Paper No: 991200
COMPARISON OF CAR-FOLLOWING MODELS FOR SIMULATION
M. F. Aycin University of Illinois at Urbana-Champaign
[email protected]
R. F. Benekohal Associate Professor in Civil Engineering University of Illinois at Urbana-Champaign
[email protected]
Newmark Civil Engineering Laboratory / MC-250 205 N. Mathews Ave., Urbana, IL, 61801-2352 tel: (217) 333-5967 fax: (217) 333-9464
Submitted for publication in the Transportation Research Records
03/30/1999
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COMPARISON OF CAR-FOLLOWING MODELS FOR SIMULATION M. F. Aycin, R. F. Benekohal ABSTRACT
This paper presents the car-following methods and algorithms of NETSIM, INTRAS, FRESIM, CARSIM and INTELSIM models. Moreover, the car-following performance of these models is compared with the field data. NETSIM, INTRAS, FRESIM and CARSIM car-following models first move the leader and then update the follower in one simulation time step. Because of this approach, these car-following models can not be used to command vehicles in real time intelligent vehicle applications in Intelligent Transportation Systems (ITS). Moreover, brake reaction times are limited by simulation time step because of this method of updating the vehicles. INTELSIM was developed in order to overcome these deficiencies. INTELSIM moves the vehicles simultaneously and produces solutions for a continuous time frame. INTELSIM produced the best agreement with the field data and required the least amount of calibration effort.
INTRODUCTION
Car-following models form the basis of microscopic simulation models and they explain the behavior of drivers in a platoon of vehicles. Two approaches are mostly used by simulation models to achieve car-following: 1- Vehicles are advanced in simulation by considering emergency braking of their leaders. 2- Vehicles are spaced out according to a certain spacing equation behind the leader in simulation. Car-following models such as NETSIM and CARSIM consider emergency braking of leaders in their algorithms. However, INTRAS and FRESIM car-following algorithms use a
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combination of the two approaches. INTRAS and FRESIM algorithms not only place the vehicles at certain locations according to a spacing equation behind their leaders but also consider emergency braking of the leaders. These simulation models, NETSIM, CARSIM, INTRAS and FRESIM, update the vehicles sequentially in the simulation. First, the leader is moved and then the follower is placed at a position satisfying the design constraints of the model. That is, these car-following models determine a vehicle’s speed and position after updating its leader for the present time step. This process is described below. The final distance (D) between vehicles is determined by the design constraints of each model. Generally, the output of these models is the acceleration (+/) of the following vehicle.
beginning of time step
follower
leader
follower
leader
end of time step D follower
leader
These car-following models, however, have some shortcomings: 1. Vehicles do not move sequentially in real world. Therefore, these car-following models can not be used to command vehicles in real world intelligent vehicle applications. 2. Reaction times of the drivers are restricted by the simulation time steps. 3. Drivers’ perception thresholds are not considered in car following. In order to solve the above problems of simulation models, INTELSIM has been developed. INTELSIM moves follower and leader simultaneously and provides solutions for a
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continuous time frame using a linear acceleration model. INTELSIM solutions are continuous and not limited with the present time step. Therefore, reaction times of the drivers are not restricted by the simulation time steps. In this study, NETSIM, CARSIM, INTRAS, FRESIM, and INTELSIM car-following methods are compared with each other. Moreover, their car-following performance is compared with the field data. Furthermore, a number of modifications to FRESIM and INTRAS models have been proposed in order to enhance the performance of these models. The derivation of each car-following algorithm is also presented since the derivations of some of these models are not available from the published papers. We believe that presenting car-following derivations of these models by using a common notation, comparing car-following approaches and the simulation results of these models with each other will be a valuable reference for researchers.
CAR-FOLLOWING MODELS
NETSIM Model
NETSIM is an urban street network simulation model. In NETSIM car following, the leader is first brought to its new position when the simulation time is advanced by one time step. The follower, then, is moved to a certain location such that if the leader decelerates at the maximum deceleration limit, the follower will be able to stop without colliding with the leader. The main purpose of the car-following logic is to prevent collisions at any situation. The car-following algorithm is developed as illustrated below:
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leader sLT
XL VL
XsL L
Vfi
X if
Vf
sf
r
sfT
Xsf
follower
Vfi = Speed of follower at the beginning of the time step VL ,Vf = Speed of leader and follower at the end of time step, respectively XL = Position of leader at the end of the time step XsL ,Xsf = Stopped position of leader and follower, respectively Xif = Position of the follower at the beginning of the time step sLT, sfT = Distance to stop the leader and follower, respectively sf = Distance follower travels during the time step r = Distance follower travels due to the reaction time L = Length of the leader T = Time step Conditions are: XsL Xsf L XL + sLT Xif sf r sfT L
(1) (2)
The distance to stop the leader is: 2
sL
T
sf
T
V L 2dl
(3)
The distance to stop the follower is:
Vf
2
2df
(4)
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Where, dl and df are the deceleration rates of the leader and the follower. The simulation time step of NETSIM is 1 sec and is fixed. Therefore, Vf = Vfi + af
(5)
Vf2 = (Vfi)2 + 2*Vfi*af + af2
(6)
Where af is the acceleration of the follower to be found. NETSIM neglects the term af2 and equation (4) is rewritten as:
(V f ) 2 2 *V f * a f i
sf
T
i
(7)
2 * df
Similarly,
sf = Vfi + 0.5*af
(8)
and
r = Vf * c = (Vfi + af )*c
(9)
s = XL Xif L
(10)
Where, c is the reaction time. If equations (3) to (10) are inserted into equation (2): i
i
2 (V f ) 2 V f * a f V 1 i i X L L X f V f a f V f * c a f * c L 2 * dl 2 2 * df df
s V
i f
i i 2 (V f ) 2 Vf VL 1 * (1 c) a f * c 2 * dl 2 * df 2 df
(11)
(12)
Therefore, af is obtained as: (13)
a f F1 / F2 where,
2
V * df i F1 2 * s V f * (1 c) * df L (V f ) 2 dl i
F2 df * (2c 1) 2 *V f
i
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The vehicles in NETSIM are updated by the following equations of motion:
Vf V fi a f * T X f X V *T a f *T i f
i f
(14) 2
FRESIM and INTRAS Car-Following Models
INTRAS is a microscopic freeway simulation model which was introduced in 1980’s. In 1994, FRESIM was developed with enhancements to the INTRAS model however, the car-following algorithm of INTRAS remained unchanged in FRESIM. Therefore, the below equations also apply to FRESIM. INTRAS utilizes PITT Car-Following model which performs the car-following between simulated vehicles by maintaining a space headway of h(t) = L+ k* Vf + 10 + b*k*(VL Vf) between them. Here, L is the vehicle length of the leader, k is the driver sensitivity factor and b is a calibration constant which is defined as: b = 0.1, if (VL Vf ) 10
(15)
= 0, otherwise, In INTRAS, similar to NETSIM, the leader is first advanced to its new position at the end of time step. The follower is, then, brought to a space headway of h(t) behind the leader. An acceleration value to bring the vehicle to this space headway in one time step is calculated as follows by using the notation in page 4: XL (Xfi + sf) =L + 10 + k*Vf + b*k*( VL Vf)2
(16)
where, Vf, VL are at the end of the time step. Therefore, Vf = Vif + af *T
sf = Vif *T + af *T2 /2
(17) (18)
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where af is the required acceleration value to be found. (17) and (18) are placed in (16) to obtain: XL (Xfi + Vfi *T + af *T2 /2) = L+10+k*(Vfi +af *T)+b*k*( VL Vfi )2
(19)
Note that af*T is neglected in equation (17) to obtain (VL Vif)2 in (19). Equation (19) yields the below car-following equation: af = 2( XL Xfi L 10 Vfi *(k+T) b*k*( VL Vfi )2 ) / ( T2 + 2*k*T )
(20)
The reaction time is introduced into the car-following equations as follows: the speed and position of the leader are updated after the reaction time, c, Vf = Vfi + af *(T-c)
(21)
Xf = Xfi + Vfi *T+ af *(T-c)2 / 2 here,
c < T.
Since vehicles are updated sequentially in INTRAS, the reaction times must be smaller than the time step, which is 1 sec, Moreover, INTRAS uses fixed reaction times of 0.3 sec for deceleration and 0.2 sec for acceleration for all vehicles. INTRAS has emergency constraint equations which checks the acceleration found in Equation 20 for emergency deceleration of the leader to stop. The emergency constraint equations are given in detail in [1].
CARSIM Car-Following Model
CARSIM, CAR-following SIMulation model, was developed by Benekohal [2] in order to solve the problems INTRAS have in simulating stop-and-go traffic. CARSIM incorporates a collision algorithm and a minimum separation constraint for car following. The vehicles are moved sequentially in simulation as in NETSIM and INTRAS.
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Minimum separation constraint is given as: XL (Xfi + Vfi * T + 0.5*(af)* T2) L + K
(22)
where, K is the buffer space between the vehicles af is the followers acceleration rate to satisfy the spacing constraint. It is found by using equality in Equation (22). The Collision avoidance algorithm is given in Equation (23): XL (Xfi + Vfi * T + 0.5*(af)* T2) L K Expression
(23)
2 Vf V 2 Expression max V f * c, V f * c L 2 * df 2 * dl where,
V f V f a f *T i
The acceleration to be applied is the smallest positive value from equation (22) or (23) or the acceleration to reach the desired speed or the acceleration limit of the vehicle. The deceleration required is either calculated from Equation (23) or the minimum of Equation (22) or (23), compared to the comfortable deceleration and emergency deceleration rates. The resultant acceleration value (+ or ) is used in Equation 14 to update the vehicles as in NETSIM.
DEFICIENCIES OF THE CAR-FOLLOWING MODELS
The above car-following models move the vehicles sequentially in simulation. This method of updating the vehicles prevents the application of reaction times that are greater than the simulation time step. Moreover, vehicles do not move sequentially in the real world. Therefore, NETSIM, FRESIM, INTRAS and CARSIM car-following algorithms can not be used in controllers which command vehicles in real world, real time. Autonomous intelligent cruise control (AICC) systems are examples of such applications.
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Furthermore, since the position of the follower must be specified exactly for each time step for models such as FRESIM and INTRAS, the difficulty arises when one type of spacing equation is applied to different conditions such as stop-and-go (congested) and non-congested traffic. It is known that drivers do not car-follow in the same manner in every situation especially under congested and in non-congested conditions. Therefore, a spacing equation that places the drivers at certain separations at each time step is not going to perform equally for every situation. That is, the spacing equation calibrated for one condition does not perform well for another condition. Wicks [1] states about validation of INTRAS algorithm that ‘the behavior of platoon was simulated for 50 sec. As a result of examining position trajectories in detail, it was noticed that even for this comparatively short period of time, individual drivers tend to change their “type” of car-following behavior; i.e. their desired car-following distance’. NETSIM and CARSIM perform car-following by considering emergency braking of the leader. This can be argued that, drivers do not consider emergency braking of their leaders and do not have the information about deceleration capability of their leaders. Although CARSIM has a spacing constraint (Equation 22), this equation only assures that the vehicles are keeping the minimum distance (L + K) during car following. NETSIM and CARSIM algorithms anticipate that drivers are going to lose some amount of time equal to their reaction time in case the leader goes through emergency deceleration. However, reaction times are not applied in updating the vehicles in Equation 14. The vehicles are updated as if there is no reaction time. Because of the way the reaction time is used, the drivers with high reaction times follow the vehicles at greater spacings than the drivers with low reaction times in NETSIM and CARSIM. FRESIM and INTRAS apply the reactions correctly as seen in Equation 21. However, when Equation 21 is examined, the accelerations that vehicles have during the reaction time period, c, are neglected and assumed zero. Moreover, reaction times are limited by the simulation time step and fixed reaction times of 0.3-sec and 0.2-sec are used for all vehicles.
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The above-presented car-following models do not consider drivers’ perception thresholds. It is known that drivers can not perceive very small changes in the speed and acceleration difference and headway deviation. Because of the above deficiencies of car-following models, actual driver behavior in carfollowing can not be simulated realistically. INTELSIM has been developed in order to solve these problems of car-following models.
INTELSIM (INTELligent Vehicle SIMulatior)
INTELSIM has been developed in order to simulate the driver car-following behavior as close to reality as possible and to simulate AICC vehicles [3]. INTELSIM was formulated by combining the information about drivers’ car-following behavior from the literature. The principles used in INTELSIM car-following model are: 1. A driver reacts to a decrease in the speed of its leader by trying to equalize his speed with that of the leader’s in order to maintain his spacing [4]. 2. The preferred time headway (tp) is the time headway of a driver during steady-state carfollowing [5]. 3. The separation at the steady-state is named as Desired Space and can be expressed as: Desired Space = Speed * Preferred Time Headway 4.
(24)
A linear acceleration/deceleration model can represent drivers’ coming to a stop or acceleration to desired speeds behavior [6]. Similarly, drivers use the same principles to reach the steady state with their leaders during car-following [7].
5. Drivers have perception thresholds to changes in the speed and acceleration of the leader and to the headway deviation [8]. INTELSIM provides continuous solutions using a linear acceleration model. INTELSIM moves vehicles simultaneously and because of continuity, simulation time steps do not restrict
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the reactions of vehicles. Moreover, INTELSIM can be used in the controllers that move the vehicles in real world, real time. INTELSIM’s car-following approach can be described as follows: Assume that a leader and follower pair is initially separated by a distance x at time t = t0 and they have different speeds. The follower will reach the steady state with the leader at time t= t 1 at its desired spacing. A slope of acceleration is calculated that will bring the follower to steady state. The carfollowing equation is given by Equation (25) 0.166 * (a)t0+c * t2 + (0.666*(V)t0+c + aL * tp) * t (x)t0+c + vl* tp = 0
(25)
where, t = time to reach the steady state tp = preferred time headway (V)t0+c = (vf vL)t0+c (a)t0+c = (af aL)to+c Required slope value is found from (26) sf = 2 * ((V)t0+c + (a)t0+c* t ) / t2
(26)
This slope is applied after the reaction time at time t = t0+ c. As a check to the car-following algorithm, the time required to reach the steady state condition is compared with the time the leader needs to come to a stop at its present rate of deceleration. The derivation of the car-following algorithm is explained in detail [9]. Equation (27) is used to update the vehicles. A slope term is added to the equations of motion used by NETSIM and CARSIM.
( a) t1 ( a) t 0 s * T t1
(a)
t
dT (v) t1 (v) t 0 (a) t 0 * T 0.5 * s * T 2
t0
t1
(v) dT ( x) t
t0
t1
( x) t 0 (v) t 0 * T 0.5 * (a) t 0 * T 2 0.167 * s * T 3
(27)
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Note that Equation (27) is used if the acceleration and slope remains constant between the previous time step and the current time step. If a new acceleration value is to be applied during this time period, Equation (28) is used:
(a) t1 (a) t 0 c s t 0 c * (T c)
(28)
(v) t1 (v) t 0 (a) t 0 * c 0.5 * (s) t 0 * (c) 2 (a) to c * (T c) 0.5 * (s) t 0 c * (T c) 2
( x) t1 ( x) t 0 (v) t 0 * c 0.5 * (a ) t 0 * (c) 2 0.167 * ( s) t 0 * (c) 3 (v) t 0 c * (T c) 0.5 * (a ) t 0 c * (T c) 2 0.167 * ( s) t 0 c * (T c) 3 Where, c = Time difference between the previous update time and the time to apply the reaction (a)t0+c = New acceleration to be applied after the reaction time (s)t0+c = New slope to be applied after the reaction time (v)to+c = Speed at the end of reaction time, given by Equation (29):
(v) t 0 c (v) t 0 (a) t 0 * c 0.5 * ( s) t 0 * c
(29)
In Equation (28), a reaction which was scheduled in a past time step, is to be applied at a time that falls in between present and previous simulation time steps. A follower reaches the steady state with its leader at a certain time in the future. Therefore, the spacings are not specified at each time step. This approach reduces the need to precisely specify the vehicle spacings and reduces the model calibration efforts.
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COMPARISON OF CAR-FOLLOWING PERFORMANCE OF THE MODELS
Software
Separate simulation programs were written for each car-following model to be able to compare the performance of each model with the field data. In the simulations, 13 vehicles were all given starting positions, speeds and accelerations as in the field data. These vehicles followed the field leader, whose position and speed were input from the data, under the command of one of the car-following models. The same vehicle characteristics were used in all simulations.
Data Set
The data collected by Treiterer [10] were utilized in the study. The vehicles in the data set remained in car-following for 135 seconds and experienced a stop-and-go condition. This data set provided positions, speeds, and accelerations of vehicles for 1-sec time intervals. The preferred time headways of drivers in the data set were found by averaging the time headways of a vehicle at the same speeds with its leader. The preferred time headways of the drivers in the field data were found to be in the range 1.1 sec to 1.9 sec with an average of 1.47 sec. The reaction times of the drivers are not reported in the field data. However, the reaction times of the drivers were estimated to be in the range 0.88 sec to 1.51 sec. Aycin [9] explains the calculation of preferred time headways and reaction times in detail.
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Methodology
Macroscopic measures of average speed, density and volume versus time plots were obtained to compare the car-following models to field data. Only average speed and density versus time plots are included in this paper since volume is a product of speed and density. In the density versus time plots, density values are calculated by: D = 5280* {N / (Xfirst Xlast + L)}
(30)
where, D = Density, vehicles per mile N = Number of vehicles in platoon, 13 in our case L = Car length of the last vehicle, ft. Xfirst, Xlast = Positions in ft of the first and last vehicles in platoon at any given time.
FRESIM and INTRAS Simulations
In FRESIM and INTRAS drivers are generated with driver sensitivity factors or k values. The mean k value is the determinant factor for density and volume outcomes. Therefore, calibration of FRESIM and INTRAS to yield reasonable density and volume figures comparable to field data involves selecting a suitable range of k values. INTRAS default values of k are from 1-1.9 in increments of 0.1, each corresponding to a particular type of driver [11]. Moreover, INTRAS increases the vehicle length by 3 ft for stopped separation. Therefore, the effective vehicle length used in the simulations is 18-ft [1]. Three sets of INTRAS simulation runs were performed with k values of 1, 1.45 and 1.9 from range 1-1.9, for all the vehicles in simulation. Average speed and density versus time plots (Figure 1) show that k=1 provided closest speed and density approximation to the field data. Since k = 1 is the smallest value from range 1-1.9, new range of k values were needed.
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FRESIM uses a new set of k values ranging from 0.6-1.5. Better results were obtained when we ran the simulation with randomly generated k values from this range. The best results of 10 random simulation runs are given in Figure 2. Although FRESIM provided better results than INTRAS due to the k range it uses, there is still a need for some improvement. As can be seen from Figure 2, average k of 0.9 provided closest results to the field data for the congested condition when the vehicles were coming to a stop. On the other hand k = 1.06 yielded density and volume figures identical to the field data for non-congested conditions. Consequently, FRESIM did not provide good results for congested and non-congested conditions at the same time. The density and volumes could be improved for congested condition at the expense of density and volumes for non-congested conditions. The reason to this is that, FRESIM and INTRAS use one type of equation that can not be calibrated for congested and non-congested conditions separately. In order to improve the simulation results, a new set of equations that can simulate stop-and-go conditions without affecting freeway performance will be presented. Another problem with FRESIM and INTRAS is that, it is difficult to come up with the right k values. k parameter is known to affect the throughput or capacity outcomes however, it is not clear what k (driver sensitivity) parameter refers to at an individual vehicle level. Next, we will also propose a method to improve k parameter selection in FRESIM and INTRAS.
Proposed Method
Aycin [9] used preferred time headways of drivers in order to simulate their car-following on the freeways. The desired spacing equation was given by (24). The vehicles in INTELSIM try to reach their desired spacings in steady state with their leaders. INTRAS, on the other hand, places the vehicles at the below space headway, h(t), at every simulation time step: h(t) = L + 10 + k * Vf + b*k*( VL Vf)2
(31)
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If we ignore the adjustment factor b*k*(VL Vf), Equation (31) is similar to Equation (24) where the preferred time headway is the time headway between front bumper of follower to rear bumper of leader. Therefore, k parameter in INTRAS and FRESIM is indeed a time headway expression for drivers. An alternative representation of INTRAS spacing equation can be: h(t) = L + tp * Vf + b*tp * ( VL Vf)2
(32)
where, tp = preferred time headway Note that 10 ft of extra spacing has been dropped and the actual vehicle lengths (15ft) are used. Moreover, emergency constraint of INTRAS was also modified as follows: If the leader decelerates at the maximum deceleration rate to stop, follower must be able to stop behind the leader at its buffer space apart. The distance that the follower travels due to its reaction time is also included. af is to satisfy below equation:
i V f (a f ) * T V L2 i i i 2 XL X f V f * T 0.5 * a f * T V f (a f ) * T * c 2 * dl 2 * df
2
(33) L K 0
Note that this equation is similar to CARSIM car-following equation. If the leader has already stopped, follower must come to a stop at its buffer spacing behind the leader. Note here that, Equation (34) may not bring the vehicle to a stop at the end of the simulation time step: af = 0.5* (VfI)2 / ( XLs Xfi L K )
(34)
As mentioned earlier, Equation 21 does not consider any acceleration that is present during the reaction time. We recommend that it is changed as follows:
Vf V fi a if * c a f * (T c) 1 X f X V * c a if * c 2 (V f ) c * (T c) 0.5 * a f * (T c) 2 2 i f
i f
(36)
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where, afi = acceleration present at the beginning of time step af = acceleration calculated for the present time step
(V f ) c V fi a if * c The simulation runs by using the proposed method yielded very good agreement with the field data (Figure 2). FRESIM and INTRAS specify only 10 different types of drivers. Instead, a suitable range for the preferred time headways of drivers can be specified to represent the driver population.
NETSIM Simulations
Although NETSIM is an urban street simulation program, it is included in this study because the field data has a stop-and-go portion that NETSIM can simulate. Moreover, we are trying to find out why NETSIM is particularly used for urban street simulations. NETSIM car-following equation does not have parameters to be calibrated unlike INTRAS. However, maximum deceleration rates of following and leading vehicles and reaction times of the drivers could be adjusted to simulate the field data. First simulations were performed with default values. The maximum deceleration rate for both leader and follower was selected as the default 12 ft/sec2 and the brake reaction time or “lag” was taken as 1 sec for all the vehicles. NETSIM also adds a 3 ft buffer space to the vehicle length as the buffer space in stopped separation.
Discussion of NETSIM Results
Density and volume versus time plots show that NETSIM default values produce much higher densities and volumes than the field data (Figure 3). Utilizing the field reaction times with an
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average of 1.15-sec instead of 1-sec. reaction lag produced better results. This result is due to the fact that, drivers with high reaction times car-follow at further distances than drivers with low reaction times in NETSIM. The effect of inserting actual buffer spaces of the vehicles ranging from 5-17 ft, instead of 3-ft buffer with the field reactions produced lower densities. Since NETSIM includes these buffers to vehicle length to find the “effective vehicle length”, using larger effective lengths affected the overall performance of the simulation, instead of affecting only the stop-and-go portion. The best results obtained came from the use of 16 ft/sec2 deceleration rates for the leaders and 12 ft/sec2 for the followers with default values. NETSIM, in general, did not space out the vehicles as speeds increased and provided too close car-following for high speed conditions. The use of different deceleration rates for followers and leaders was found to be the best strategy to calibrate NETSIM for freeway data. On the other hand, NETSIM can easily be calibrated for congested conditions on freeways which very much resemble urban street situations.
CARSIM Simulations
CARSIM uses different reaction times and buffer spaces to show dual traffic behavior for congested and non-congested conditions. If the density is less than 60 vpm, traffic is considered non-congested and “surprised” brake reaction times with maximum deceleration rates of 16 ft/sec2 for both leaders and followers are utilized. For congested conditions, maximum deceleration rates of 13 ft/sec2 and 16 ft/sec2 are used for the followers and leaders, respectively. Moreover, a buffer spacing of 10 ft was used for non-congested conditions as opposed to 5-7 ft of buffer spacing for congested conditions.
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Discussion of CARSIM Results
First simulation runs were performed by using the reaction times of the drivers from the field. Density and average speed plots for this run provided good agreement with the field data. (Figure 4). Since CARSIM utilizes buffer spaces of the vehicles, 5 to 17 ft of buffer spaces from the field were substituted in place of default buffer spaces for the second runs. The results did not differ from the first run’s because these buffer spaces are used if the speeds are less than 7.3 ft/sec [2]. In both simulation runs, the vehicles were car-following each other at closer spacings than the vehicles in the field after the stop-and-go region. In order to see the effect of various reaction times on the car-following, simulation runs were performed with randomly generated reaction times from a cumulative distribution based on Johansson and Rumer’s data [2]. Different reaction times shifted the density plots as expected. In order to show this point clearly, in one case, drivers with high reaction times, 1.2 sec on the average, and in the other one, drivers with low reaction times, 0.8 sec on the average, were generated. The results are shown in Figure 4. The results show that, reaction times can be used to calibrate CARSIM. Higher reaction times space out the vehicles and decrease densities. On the other hand, shorter reaction times cause closer car-following in simulation and increase densities. This is; however, not necessarily be the case in real world because drivers’ car-following distances may not depend on their reaction times.
INTELSIM Simulations
INTELSIM was run with drivers’ preferred time headways, reaction times and buffer spaces obtained from the field data. INTELSIM gave the closest results to the field data among the carfollowing models compared (Figure 5). Moreover, INTELSIM was able to use the information
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from the field data directly, which reduced calibration time considerably. These results can be attributed to the fact that INTELSIM uses a different car-following approach than the other models and aims to simulate actual driver behavior in car-following.
Statistical Analyses and Discussion of Results
Since the vehicles in the simulations were following the leader from the field data, average speed versus time plots did not show much variation in between models and in between runs for a particular model. Therefore, in most of the cases, the average density variations between field data and simulation results determined the success of each run. Regression analyses were performed between simulation results and the field data. Correlation coefficients (R2) of simulation results versus field data for all the simulation runs are given in Table 1. Regression analyses results show that there are almost no differences between models in terms of their R2 values. This finding is rather unexpected because the density versus time plots in Figures 1-5 show that there are differences between models and even the same model performs differently depending on the calibrations performed. The results of the regression analysis suggest that there might be problems in the data set or regression analysis may not be appropriate. Regression analysis assumes that estimation errors are uncorrelated. However, the speed and density values are correlated with the next and previous speed and density values. Moreover, residual plots of fitted regression lines suggest that there is non-constant variance in the regression. Therefore, regression analysis results are not meaningful for this type of data. Therefore, the simulation results will be compared to the field data visually. Since calibrations performed on a model play a very important role in model fitting to field data, they can determine how good a model is compared to another model. Therefore, carfollowing models can be evaluated for their performance by considering the following:
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1- How well a calibrated model can simulate field data. Comparing microscopic and macroscopic plots is required for this task. 2- The amount of calibration effort required to make a model fit to the field data. 3- How well the calibrations applied to a particular model reflects the field data. 4- The ease at which a model can utilize the available information from the field. According to the above criteria, INTELSIM produced the best fit to the field data among the group of models compared. Moreover, INTELSIM used the information from the field and consequently it required the least amount of calibration. The Proposed FRESIM comes second because it produced good results by using the information from the field data. CARSIM’s performance was better for stop-and-go region than FRESIM’s. However, FRESIM showed better performance for non-congested conditions than CARSIM. FRESIM performed better than INTRAS because of the k parameter range it employed. NETSIM was developed for urban streets, therefore, it required some tricky calibrations to make it work for the field data.
CONCLUSIONS
This paper presented the similarities and differences of well-known car-following models and compared their performance with the field data. NETSIM, CARSIM, FRESIM and INTRAS sequentially update the vehicles. This approach prevents the applications of these models to situations where the vehicles are commanded by real time controllers. Moreover, brake reaction times can not be greater than the simulation time step because of this approach. Although NETSIM is developed for urban street simulations, its car-following model yielded good agreement with the field data for stop-and-go condition. However, it could not perform well in non-congested conditions. NETSIM did not space out the vehicles as speeds increased because NETSIM algorithm only aims to prevent collisions. Therefore, it provides too close car-following for high speed conditions.
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FRESIM provided results that were similar to those from field data either for noncongested or congested conditions but not for both at the same time. FRESIM and INTRAS require proper selection of “k” parameter which determines the throughput from the simulation. FRESIM utilizes a k parameter range that yields better agreement with the field data than INTRAS model; however, the selection of a mean k value is not straightforward. It was shown that k parameter is a time headway assignment for the drivers. Therefore, using t p (preferred time headway) instead of k parameter in FRESIM and INTRAS algorithm makes them easier to calibrate. The proposed modifications to FRESIM and INTRAS car-following models yielded very good agreement with the field data. CARSIM is a more detailed model than NETSIM, INTRAS and FRESIM. It tries to simulate dual traffic behavior in congested and in non-congested conditions. Therefore, it is easy to calibrate for stop-and-go conditions and yields good results. INTELSIM required the least amount of calibration effort since it was able to use driver characteristics (preferred time headway, buffer spaces) from the field. INTELSIM updates the vehicles simultaneously. Therefore, it can be used to simulate vehicles commanded by controllers such as AICC. Moreover, reaction times of drivers are not restricted by the simulation time steps. Furthermore, INTELSIM produced the best agreement with the field data. Regression analysis between field data and simulation results did not provide meaningful results due to the correlation that exist between data points. This comparison was based on one data set for freeway traffic. Therefore, more field data should be collected for further validation and comparison of car-following models and to understand driver behavior in car-following. Moreover, field data is required to determine the distribution of the drivers’ preferred time headways. In addition, the relationship between the drivers’ preferred time headways and their reaction times must be examined.
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REFERENCES 1- Wicks, D.A., Andrews B.J. Development and Testing of INTRAS, a Microscopic Freeway Simulation Model, Vol. 1: Program Design, Parameter Calibration and Freeway Dynamics Component Development. Report FHWA/RD-80/106.FHA, U.S. Department of Transportation, 1980. 2- Benekohal R.F., Treiterer J. CARSIM: Car-following Model for Simulation of Traffic in Normal and Stop-and-Go Conditions. In Transportation Research Record 1194, TRB, National Research Council, Washington, D.C., 1988. 3- Aycin M. F., Benekohal R. F. A Linear Acceleration Car-Following Algorithm For Autonomous Intelligent Cruise Control Systems, Proceedings of the Fifth International Conference on Applications of Advanced Technologies in Transportation Engineering, 1998 4- Michaels R., Solomon D. Effect of Speed Change Information on Spacing between Vehicles, Public Roads v.31, no. 12, 1962. 5- Winsum W.V., Heino A. Choice of Time-Headway in Car-Following and The Role of Time to Collision Information in Braking, Ergonomics, v.39, pp. 579-592, 1996. 6- Lee C.,Rioux T., The TEXAS Model for Intersection Traffic Development, Research report, University of TEXAS at Austin, December 1977. 7- Spurr R.T. Subjective Aspects of Braking, Automotive Engineer, February 1969. 8- Hattori Y., Asano K., Iwama and Shigematsu T. Analysis of Driver’s Decelerating Strategy in a Car-following Situation, Vehicle System Dynamics, v.24, pp. 299-311, 1995. 9- Aycin M. F., Benekohal R. F. A Linear Acceleration Car-Following Model Development and Validation, Transportation Research Record, No: 1644, p.10-19, 1998. 10-Treiterer, J. Investigation of Traffic Dynamics by Aerial Photogrammetry Techniques, Transportation Research Center, Department of Civil Engineering, Ohio State University, Final Report EES 278, Feb. 1975.
Aycin & Benekohal 11- Cheu,R., Recker W., Ritchie S., Calibration of INTRAS for Simulation of 30-sec Loop Detector Output, Transportation Research Record 1457, Dec. 1994 p.208-215.
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Average speed (m/sec)
25
20
15
10
5
0 0
20
40
60
80
100
120
140
100
120
140
Time (sec)
140
Density (veh/km)
120 100 80 60 40 20 0 0
20
40
60
80
Time (sec) k=1
k=1.45
k=1.9
field data
Figure 1) INTRAS average speed and density versus time plots for k values of 1, 1.45 and 1.9.
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Average speed (m/sec)
25 20 15
10 5 0 0
20
40
60
80
100
120
140
Time (sec) 140
Density (veh/km)
120 100 80 60 40 20 0 0
20
field data
40
k=0.9
60 80 Time (sec) k=1.06
100
120
Proposed FRESIM Method
Figure 2) FRESIM average speed and density versus time plots for random k values from range 0.6-1.5. Proposed FRESIM model results are also presented.
140
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Average speed (m/sec)
25 20 15 10 5 0 0
20
40
60 80 Time (sec)
100
120
140
140
Density (veh/km)
120 100 80 60 40 20 0 0
20 field reac.
40 field data
60 80 Time (sec) alternative
100 NETSIM
120
140 buffers
Figure 3) NETSIM speed and density versus time plots Legends NETSIM
Explanation default values
alternative
assuming 16 ft/sec2 deceleration for leader, 12 ft/sec2 for follower in car-following
buffers
default 3 ft buffer is replaced by field buffer values in stopping
field reac.
field reaction times are used instead of fixed 1 sec reaction time (lag).
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Average Speed (m/sec)
25 20 15 10 5 0 0
20
40
60 80 Time (sec)
100
120
140
140
Density (veh/km)
120 100 80 60 40 20 0 0
20 default
40
60 80 Time (sec)
field data
modified
100 high BRT
120
140
low BRT
Figure 4) CARSIM speed and density versus time plots Legends
Explanation
default
field reaction times are used with CARSIM default values
modified
field reaction times and buffer spaces are used instead of default.
highlow BRT
runs with drivers with especially high and low reaction times, respectively.
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Average speed (m/sec)
25 20 15 10 5 INTELSIM
Field data
0 0
20
40
60
80
100
120
140
Time (sec)
140
Density (veh/km)
120 100 80 60 40 20 INTELSIM
Field data
0 0
20
40
60 80 Time (sec)
100
Figure 5) INTELSIM speed and density versus time plots
120
140
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Table 1: Correlation coefficients of simulated versus actual densities of all the simulation runs for each model R2 NETSIM Simulations
Density
netsim
alternative
field react.
buffers
0.94
0.93
0.95
0.94
INTRAS Simulations
Density
k=1
k=1.45
k=1.9
0.95
0.97
0.94
FRESIM Simulations
Density
k=0.9
k=1.06
k=1.16
proposed method
0.93
0.97
0.97
0.98
CARSIM Simulations
Density
default
modified
high BRT
low BRT
0.94
0.93
0.95
0.89
INTELSIM Simulations Density
0.99
