sdarticle (22)

Transportation Research Part C xxx (2011) xxx–xxx

Contents lists available at ScienceDirect

Transportation Research Part C

journal homepage: www.elsevier .com/locate / t rc

An improved cellular automata model for heterogeneous work zone traffic

Qiang Meng ⇑, Jinxian WengDepartment of Civil and Environmental Engineering, National University of Singapore, 117576 Singapore, Singapore

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 June 2010Received in revised form 26 February 2011Accepted 28 February 2011Available online xxxx

Keywords:Work zoneHeterogeneous trafficCellular automataTraffic simulationTraffic delayModel calibration and validation

0968-090X/$ - see front matter � 2011 Elsevier Ltddoi:10.1016/j.trc.2011.02.011

⇑ Corresponding author. Tel.: +65 6516 5494; faxE-mail address: [email protected] (Q. Meng).

Please cite this article in press as: Meng, Q., WRes. Part C (2011), doi:10.1016/j.trc.2011.02.0

This paper aims to develop an improved cellular automata (ICA) model for simulating het-erogeneous traffic in work zone. The proposed ICA model includes the forwarding rules toupdate longitudinal speeds and positions of work zone vehicles. The randomization prob-ability parameter used by the ICA is formulated as a function of the activity length, thetransition length and the volumes of different types of vehicles traveling across work zone.Compared to the existing cellular automata models, the ICA model possesses a novel andrealistic lateral speed and position updating rule so that the simulation of vehicle’s lateralmovement in work zone is close to the reality. The ICA model is calibrated and validatedmicroscopically and macroscopically by using the real work zone data. Comparisons offield data and ICA for trajectories, speed and speed–flow relationship in work zone showvery close agreement. Finally, the proposed ICA model is applied to estimate traffic delayoccurred in work zone.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

The presence of work zone could increase traffic delay. The accurate estimation of traffic delay in work zone is of utmostimportance for traffic engineers because the estimation result can affect the efficiency of work zone plans and traffic man-agement strategies. Microscopic traffic simulation is one of the efficient methods to estimate traffic delay in work zone. Asdeemed by Bham and Benekohal (2004), current microscopic simulation tools (i.e., CORSIM) are capable of simulating nor-mal or near-normal traffic while they require high computational resources and long execution time. However, Maze andKamyab (1999) pointed out that these tools cannot well describe interactions between vehicles and work zone configura-tions because work zone is simulated through a prolonged incident blockage where there is no transition area.

Several cellular automata (CA) models, such as CELLSIM (Bham and Benekohal, 2004) and TRANSIMS, have been devel-oped for traffic simulation. For a CA model, the randomization probability parameter reflects likelihood of driver speedingup or slowing down the traveling speed. It can be used to describe stochastic driver acceleration-deceleration behavior. How-ever, this important parameter is assigned a hypothetical constant value in the existing CA models so that they can only pro-vide a ‘‘coarse’’ description of traffic operations. In reality, the randomization probability is not a constant value for workzone traffic. It varies with traffic flow and work zone configuration factors including the activity length and the transitionlength (Meng and Weng, 2010). Compared with the normal road traffic, work zone forbids lane changes from the throughlane to the closed lane in transition area. However, the lane changing rules in existing CA models are unable to cope withthis realistic constraint. Therefore, an improved cellular automata (ICA) model should be developed to simulate the realisticheterogeneous work zone traffic.

In the ICA model, the randomization probability parameter should be modeled as a function of traffic flow and work zoneconfiguration. Compared with the existing CA models, the ICA model will also add a new lateral speed and position updating

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eng, J. An improved cellular automata model for heterogeneous work zone traffic. Transport.11

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Nomenclature

xtn; y

tn

� �the top-right position of vehicle n at time t

xtn the longitudinal position of vehicle n at time t

ytn the lateral position of vehicle n at time t

v tn the speed of vehicle n at time t, where v t

n ¼ 0;1;2; . . . ;vkmax

Vpos the posted speed limitvk

max the maximal speed of vehicle type k (1 for light vehicle; 2 for heavy vehicle)vn

max the maximal speed of vehicle nbt

n the brake light status of vehicle n at time t (0 if the brake light is off; 1 if the brake light is on)ln the length of vehicle nln the width of vehicle ndt

n the available front gap between vehicle n and its leading vehicle at time t, where dtn ¼ xt

n�1 � xtn � ln�1ðkÞ. Note

that the available front gap of vehicle n in Lane 1 would be dtn ¼ x1 � xt

n � ytn � Lt=5 as it approaches the transition

areath

n the available time headway of vehicle n at time t, where thn ¼ dt

n=v tn

an v t�1n ; k

� �the acceleration rate of vehicle n which belongs to type k at time t

dn(k) the deceleration rate of vehicle n which belongs to type kdsecurity the security longitudinal distance between two vehiclesdt

n;n;f the available front gap between vehicle n and its front neighboring vehicle in the target lane at time tdt

n;b;b the available back gap between vehicle n and its back neighboring vehicle in the target lane at time tvn;b

max the maximum speed of the back neighboring vehicleyt

n;b the lateral position of the back neighboring vehicle at time tTLn the number of target lane that vehicle n expects to move intofL the light vehicle volumefH the heavy vehicle volumeLa the activity length in work zoneLt the transition length in work zonep1(fL, fH) the randomization probability outside work zonep2(fL, fH, La, Lt) the randomization probability in work zoneDwz traffic delay occurred in work zoneTwz travel time of a vehicle traveling across work zoneT0 travel time for a vehicle to travel outside work zone

2 Q. Meng, J. Weng / Transportation Research Part C xxx (2011) xxx–xxx

rule to account for the fact that it usually takes more than two seconds for a vehicle to complete a lane change in reality. Thedeveloped ICA model can be applied to estimate traffic delay in work zone.

1.1. Literature review

Many microscopic traffic simulation tools such as INTEGRATION, CORSIM and PARAMICS have been used to simulate nor-mal or near-normal traffic. Wu (2000) applied INTEGRATION to estimate traffic delay in work zones and found that NTEGRA-TION is only applicable for estimating traffic delay in light traffic conditions. Chan (2002) used PARAMICS to estimate trafficdelay due to lane closure during maintenance activities. It was found that PARAMICS requires high computational resourcesand long execution time. Yang et al. (2008) developed a method integrating the deterministic queuing theory and CORSIM tocalculate work zone delay. Although this method needs less simulation time, it cannot provide high estimation accuracy.

The cellular automata (CA) scheme has been widely employed for freeway traffic simulation but also for pedestrian trafficsimulation (Blue and Adler, 2001), railway traffic simulation (Li et al., 2005) and intersection traffic simulation (Spyropoulou,2007). Cremer and Ludwig (1986) first proposed a cellular automata (CA) model for vehicular traffic. Nagel and Schrecken-berg (1992) developed a traffic flow model based on the CA concept, which was found to have computational advantages inmodeling complex systems. Knospe et al. (2000) proposed brake light models based on Nagel’s CA concept in order to reflectthe fact that the follower vehicle behavior is dependent on the brake light status of its leading vehicle. Larraga et al. (2005)gave a modified CA model by altering the deceleration rule to simulate traffic in a single-lane highway with a ring topology.

Since single-lane CA models cannot represent real-world traffic, various multiple-lane homogenous CA models have beendeveloped (Nagatani, 1994; Jia et al., 2005; Meng and Weng, 2010). However, theses homogenous CA models are based onthe homogenous traffic flow while the real-world traffic is usually heterogeneous. One method to solve this problem is firstto convert different vehicle types into a standard vehicle type by using an equivalency factor and then the homogenous CAmodels can be applied. Nevertheless, the main drawback of this method is its difficulty to interpret the interactions of vehi-cles of different types. Therefore, some researchers developed heterogeneous CA models for heterogeneous traffic. For exam-ple, Chowdhury et al. (1997) presented a two-lane traffic CA model with two different types of vehicles. Lan and Chang(2005) modeled the heterogeneous traffic comprising of cars and two wheelers by using their improved CA model. However,

Please cite this article in press as: Meng, Q., Weng, J. An improved cellular automata model for heterogeneous work zone traffic. Transport.Res. Part C (2011), doi:10.1016/j.trc.2011.02.011


Q. Meng, J. Weng / Transportation Research Part C xxx (2011) xxx–xxx 3

their improved model was deterministic and no randomization rule was applied to reflect driver behavior. Mallikarjuna andRao (2009) modified the basic structure of CA model in order to incorporate heterogeneous traffic flow characteristics.

In the multi-lane CA models, it also inevitably refers to lane changing behavior. Rickert et al. (1996) introduced a set oflane changing rules to characterize lane changing behavior in the two-lane road without lane reductions. To simulate workzone traffic, Nassab et al. (2006) gave symmetric lane changing rules to control vehicle’s lateral movement near a partial laneclosure. However, the length of transition area was assumed as two cells in their study, which is inconsistent with the real-world work zone configuration. Meng and Weng (2010) remedied the lane changing rules addressed by Nassab et al. (2006)for work zone traffic. Nevertheless, one deficiency of their lane changing rules is that a lane change maneuver is completed ina second. This is inconsistent with the field observation that it takes at least 2 s for a vehicle to complete a lateral movement(Gundaliya et al., 2008). Therefore, more realistic lane changing rules should be introduced for the heterogeneous work zonetraffic.

Although most previous multi-lane CA models have been used for traffic simulation, they may only provide a ‘‘coarse’’description of traffic operations. This is because the randomization probability parameter in their CA models is assignedby a hypothetical value. The hypothetical value cannot replicate the real-world traffic. To describe realistic driver behaviorand vehicular behavior, Gundaliya et al. (2008) calibrated the randomization probability parameter by using one set of nor-mal traffic data. Meng and Weng (2010) first calibrated the randomization parameter by using observed work zone data tosimulate the homogenous work zone traffic. This parameter was then modeled as a function of the activity length, transitionlength and traffic flow. Wang and Murray-Tuite (2010) developed a multi-lane CA model to replicate congestion propagationand queue dissipation in order to estimate travel time related to an incident. In their study, the CA model was calibratedusing traffic data collected from I-66 where there are more than three lanes per direction.

1.2. Objectives and contributions

A cellular automata model is useful to simulate wok zone traffic because of its simplicity and high computational effi-ciency. More importantly, it has the capability of capturing vehicle dynamics and relating them to traffic flow characteristics.Therefore, the purpose of this paper is to develop an improved cellular automata (ICA) model for the heterogeneous traffic inwork zone. In this paper, heterogeneous traffic in work zone consists of two different types of vehicles (light vehicle and hea-vy vehicle).

The contribution of this paper is three fold. Firstly, this paper develops a comprehensive CA model that can describe thedynamics and interactions of vehicles of different types in work zone. Secondly, one realistic lateral speed and positionupdating rule and two lane change constraint rules are proposed so that the simulated lateral movement behavior in workzone is close to the reality. Thirdly, the developed model improves the existing forwarding and lane changing rules accordingto the unique traffic flow characteristics in work zone.

2. Model development

2.1. Work zone configuration

According to the guidelines made by Land Transport Authority (LTA) of Singapore, work zone consists of the followingareas: advance warning area, transition area, activity area and termination area. The length of advance warning area, de-noted by Ls, is the distance from the advance warning sign to the start of transition area. The length of activity area, denotedby La, is defined as the length of section under working activity. Lt is the length of transition area where vehicles deceleratefrom their approaching speed to the limited speed along the activity area. The termination area, which is used to channeltraffic back to its normal traffic path, has the same length of Lt. The lane width varies from 3.3 m to 3.6 m in Singapore. Thispaper assumes that each lane has the uniform width of 3.5 m. Fig. 1 depicts a work zone placed between the positions x1 andx4 on Lane 1. It is assumed that the work zone causing one partial lane reduction is of length Lw = La + 2Lt.

2.2. Cell and vehicle sizes

In previous CA models, researchers assumed that each cell has a uniform length of 7.5 m and cell width is equal to lanewidth. Each vehicle has the uniform size and occupies one cell. Obviously, such cell size is too coarse, which leads to unre-alistic acceleration and deceleration rates. The uniform vehicle size cannot account for the fact that different types of vehicleshave different vehicle sizes.

Although a smaller cell size can represent different types of vehicles more accurately, it requires a huge memory for com-putation. Therefore, we should define a fine cell size that is not only able to capture different types of vehicles’ dimensionsbut also reduces the computational resources. According to the actual sizes of different vehicle types listed in Table 1, wetake the length and width of a fine cell as 0.5 m and 0.7 m, respectively. Hence, each lane laterally consists of five cells. Con-sidering the clearance of two stopped vehicles, the vehicle size represented in this paper should be slightly larger than theactual size. Therefore, a light vehicle (i.e., car) in this paper occupies 9 � 3 cells and a heavy vehicle (i.e., truck) takes away



Activity Area

Termination Area

Lt L a L t

Lane 1Transition

Area

Lane 2

Lane 3

0

5

10

15

Ls

x0 x1 x2 x3 x4

y

x

Fig. 1. Schematic representation of work zone.

Table 1Details of different types of vehicles.

Vehicle type Length (longitudinal) Width (lateral)

Actual (m) ICA (cell/m) Clearance (m) Actual (m) ICA (cell/m) Clearance (m)

Light (i.e. car) 4.2 9/4.5 0.3 1.7 3/2.1 0.4Heavy (i.e., truck) 7.2 16/8.0 0.8 2.5 4/2.8 0.3


16 � 4 cells. The comparison of vehicle sizes taken in this paper versus actual sizes is shown in Table 1. It can be seen that thephysical representation of the vehicle in this paper is very close to the reality.

2.3. An improved cellular automata (ICA) model incorporating with work zone configuration

Forwarding rules and lane changing rules are employed to determine vehicles’ longitudinal and lateral movements ateach time step, respectively. Here a time step is one second in the ICA model. Vehicles can be generated either by the neg-ative exponential distribution or by the distribution of the observed arrival pattern through survey. The generated vehicleswill travel from the leftmost to the rightmost of road.

2.3.1. Forwarding rulesThe brake light (BL) model addressed by Knospe et al. (2000) deserves much attention because it utilizes the interaction

time headway and the status of brake light to determine whether there are vehicle interactions. Therefore, the forwardingrules for the ICA model are similar to the BL rules with the following three modifications due to the unique traffic charac-teristics in work zone:

(1) As deemed by Meng and Weng (2010), driver acceleration-deceleration behavior varies with traffic flow and workzone configuration. In this paper, the randomization probability in work zone should be modeled as a function ofthe factors of the light vehicle volume, the heavy vehicle volume, the activity length and the transition length. Therandomization probability function outside work zone is dependent on the light and heavy vehicle volumes.

(2) In reality, traffic engineers usually post speed limits at the advance warning sign (position x0) to limit the vehicle’straveling speed. Therefore, the allowed maximum speed for vehicles traveling in work zone should not be larger thanthe posted speed limit Vpos.

(3) The available front gap for a vehicle in the blocked lane depends on the vehicle position and work zone configuration.

Let ðxtn; y

tnÞ be the top-right position of vehicle n at time t; bt

n denotes the brake light status of vehicle n at time t (=0 if thebrake light is off; =1 if the brake light is on); v t

n is the speed of vehicle n at time t, which can take one of the values0;1;2; . . . ;vk

max. vkmax represents the allowed maximum speed for a vehicle of type k, where k = 1 for a light vehicle and

k = 2 for a heavy vehicle; ln(k) is the length of vehicle n; wn(k) is the width of vehicle n; dtn is the available front gap between

vehicle n and its leading vehicle, where dtn ¼ xt

n�1 � xtn � ln�1ðkÞ. Note that the available front gap for vehicle n in Lane 1

(blocked lane) should be separately calculated as dtn ¼ x1 � xt

n þ ytn � Lt=5 when it is approaching transition area. th

n is the avail-able time headway of vehicle n at time t, where th

n ¼ dtn=v t

n. Therefore, the ICA model employs the following consecutive for-warding rules that are performed in parallel for all vehicles to update the vehicles’ longitudinal speeds and positions:




Rule 0 (Determination of randomization probability and allowed maximum speed).Outside work zone (i.e., xt

n < x0orxtn > x4), p = p1(fL, fH), vn

max ¼ vkmax.

In work zone (i.e., x0 6 xtn 6 x4), p ¼ p2ðfL; fH; La; LtÞ;vn

max ¼min Vpos;vkmax

� �.

Rule 1 (Acceleration). If the available time headway thn is greater than the interaction headway ts or the status of brake

lights for vehicle n and its leading vehicle both are equal to zero, namely, if ðbt�1n ¼ 0andbt�1

n�1 ¼ 0Þ or ðthn > tsÞ, then

v tn ¼min v t�1

n þ anðv t�1n ; kÞ;vn

max

� �. Here anðv t�1

n ; kÞ is the acceleration rate of vehicle type k.Rule 2 (Deceleration). Calculate the effective available front gap after considering the anticipated speed of the leadingvehicle:

dtn;eff ¼ dt

n þmax min v t�1n�1;d

tn�1|fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl}

anticipated speed of leading vehicle

�dsecurity;0

8><>:

9>=>;

If dtn;eff < v t

n, the speed of vehicle n is reduced to dtn;eff : v t

n ¼minðv tn; d

tn;eff Þ. If v t

n < v t�1n , the brake light status of vehicle n is

updated as 1, namely, btn ¼ 1.

Rule 3 (Randomization). Update the speed of vehicle n: v tn ¼maxðv t

n � dnðkÞ;0Þ with the randomization probability p.Here dn (k) is the deceleration rate of a vehicle of type k.Rule 4 (Vehicle movement). Each vehicle moves forward according to its new speed, xt

n ¼ xt�1n þ v t

n.

In the ICA model, the speeds of all vehicles updates simultaneously at each second. In each lane, the rightmost vehiclesupdate first and then the next one will be taken into consideration.

2.3.2. Lane changing rulesThe lane changing rules for the ICA model employ two criteria including incentive criterion and safety criterion that are

used in previous CA models. According to the unique work zone traffic characteristics, the ICA model also adds three sup-plementary rules including one lateral speed and position updating rule and two lane change constraint rules in work zone.

Incentive criterion

1. v tn > dt

n and v tn > v t

n�1;2. dt

n < dtn;n;f . Here dt

n;n;f is the available front gap between vehicle n and its front neighboring vehicle in the target lane.

Safety criterion

3. dtn;b;b > vn;b

max andyt

n;b > ytn þwnðkÞ; if chaning to the right

ytn > yt

n;b þwn;bðkÞ; if chaning to the left

�, where dt

n;b;b is the available back gap between vehicle n

and its back neighboring vehicle in the target lane, vn;bmax is the maximum speed of its back neighboring vehicle, yt

n;b isthe lateral position of its back neighboring vehicle at time t; yt

n is the lateral position of vehicle n at time t. This criterionensures that vehicle n cannot collide with its back neighboring vehicle in the target lane.

If the vehicle perceives that the above criteria are both satisfied, then it will make a lateral movement decision with aspecified probability.

Lateral speed and position updating rule

4. In reality, it usually takes a vehicle at least two seconds to complete a lateral movement. According to Chovan et al.(1994), the maximal lateral speed is not more than 1.0 m/s (2 cell/s). Therefore, a realistic lateral speed and positionupdating rule is adopted so that the vehicle’s lateral movement is close to the reality, shown as follows:

PleaseRes. P

ytn ¼

minfyt�1n þ 2;5� TLn � lnðkÞg if changing to the right

maxfyt�1n � 2;5� TLn � lnðkÞg if changing to the left

5� TLn � lnðkÞ; if no change

8>><>>: ð1Þ

where TLn is the number of target lane that the vehicle n desires to move into. From this rule, we can find that a vehicle al-ways travels along each lane marking when there is no change.

Lane change constraint rules in work zone

5. The lane changing rules quoted above can precisely describe lane changing behavior in activity area while an additionalrule should be added in advance warning area. This is because, in a simultaneous update, it is possible in advance warningarea that a vehicle from Lane 1 and a vehicle from the Lane 3 go to the overlapped cells in Lane 2, resulting in a lateralcollision. In order to avoid this collision, we choose a vehicle at random and thereby allow it to perform its requested lanechange in advance warning area.

cite this article in press as: Meng, Q., Weng, J. An improved cellular automata model for heterogeneous work zone traffic. Transport.art C (2011), doi:10.1016/j.trc.2011.02.011



6. Since vehicles in Lane 1 are ultimately redirected to Lane 2, the lane change from Lane 2 to Lane 1 is hence forbidden intransition area. Similarly, for the safety consideration, it is not allowed for vehicles in Lane 1 to take lane changes intoLane 2 in termination area.

3. Model calibration

To simulate the heterogeneous work zone traffic, the developed ICA model requires inputting four parameters: maximumspeed, acceleration rate, deceleration rate and randomization probability. These parameters should be calibrated first in or-der to replicate the real heterogeneous work zone traffic.

3.1. Data collection

Twenty-one sets of expressway work zone data and nine sets of arterial work zone data, respectively collected at the six-lane two-way PIE expressway and arterial roads in Singapore, are used to calibrate the four input parameters used by the ICAmodel. Each set of work zone data consists of light vehicle volume, heavy vehicle volume, activity length and transitionlength, traffic speeds in and outside work zone.

The light and heavy vehicle volumes are directly measured from the collected videos recorded at the upstream of workzone. The traffic speeds in and outside of work zone are captured by two laser guns stationed at the center of activity areaand the start of advance warning area, respectively.

3.2. Calibration results

The observed maximum traffic speed in the PIE expressway is about 109 km/h (�60 cell/s) outside work zone and about80 km/h (Vpos � 45 cell/s) in work zone. Similarly, the maximum speeds outside and in arterial work zone are respectively setas 45 cell/s and 35 cell/s for the ICA model.

According to the work of Mallikarjuna and Rao (2007), the acceleration rate and deceleration rate vary with the vehicle type.In addition, the vehicle’s acceleration rate is also affected by the traveling speed (Bham and Benekohal, 2004). The proposed ICAmodel uses the acceleration and deceleration rates provided by Mallikarjuna and Rao (2007, 2009), as shown in Table 2.

The randomization probability parameters in the ICA model are replaced by randomization probability functions. To formu-late these randomization functions, we can refer to the polynomial regression method proposed by Meng and Weng (2010) tocalibrate randomization probability functions. This simple method is briefly illustrated as follows: the randomization probabil-ity for each data set is first calibrated by means of a trial-and-error method. After the randomization probabilities for all calibra-tion data sets are obtained, the randomization probability is then formulated as a polynomial function of its influencing factors.

Using the collected expressway and arterial work zone data, the randomization probability functions for the ICA modelcan be calibrated as below:

(a) Outside work zone:

Table 2Calibrat

Vari

Acce

Dece

Inter

Secu

Max

Rand

Note: va Soub Sou

PleaseRes. P

p1ðfL; fHÞ ¼ 0:541� 6:80� 10�5 � fL � 1:28� 10�4 � fH;R2 ¼ 91:0% in expressway

0:509� 8:40� 10�5 � fL � 1:20� 10�4 � fH;R2 ¼ 99:1% in arterial road

�ð2Þ

ion results for the ICA model.

able Condition Light vehicle (k = 1) Heavy vehicle (k = 2)

leration ratea anðv t�1n ; kÞ ðcell=s2Þ v t�1

n 6 11 cell=s 4 2

11 cell=s < v t�1n 6 22 cell=s 3 1

v t�1n > 22 cell=s 2 1

leration ratea dn(k) (cell/s2) 4 3

action headwaya ts (s) 6 6

rity distanceb dsecurity (cell) 9 21

imum speed vkmaxðcell=sÞ Expressway 60 60

Expressway work zone 45 45Arterial road 45 45Arterial work zone 35 35

omization probability p Expressway: p1 = 0.541 � 6.80 � 10�5fL � 1.28 � 10�4fH

Expressway work zone: p2 = 0.425 � 3.00 � 10�5La � 1.24 � 10�4fL � 1.30 � 10�4fH

Arterial road: p1 = 0.509 � 8.40 � 10�5fL � 1.20 � 10�4fH

Arterial work zone: p2 = 0.347 � 1.0 � 10�4La + 2.27 � 10�4Lt � 6.6 � 10�5fL � 2.0 � 10�4fH

t�1n is the traveling speed of a vehicle at the start time of t.rce from Mallikarjuna and Rao (2007).rce from Mallikarjuna and Rao (2009).




(b) In work zone:For expressway work zone

PleaseRes. P

p2ðfL; fH; La; LtÞ ¼ 0:425� 3:00� 10�5La � 1:24� 10�4fL � 1:30� 10�4fH;R2 ¼ 93:2% ð3Þ

For arterial work zone

p2ðfL; fH; La; LtÞ ¼ 0:347� 1:00� 10�4La þ 2:27� 10�4Lt � 6:60� 10�5fL � 2:00� 10�4fH;R2 ¼ 99:8% ð4Þ

It should be noted that all the coefficients associated with the independent variables shown in Eqs. (2)–(4) are significantlydifferent from zero at 0.05 level. It can be seen that the randomization probability decreases with the light and heavy vehiclevolumes. The negative coefficient of the activity length variable implies that the randomization probability is negatively af-fected by the activity length in work zone. Table 2 summarizes the calibration results of the ICA model.

4. Model validation

The validation of ICA model is conducted at microscopic and macroscopic levels. In microscopic validation, both positionand speed of individual vehicles generated from the ICA model are compared to the field data. In macroscopic validation, wecompare speed–flow relationships from the ICA model and the field data.

4.1. Microscopic validation

According to the work of Benekohal (1989), microscopic validation requires the comparison of vehicle trajectories andspeeds from the simulation against the field data. We hence use the arterial work zone data collected from an arterial workzone site located in Ang Mokio Avenue 3 of Singapore in 2009 for the microscopic validation. In this work zone site, thelength of advance warning area Ls is about 140 m. The transition length Lt and activity length La are about 30 m and80 m, respectively. A stretch of 140 m along the advance warning area and transition area is considered. Positions and speedsof 38 individual vehicles including 29 light vehicles and 9 heavy vehicles in a platoon are captured within 75 s. The random-ization probability in work zone is 0.163. In order to generate the same initial headway, the ICA model uses the observedarrival distribution pattern to generate vehicles in this section.

Fig. 2a and b shows the longitudinal trajectories of 38 vehicles in Lanes 1 and 2 from the ICA model and field data. Here-after, a vehicle initially generated from Lane 1 is defined as a merging vehicle (C) while it is considered as a through vehicle(V) if it is initially generated from Lane 2. From the figure, it can be clearly seen that the longitudinal positions of most merg-ing/through vehicles from the ICA model and field data show close agreement for every second. However, there still exists alittle large error of initial positions for some vehicles (C4, C7, V7 and V8) because of the discrete nature of the model. Nev-ertheless, the longitudinal trajectory patterns from the simulation are similar to those from the observed data. Similarly, thelateral trajectory patterns as well as lane change durations are close to the field data, shown in Figs. 3 and 4.

To further investigate whether the ICA model can well characterize the dynamic vehicle behavior, we employ error tests toquantitatively measure the closeness of fit of individual vehicle speed from the simulation compared to the field data. In previ-ous studies (Bham and Benekohal, 2004; Meng and Weng, 2010), the following four error tests are used to compare the simu-lation results with the field data: (1) Root mean square error (RMSE); (2) Root mean square percent error (RMSPE); (3) Meanpercent error (MPE); and (4) Theil’s inequality coefficient (U) that is usually used in econometrics (Pindyck and Rubinfeld, 1998).

The root mean square error (RMSE) is defined as:

RMSE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

No

XNo

n¼1

ysn � y0

n

� �2

vuut ð5Þ

where ysn is the nth simulated value from the ICA model, y0

n is the corresponding observed value from field data, No is thenumber of observations.

The root mean square percent error (RMSPE), mean percent error (MPE) and Theil’s inequality coefficient (U) are respec-tively expressed as

RMSPE ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

No

XNo

n¼1

ysn � y0

n

y0n

2s

ð6Þ

MPE ¼ 1No

XNo

n¼1

ysn � y0

n

y0n

ð7Þ

U ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

No

PNo

n¼1ðys

n � y0nÞ

2

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

No

PNo

n¼1ðys

nÞ2

sþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

No

PNo

n¼1ðy0

nÞ2

s ð8Þ




In this paper, the above four tests are performed on the speed of merging and through vehicles from the simulation versusthe field data at each second. Table 3 presents the results of tests for vehicle speed at each second. The value of MPE is po-sitive for most individual vehicles. Only five vehicles C8, C9, V11, V16 and V21 have negative MPE. The average MPE for all

Time (sec)

V1 C1 V2V2 V3 C2 V4 C3 V5 C4 C5 C6 V6 V7 V8 V9 V10 V11 C7 V12 V13 V14C8

20

40

60

80

100

120

140

20

40

60

80

100

120

140

Lon

gitu

dina

l pos

itio

n (m

)L

ongi

tudi

nal p

osit

ion

(m)

Field data

ICA model

Field data

ICA model

9C8C7C6C5C4C3C2C1C

0 5 10 15 20 25 30 35 40 45

(a) Lane 1

0 5 1011 15 20 25 30 35 40 45

Time (sec)(b) Lane 2

Fig. 2. Comparison of longitudinal vehicle trajectories in Lanes 1 and 2 from ICA model against field data.

0.0

0.7

1.4

2.1

2.8

3.5

4.2

4.9

5.6

6.3

7.0

0 10 20 30 40 50

Time (sec)

Lat

eral

pos

itio

n (m

)

Field data

ICA model

Fig. 3. Comparison of lateral vehicle trajectories in Lane 1 from the ICA model against field data.




vehicles is positive (�6%), suggesting that there exists a slight over-estimation of individual speed at work zone from thesimulation. The RMSPE is less than 20% for 33 vehicles. Only five vehicles C3, V9, V12, V14 and V17 have RMSPE higher than20%. It should be noted that vehicles C3 and V9 are two heavy vehicles. Higher RMSPE of these five vehicles may be due totheir lower speeds. The smaller denominator (observed speed) of Eq. (6) can produce higher error value. To further investi-gate these five vehicles, we then check their RMSE and U. According to Table 3, it can be clearly seen that the vehicle C3 hasthe largest RMSE of 3.97, followed by vehicle V9 (3.64), among 38 vehicles. Likewise, these two heavy vehicles also have

1

2

3

4

5

1 2 3 4 5 6 7 8 9

Merging vehicle (C#)

Lan

e ch

ange

dur

atio

n (s

ec)

Field dataICA model

Fig. 4. Comparison of lane change duration from the ICA model against the field data.

Table 3Error tests for speed of individual vehicles.

Lane # Vehicle# MPE (%) RMSPE (%) RMSE U

Lane 1 C1 (lighta) 6.30 11.39 2.15 0.0557C2 (light) 14.87 20.15 2.87 0.0801C3 (heavy) 22.05 39.65 3.97 0.1130C4 (light) 2.23 9.90 1.64 0.0436C5 (light) 3.92 16.97 3.39 0.0862C6 (heavy) 2.15 4.31 0.79 0.0210C7 (light) 5.20 12.28 1.94 0.0526C8 (light) �1.02 7.27 1.19 0.0336C9 (light) �2.33 3.57 1.00 0.0192C10 (heavy) 5.71 9.38 1.59 0.0434C11 (light) 2.13 8.41 1.41 0.0380C12 (heavy) 12.58 18.70 2.80 0.0785

Lane 2 V1 (light) 3.73 8.93 1.72 0.0464V2 (light) 16.39 19.69 3.39 0.0930V3 (light) 12.80 15.65 2.40 0.0679V4 (heavy) 11.95 16.01 2.47 0.0694V5 (light) 0.42 2.82 0.53 0.0140V6 (light) 1.27 3.66 0.67 0.0180V7 (light) 3.01 7.02 1.22 0.0331V8 (light) 4.23 13.36 2.09 0.0579V9 (heavy) 18.98 28.13 3.64 0.1026V10 (light) 6.23 10.59 1.73 0.0471V11 (light) �1.29 12.98 2.29 0.0609V12 (light) 16.39 25.72 3.40 0.0963V13 (light) 7.55 11.54 1.64 0.0525V14 (light) 14.87 38.24 3.13 0.1049V15 (light) 2.29 10.26 1.87 0.0504V16 (light) �13.14 19.22 3.61 0.1032V17 (light) 14.10 24.81 3.30 0.0914V18 (light) 3.39 9.54 1.66 0.0447V19 (light) 1.14 13.19 2.42 0.0647V20 (heavy) 6.46 12.39 1.96 0.0538V21 (light) �0.67 7.61 1.43 0.0374V22 (heavy) 6.95 11.20 1.85 0.0506V23 (light) 0.71 14.10 2.43 0.0651V24 (light) 8.10 13.82 2.07 0.0597V25 (heavy) 2.44 4.87 0.88 0.0239V26 (light) 8.87 12.28 2.00 0.0559

Average 6.08 13.94 2.11 0.0587

a Vehicle type in parentheses.




slightly higher coefficients U, compared with other vehicles. One possible reason for the higher RMSE and U of vehicles C3and V9 could be that the there exist measurement errors in the field survey. Nevertheless, the RMSE and U for the rest ofvehicles are all acceptable. Meanwhile, the average RMSE is only 2.11 and the average U is very close to zero. These relativelysmall and acceptable errors of speed of each vehicle between the simulation and field data present adequate evidence thatthe ICA model could well describe work zone traffic dynamics at the microscopic level.

4.2. Macroscopic validation

To investigate the model validity, we also perform a macroscopic evaluation to identify the overall ICA model perfor-mance. In macroscopic validation, the speed–flow relationship is investigated to evaluate how well the ICA model performs.The ICA model first simulates the speed–flow relationship for the following two work zones:

(a) Expressway work zone. La = 330 m, heavy vehicle percentage = 28%.(b) Arterial work zone. La = 180 m, Lt = 90 m, heavy vehicle percentage = 28%.

Fig. 5 shows the simulated speed–flow relationships for all various flow levels from zero to the maximum in the abovetwo work zones. From the figure, it can be clearly seen that the speed–flow shapes are very similar to the standardizedshapes. Hence, we can infer that the ICA model could simulate work zone traffic well at the macroscopic level.

In this section, another 20 PIE expressway work zone data sets and 6 arterial work zone data sets from Meng and Weng(2010) are also used for the macroscopic validation to support the above claim. These work zone data sets cover various traf-fic flow levels from light to high. Based on the observed light and heavy vehicle volumes in each work zone, the ICA modelcould output the corresponding traffic speed in work zone.

In expressway work zone, the observed and simulated speed–flow relationship from the ICA model is shown in Fig. 6a.From this figure, it can be seen that the simulated speed–flow relationship from the ICA model well matches with the field

0

10

20

30

40

50

60

70

0

10

20

30

40

50

60

70

80

90

0 500 1000 1500 2000 2500 3000 3500

0 500 1000 1500 2000 2500 3000

(a) Expressway work zone

(b) Arterial work zone

Spee

d (k

m/h

)Sp

eed

(km

/h)

Flow (vph)

Flow (vph)

Fig. 5. Simulated speed–flow relationships from the ICA model.



60

65

70

75

80

2200 2300 2400 2500 2600 2700 2800 2900 3000 3100

Flow (vph)

Spee

d (k

m/h

)Field data

ICA model(33%

*)

(29%) (32%) (27%)

(33%)

(22%)

(26%)

(24%)

(30%)

(30%)

(31%) (29%)

50

55

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65

Flow (vph)800 1000 1200 1400 1600 1800 2000 2200

Spee

d (k

m/h

)

Field data

ICA model(25%)

(23%)

(19%)(19%)

(22%)

(18%)

(a) Expressway work zone

(b) Arterial work zone

Fig. 6. Comparison of speed–flow relationship from the ICA simulation versus field data.


data under various traffic flow levels. Interestingly, it also shows that the ICA model performs better when there is a highervehicle percentage. The results for arterial work zone from the ICA model and the field data also show very good agreement,shown in Fig. 6b. These satisfactory simulated results further confirm that the ICA model is able to reproduce the realisticwork zone traffic with great accuracy at macroscopic level.

5. Applications

The presence of work zone could increase traffic delay because lane reductions reduce road capacity. As discussed above,the ICA model could simulate work zone traffic more accurately. Therefore, we can apply the ICA model to estimate trafficdelay occurred in work zone.

Traffic delay Dwz in work zone is defined as the difference between travel times in and outside work zone:

PleaseRes. P

Dwz ¼ Twz � T0 ð9Þ

where Twz is the average travel time of a vehicle traveling across the distance of Lwz in work zone and T0 is the average timefor a vehicle to travel across the distance of Lwz outside work zone.

We still use 20 expressway work zone datasets and 6 arterial work zone datasets from the work of Meng and Weng(2010) in this section. In addition, we assume that the proportion of vehicles to be assigned for the ICA simulation is 0.3



Table 4Statistical simulated traffic delay results.

Model Work zone type MPE (%) RMSPE (%) U R2

ICA model Expressway work zone 2.21 9.38 0.0456 0.9039Arterial work zone 5.78 7.82 0.0359 0.9157

PARAMICS Expressway work zone �4.11 13.74 0.0721 0.8348Arterial work zone 11.74 24.82 0.0824 0.5533

CA modela Expressway work zone 0.68 9.84 0.0649 0.8833Arterial work zone 0.61 10.21 0.0463 0.8778

a Source from Meng and Weng (2010).

0.00

2.00

4.00

6.00

8.00

10.00

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Work zone scenario #

Tra

ffic

del

ay (

sec/

veh)

Field data

ICA model

0.00

0.50

1.00

1.50

2.00

2.50

3.00

1 2 3 4 5 6

Work zone scenario #

Tra

ffic

del

ay (

sec/

veh)

Field data

ICA model

Fig. 7. Comparisons of traffic delay from the ICA simulation against the field data.


for Lane 1, 0.5 for Lane 2 and 0.2 for Lane 3, respectively. Fig. 7a and b shows estimated traffic delay from the ICA model inthis paper. It can be seen that the estimated traffic delay closely match the observed data. The figure visually confirms thatthe ICA model has high accuracy for estimating traffic delay in work zone.

To support the visual claim, we carry out the error tests for traffic delay and the results are shown in Table 4. Due to thesmaller sample size, the arterial work zone has big errors that the expressway work zone. Nevertheless, these statistic errorsare very small. For the purpose of accuracy comparison, we also apply PARAMICS and one traditional CA model of Meng andWeng (2010) to estimate traffic delay in work zone. In PARAMICS, only three sensitive system parameters including meantarget headway, mean reaction time and minimum gap are required to be calibrated. A conventional genetic algorithm isemployed to calibrate the three parameters. The calibrated values for the three parameters are respectively 1.5 s, 0.6 sand 1.5 m for expressway work zones. For arterial work zones, the calibrated values are respectively 1.25 s, 1.0 s and 1.0 m.

Table 4 also shows the statistical simulated results from PARAMICS and the traditional CA model. It can be found that theestimation accuracy of traffic delay at expressway work zones from PARAMICS is a little lower than that from the ICA model.However, the ICA model provides much higher accuracy than PARMICS for the estimation of traffic delay occurred in arterialwork zone. Note that the small difference between the numbers of overestimates and underestimates from the CA modelcauses that the MPE of the CA model is a little lower. Nevertheless, the ICA model has lower values for the other three mea-sures, compared with the CA model. This suggests that the ICA model outperforms the CA model. Therefore, we can concludethat the ICA model is a good alternative to accurately estimate traffic delay occurred in work zone.

6. Conclusions

This paper developed an improved cellular automata (ICA) model to mimic heterogeneous traffic in work zone. In order togive a better representation of the unit of vehicle, the ICA model took a fine cell size as 0.5 m (length) � 0.7 m (width). For-




warding rules and lane changing rules were employed to manage the vehicle’s longitudinal and lateral movements, respec-tively. Due to the unique traffic flow characteristics in work zone, the forwarding rules have been modified based on thebrake light (BL) model. More realistic lane changing rules are proposed in the ICA model so that the simulated lateral move-ment behavior is close to the reality.

The developed ICA model was calibrated and validated microscopically and macroscopically using the real expresswayand arterial work zone data. The validation results showed that the ICA model could well simulate the heterogeneous trafficin work zone. Finally, the ICA model was applied to estimate traffic delay occurred in work zone. The estimated work zonetraffic delay from the ICA model was accurately consistent with the field data. It was also observed that the ICA model per-forms better than PARAMICS in terms of traffic delay estimation accuracy. However, one limitation of the ICA model is thatthe accuracy of estimates may depend on the sample size. As a future study, the ICA model will take into account the possiblelane changing behavior that vehicles in Lane 2 may change to Lane 3 in order to avoid merging conflicts from Lane 1.

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