai n fcetdiigsrtge while strategies driving efficient and Automatic Vhceifatutr omncto pn pnew up opens communication —Vehicle-infrastructure .I I. NTRODUCTION prahn rfclight traffic a approaching atnTebr n reKesting Arne and Treiber, Martin se,Germany. esden, ne,Tech- ences, comfort, g n start”. ing es1, wers and s ights. apers tions. ance in s tem uch ing de, on es of to n n e e . t www.traffic-flow-dynamics.org otnoscrfloigmdlwt mohacceleration smooth speeds a ti Assuming with a characteristics. is model it car-following [23], (IDM) continuous Model Intelligent-Driver original the .CrFloigModel Car-Following A. ID)a ecie nCatr1 ftebo [22]. book the of 11 Chapter Model” in Intelligent-Driver the described “Improved augmenting as the or (IIDM) apply re-parameterizing We by impl model. ACC strategies readily enough to represent new simple enough intuitive (ii) the to TLA, (iii) and the realistic of calibration, mode for sufficiently automatic (i) the in driving be must model speed bme-obme)gap (bumper-to-bumper) on tcniin o mlmnigtesrtge na ac an an in strategies results the the TLA. implementing discuss for we conditions IV, at point Section their concluding and the “econo start”, In strategies play. “flying actual start”, the “anticipative Se analyzes objectives. approach”, and the presents define III and tion study simulation-based this mode of work. automatic this ACC-based in the focus in will or we [21], which [19], by on light in as traffic mode proposed next equipped the the that principle, of assistant In assume states traffic communication. we future the X2V traffic, the latter, know future the vehicles the in strategy “know” While, co control [20]: lights is signal Helbing that self-controlled strategies and Lämmer the of set to a plementary investigate possible and found. a intersections been fuel has [19], reduce X2V thesis and to V2X the behavior potential between in interplay driving the destructive However, the has [18]. future information Adapting consumption this the (X2V). on signals on based the information of driver state with (V2X) traffic-adapt combining multi-institu signalization [17] the “UR:BAN” of initiative intersection” research “smart sub-project the v l 1 nodrt e ai eut,teudryn car-following underlying the results, valid get to order In ntefloigScinI,w a u h methodology the out lay we II, Section following the In signalized at traffic city on focus we contribution, this In hscatri vial o reat free for available is chapter This ftelae reads leader the of d d v t v = 0 t ceeaineuto safnto fthe of function a as equation acceleration its , TA a prt nteifrainbsdmanual information-based the in operate can (TLA)    (1 1 − − z z 2 I M II. a ) free 2 z a a s ETHODOLOGY h w speed own the , a free v o xedn h desired the exceeding not otherwise, = s ∗ ( v,v s v l n h speed the and ) ≥ traffic-light 1 , ement tional inter- 1 me- tual mic (1) ive m- As of c- d 1 2

∗ where the expressions for the desired dynamic gap s (v, vl) of the traffic light. Figure 1 reproduces these data together and the free-flow acceleration afree(v) are the same as that of with the simulation results (orange bullets) for the calibrated 2 the IDM, parameters leff = 6.5 m, a = 1.5 m/s , and T = 1.2s assuming identical vehicle-driver units. As shown in Fig. 2 for ∗ v(v vl) s (v, vl) = s0 + max vT + − , 0 , (2) the start, the resulting trajectories are comparable to observed √ 2 ab trajectories on the Lankershim Blvd as obtained from the δ v NGSIM initiative [25]. Further simulations with heterogeneous a (v) = a 1 . (3) free − v drivers and vehicles reveal that independently and uniformly " 0 # distributed values for leff , T and a with standard deviations The IIDM has the same parameter set as the IDM: desired of the order of 30% of the respective expectation value can speed v0, desired time gap T , minimum space gap s0, desired reproduce the observed data scatter and its increase with the acceleration , and desired deceleration . However, it resolves a b vehicle position (for positions n =5 and higher, the scattering two issues of the basic IDM when using it as an ACC does no longer allow to identify n). Moreover, since trucks are acceleration controller: (i) the IIDM time-gap parameter T excluded from the measurements, it is reasonable to assume describes exactly the time gap in steady-state car-following that the observed cars have an average length of 4.5m resulting situations while the actual IDM steady-state time gaps are in an expectation value s = 2 m for s . somewhat larger [23], (ii) a platoon of vehicle-drivers with 0 0 For estimating the comfortable deceleration, the approach to same desired speed v will not disperse over time as would 0 a red traffic light is relevant. Trajectories of the Lankershim be the case for the IDM. data set of the NGSIM data [25] including such situations By describing the vehicle motion with a time-continuous (Fig. 2) indicate that typical decelerations are comparable to car-following model, we have neglected the in-vehicle control typical accelerations. We assume b = 2 m/s2 [26]. Finally, for path since such models implicitly reflect an acceleration re- the desired speed, we assumed a fixed value of v = 50km/h sponse time of zero. It might be necessary to explicitly model 0 representing the usual inner-city speed limit in Germany. vehicle responses by explicit delay and PI elements when actually deploying such a system. 60

0 Veh 1 Veh 2 -20 Position [m] Veh 3 Veh 4 Time [s] -40 Veh 5 Veh 6 -60 0 5 10 15 20 25 Time [s] 120 Distance [m] 140 Fig. 1: Calibration of the microscopic model with respect to 160 the starting times and positions of a queue of waiting vehicles 180 relative to the begin of the green phase (solid circles). Data 200 NGSIM are of the measurements in Ref. [24]. 220 Lankershim 240 Blvd Longitudinal Coordinate [m] B. Calibration 375 380 385 390 395 400 Since we will investigate platoons travelling from traffic Time [s] light to traffic light, the acceleration model parameters v , 0 Fig. 2: Trajectories of the start of the simulated platoon in T , s , a, and b and the vehicle length l (including their 0 veh comparison with trajectories from the NGSIM initiative [25]. variances) should be calibrated to data of starting and stopping situations. For calibrating a, T , and the combination leff = lveh + s0 (effective vehicle length), we use the empirical results of C. Simulation Kücking [24] taken at three intersections in the city of Hannover, Germany. There, the “blocking time” of the nth While the parameters clearly are distributed due to inter- vehicle of a waiting queue (the time interval this vehicle vehicle and inter-driver variations, it is nevertheless necessary remains stopped after the light has turned green) has been to use the same vehicle population for all the following sim- measured vs. the distance of this vehicle to the stopping line ulation experiments. Specifically, we use following sequence 3

50 2 cross-section A = 2 m , a dynamic tire radius rdyn = 40 0.286m. Furthermore, we assume a ﬁve-gear transmission Veh 1 30 Veh 2 with transmission ratios of 13.90, 7.80, 5.25, 3.79, and 3.09, Veh 3 Veh 4 20 respectively, and choose the most economic gear for a given Gap [m] Veh 5 Veh 6 driving mode characterized by and dv . The engine power 10 v dt management includes overrun-fuel cutoff, idling when the 0 0 10 20 30 40 50 60 70 80 vehicle is stopped, and no energy recuperation during braking.

50 III. STRATEGIES OF THE TRAFFIC LIGHT ASSISTANT AND 40 Veh 1 Veh 2 THEIR SIMULATION 30 Veh 3 Veh 4 The appropriate TLA strategy depends essentially on the 20 Veh 5

Speed [km/h] Veh 6 arrival time at the next trafﬁc light relative to its phases. 10 Depending on the spatiotemporal position, we distinguish 0 0 10 20 30 40 50 60 70 80 following approaching situations (cf. Fig. 4): • 1.5 A stop is unavoidable and the vehicles are sufﬁciently ]

2 1 near the signal to initiate braking (red spatiotemporal 0.5 Veh 1 Veh 2 region of Fig. 4), 0 Veh 3 • -0.5 Veh 4 anticipative start compensating for the reaction time of Veh 5 -1 Veh 6 the ﬁrst vehicle (the last two seconds of the red area),

Acceleration [m/s -1.5 • flying start realized by anticipative engine braking (blue) -2 0 10 20 30 40 50 60 70 80 or proper braking (turquoise), Time [s] • free passage or sufficiently away from the intersection, so no action is necessary (green), and Fig. 3: Start and stop of the simulated platoon of heteroge- • temporary “boost” to catch the last part of the green phase neous vehicle-drivers in the reference case. (violet region). of four vehicle-driver combinations: 1. average driver (expectation values for the parameters), 2. agile driver (a increased to 2 m/s2, T = 1.8s), 3. less agile but anticipative driver (a and b decreased to 1.2 m/s2 and 1 m/s2, respectively), and 2 4. a truck (lveh = 12m, T = 1.7s, and a = b = 1 m/s ). If necessary, this sequence is repeated. The Figures 2 and 3 show the simulation result for the start-and-stop reference scenario against which the strategies of the traffic light assistant will be tested in the next section.

D. Traffic Flow Metrics In the ideal case, the TLA reduces the travel time of the equipped and the other vehicles, increases driving comfort Fig. 4: Approach situations relative to the phases of the traffic and traffic flow efficiency, and reduces fuel consumption [18]. light (stopping line at x = 0). For the color coding, see the To assess travel time, we use the average speed of a vehicle, main text. or average over all vehicles during the complete simulation run. As proxy for the driving comfort, we take the number Nothing can be done in the situation of a free passage. of stops during one simulation, or, equivalently, the fraction Moreover, the “boost” strategy implies temporarily exceeding of stopped vehicles. Traffic flow efficiency is equivalent to the speed limit which we will not pursue in this contribution. the cycle-averaged dynamic capacity, i.e., the average number In the following, we will develop and simulate the remaining of vehicles passing a traffic light per cycle in congested three strategies “approach to a stop”, “anticipative start”, and conditions in the absence of gridlocks. Finally, we determine “flying start”. Generalizing the above sketch, we will also the fuel consumption by a physics-based modal consumption investigate how other (equipped or non-equipped) vehicles will model as described in Chapter 20.4 of Ref. [22]. Such models affect the strategies. Furthermore, by a complex simulation take the simulated trajectories and some vehicle attributes over several cycles, we investigate any (positive or negative) as input and return the instantaneous consumption rate and interactions between the strategies and between equipped and the total consumption of a given vehicle. To be specific, we non-equipped vehicles. assume a mid-size car with following attributes: Characteristic map of a 118kW gasoline engine as in Fig. 20.4 of [22], A. Approach to a Stop idling power P0 = 3kW, total mass m = 1500kg, friction In certain situations, a stop behind a red light or a waiting coefficient µ = 0.015, air-drag coefficient cd = 0.32, frontal queue is unavoidable. This situation is true if (i) extrapolated 4 constant-speed arrival occurs during a red phase, and (ii) the passage, preemptive braking may avoid a stop or, at least, “flying-start” strategy of Sect. III-C would produce minimum increase the minimum speed during the approaching phase. speeds below a certain threshold which we assumed to be As depicted in Fig. 7, the strategy consists in controlling flying 2 vmin = 10km/h. Notice that this scenario may also apply the vehicle’s ACC such that a certain spatiotemporal target for approaching green traffic lights if the car cannot make it point (∆x, ∆t) relative to the stopping line and the switching to the traffic light before switching time: In such a situation, time to green is reached. This point is determined such that drivers of non-equipped cars would just go ahead braking later a minimum of speed reduction is realized without impairing and necessarily harder. While this situation is not relevant for traffic efficiency by detaching this vehicle from the platoon of improving flow efficiency, it is nevertheless possible to reduce leaders. Generally, the braking is realized by engine braking fuel consumption by early use of the engine brake, i.e., early modeled with a physics-based force model as described in activation of the overrun cut-off. Chapter 20.4 of Ref. [22] and additional mild proper braking In the car-following model, we implement this strategy by (deceleration 1 m/s2) at the beginning of the deceleration reducing the comfortable deceleration from b = 2 m/s2 to whenever kinematically necessary. 1 m/s2 (homogeneous driver-vehicle population), or by 50% for each vehicle (heterogeneous population). Reducing the desired deceleration means earlier braking, in line with this 100 strategy. v0=50 km/h s Figure 5 shows speed and consumption profiles for an 50 equipped vehicle (solid lines) vs. the reference (dotted). For a 0 speed limit of 50 km/h, the equipped vehicle itself saves about τ 3.5ml of fuel (6% for the complete start-stop cycle). The −50 two next (non-equipped) followers save about 3% and 1%, −100 l eff respectively. For a limit of 70 km/h, the potential for saving is −150 significantly higher. −200

Position relative to Traffic Light [m] 20 30 40 50 60 70 80 90 B. Anticipative Start Time [s] The rationale of the strategy of the anticipative start is to compensate for the reaction time delay τ. Since the reaction Fig. 7: Preemptive braking to avoid a stop: Spatiotemporal time is only relevant for the driver of the first vehicle in a target for the 4th vehicle (pink circle). The arrows indicate queue, the anticipative-start strategy is restricted to this vehicle how the target changes when varying the reaction time τ or (see also the empirical trajectory data, Fig. 2 bottom). In the effective length l . the reference case corresponding to the calibrated parameters eff (Fig. 6(a)), the front of the first vehicle crosses the stopping From basic kinematic theory [27] and the properties of the line about 1.5s after the change to green corresponding to IDM (Sect. II-A) it follows that the propagation velocity c of τ 0.7s (the rest of the time is needed to move the first meter the positions of the vehicles at the respective starting times is to≈ the stopping line). If this vehicle started one second earlier, constant and given by c leff /T˜ where T˜ is of the order of i.e., before the switching to green (Fig. 6(b)), the situation is ∗ the IDM parameter T . Assuming≈− a gap s of the first waiting yet safe but an average of additional vehicles can pass 0 0.5 vehicle to the stopping line and a reaction delay τ of its driver, during one green phase assuming an outflow of 1800veh/h the estimated spatiotemporal starting point of the nth vehicle after some vehicles. Considering the 12 vehicles that would reads pass in the reference scenario during the 30s long green phase ∗ of the 60s cycle, this amounts, on average, to an increase by (∆x, ∆t) = (s + [n 1] leff , τ + [n 1] T˜). (4) 0 − − 4%. An additional second can be saved, allowing 13 instead The points lie on a straight line which is consistent with of 12 vehicles per green phase, if the first vehicle stops 4m observations (filled circles in Fig. 1). While we assume that, upstream of the stopping line (instead of 1m) allowing an by additional V2X communication from a stationary detector even earlier start without compromising the safety (Fig. 6(d)). to the vehicle, the equipped vehicle knows its order number However, there are limits in terms of acceptance and available n, there are uncertainties in τ, leff , and T which depend space, so stopping 2m before the stopping line (Fig. 6(c)) is on unknown properties of the vehicles and drivers ahead. more realistic. In effect, the latter strategy variants transform Furthermore, since the strategy tries to avoid a stop, the target the anticipative start in a “flying start” which we will discuss point lies several meters upstream of and/or a few seconds now. after the anticipated starting point. Is this strategy nevertheless robust? In order to assess this, C. Flying Start we treat τ and leff (cf. Fig. 7) as free parameters of Eq. (4) If, relative to the phases, a vehicle arrives later than in to be estimated and plot the performance metrics spatial gap the previous two situations but too early to have a free s to the platoon (characterizing the dynamic capacity) and minimum speed vmin (characterizing driving comfort) as a 2 No engine braking is feasible below this speed. function of τ and leff . 5

0.07 25 Speed Veh 1 0.06 Speed, Reference Consumption Rate Veh 1 Consumption Rate, Reference 0.05 20

0.04 15 0.03 10 0.02 5 Cumulated Consumption [l] 0.01 Veh 1 Reference 0 Speed [m/s], Consumption Rate [l/h] 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Time [s] Time [s] 0.08 25 Speed Veh 1 0.07 Speed, Reference Consumption Rate Veh 1 Consumption Rate, Reference 0.06 20 0.05 15 0.04

0.03 10 0.02 5 Cumulated Consumption [l] 0.01 Veh 1 Reference 0 Speed [m/s], Consumption Rate [l/h] 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Time [s] Time [s]

Fig. 5: Fuel-saving approach to a waiting queue for speed limits of 50km/h (top) and 70km/h (bottom). Left: cumulative consumption; right: speed proﬁle and instantaneous consumption rate during the complete start-stop cycle.

5 5 Red Light Red Light 4 Veh 1 4 Green Light 3 Veh 2 3 Veh 1 2 Veh 3 2 Veh 2 Veh 4 Veh 3 1 1 Veh 4 0 0 -1 -1 -2 -2 -3 -3

Position [m] -4

-5 L_veh -5 -6 -6 -7 -7 -8 (a) Reference -8 -9 -9 (b) Anticipative Start -10 -10 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 Time [s] Time [s] 5 5 Red Light 4 Red Light Veh 1 4 Veh 1 3 Veh 2 3 Veh 2 Veh 3 2 2 Veh 3 Veh 4 Veh 4 1 1 0 0 -1 -1 -2 -2 -3 -3

Position [m] -4

Position [m] -4 -5 -5 -6 -6 -7 -7 -8 -8 -9 (c) Anticipative Start, Gap + 1m -9 (d) Anticipative Start, Gap + 3m -10 -10 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 Time [s] Time [s]

Fig. 6: Start at green from the ﬁrst position of a queue of waiting vehicles. (a) reference; (b) anticipative start; (c) anticipative start plus 1m additional gap; (d) anticipative start plus 3m additional gap. 6

Figure 8 shows these metrics for the n = 3rd vehicle D. Complex Simulation arriving at a timing such that the minimum speed would be In the previous sections, we have investigated the different vmin = 10km/h if this vehicle were not equipped. For the strategies of the TLA in isolation. However, there are interac- best estimates (e.g., leff = 6.5 m and τ =2s), this minimum tions. For example, the optimal target point of the flying-start speed is nearly doubled without compromising the capacity strategy is shifted backwards in time when equipped leading which would be indicated by an increased following gap s. vehicles apply the anticipative-start strategy. Furthermore, the The simulations also show that estimation errors have one of question remains if the TLA remains effective if there is three consequences: (i) if the queue length and dissolution significant surrounding traffic (up to the level of saturation) time are estimated too optimistically (leff and τ too small), and whether the results are sensitive to the order in which there is still a positive effect since the minimum speed is slow and fast, equipped and non-equipped vehicles arrive. increased without jeopardizing the efficiency; (ii) if the queue We investigate this by complex simulations of all strategies is massively overestimated (leff and τ significantly too large), over several cycles where we vary, in each simulation, the the whole strategy is deemed unfeasible and the approach overall traffic demand (inflow) Qin, and the penetration rate p reverts to that of non-equipped vehicles; (iii) if, however, the of equipped vehicles. Unlike the simulations of single strate- queue is only slightly overestimated, the strategy kicks in (vmin gies, we allow for full stochasticity in the vehicle composition. increases) but the capacity is reduced since s increases as At inflow, we draw, for each new vehicle, the model param- well: the car does no longer catch the platoon. A look at the eters from the independent uniform distributions specified in parameter ranges (the plots range over factors of five in both Sect. II-C and assign, with a probability p, the property “is τ and leff ) indicates that this strategy is robust when erring on equipped”. the optimistic side, if there is any doubt.

40 29.2 Finally, we mention that counting errors (e.g. due to a Single Runs Single Runs vehicle changing lanes when approaching a red trafﬁc light 39.5 29 39 28.8 meaning that this vehicle has not passed the correct stationary 38.5 28.6 38 detector) will lead to similar errors for the estimated target 28.4 37.5 point as above. Consequently, this strategy should be robust 28.2 Average Speed (km/h) 37 Average Speed (km/h) Inflow: Qin=50 Fz/h Inflow: Qin=750 Fz/h 36.5 28 with respect to counting errors as well. 0 20 40 60 80 100 0 20 40 60 80 100 Penetration Rate (%) Penetration Rate (%)

Fig. 9: Complex simulation of the overall effectiveness for all Following Gap [m] 10 34 vehicles over several cycles in terms of the average speed for 9 32 a maximum speed of 50km/h. See the main text for details. 8 30 28 7 26 Figure 9 shows the results for the performance metrics 6 24 “average speed” (which is related to the average travel time) 5 22 as a function of the penetration rate for a small trafﬁc demand 4 20 (left) and near saturation (right). Each symbol corresponds 3 18 Effective Vehicle Length [m] 2 16 to a simulation for given values of Qin and p. Due to the 1 1.5 2 2.5 3 3.5 4 4.5 5 many stochastic factors and interactions, we observe a wide Starting Delay τ (s) scattering. Determining the local average (solid lines) and 1σ ± Minimum Speed [km/h] bands (colored areas) by kernel-based linear regression (kernel 10 24 width 15 %), we nevertheless detect signiﬁcant systematic

[m] 9 22 effects. For low trafﬁc demand, we observe that travel times eff 8 20 are reduced by about 4% when going from the reference 7 18 to p = 100% penetration. Similar ﬁgures apply to the 6 16 fuel consumption. Furthermore, the effects essentially increase 5 linearly with p, so the relative performance indexes I and I 4 14 T C 3 12 with respect to travel time Tt and fuel consumption C,

Effective Vehicle Length l 2 10 1 ∂Tt 1 ∂C 1 1.5 2 2.5 3 3.5 4 4.5 5 ITt = , IC = (5) Starting Delay τ [s] −Tt ∂p −C ∂p are both constant and of the order of 4%. The performance Fig. 8: Robustness of the preemptive braking strategy for a index relative to the number of stops is significantly higher. maximum speed of 50km/h. Shown is its efficiency for the 3rd Moreover, with an elevated maximum speed of 70km/h vehicle in terms of the minimum speed during the approach (Fig. 10), all performance figures increase significantly reach- (left) and the gap once this vehicle is 50m downstream of the ing up to 30% for the reduction of the number of stops for traffic light (right). low demand. For higher traffic demand (right columns of the Figs. 9 and 10), the relative performance of the TLA decreases for all criteria except for the metrics “dynamic capacity”. 7

60.5 44.5 Single Runs Single Runs 60 44 equipped leader. 59.5 43.5 59 58.5 43 58 42.5 57.5 42 ACKNOWLEDGMENTS 57 41.5 56.5 41 56 We kindly acknowledges financial support from the Volks- Average Speed (km/h) 55.5 Average Speed (km/h) 40.5 Inflow: Qin=50 Fz/h Inflow: Qin=750 Fz/h 55 40 wagen AG within the German research project KOLINE. 0 20 40 60 80 100 0 20 40 60 80 100 Penetration Rate (%) Penetration Rate (%) 0.4 Single Runs 0.8 0.38 Single Runs 0.75 REFERENCES 0.36 0.34 0.7 [1] P. Papadimitratos, A. La Fortelle, K. Evenssen, R. Brignolo, and 0.32 0.65 0.3 S. Cosenza, “Vehicular communication systems: Enabling technologies, 0.6 0.28 applications, and future outlook on intelligent transportation,” Commu- #Stops/Vehicle (1) 0.26 #Stops/Vehicle (1) 0.55 nications Magazine, IEEE, vol. 47, no. 11, pp. 84–95, 2009. Inflow: Qin=50 Fz/h Inflow: Qin=750 Fz/h 0.24 0.5 [2] H. Hartenstein and K. 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Martin Treiber received his Doctoral degree in Physics in 1996 from Universität Bayreuth, Ger- many. He is lecturer at the Chair for Traffic Mod- eling and Econometrics at Technische Universität Dresden, Germany. He has been involved in many ITS initiatives and in several research projects of Volkswagen AG. Together with Arne Kesting, he authors the textbook “Traffic Flow Dynamics”. His research interests include vehicular traffic dynamics and modeling, traffic data analysis & state estimation, driver assistance systems, and the study of macroeconomic impacts of motorized individual traffic.

Arne Kesting received the Diploma degree in Physics from Freie Universität Berlin, Germany, and the Doctoral degree from Technische Universität Dresden, Germany, in 2002 and 2008, respectively. In 2009, he received the IEEE ITS Best Ph.D. Dissertation Award for the thesis entitled “Micro- scopic Modeling of Human and Automated Driving: Towards Traffic-Adaptive Cruise Control”. He is a senior software developer at TomTom working on real-time traffic information services. His research interests include data analysis and fusion, microscopic traffic simulation, and advanced driver-assistant systems.