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Impacts of traffic congestion on fuel rate, dissipation and particle emission in a single lane based on Nasch Model
Physica A 503 (2018) 154–162
Contents lists available at ScienceDirect
Physica A journal homepage: www.elsevier.com/locate/physa
Impacts of traffic congestion on fuel rate, dissipation and particle emission in a single lane based on Nasch Model Wei Pan a , Yu Xue b , Hong-Di He c , Wei-Zhen Lu a, * a b c
Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong Institute of Physical Science and Engineering, Guangxi University, Nanning 530004, China Logistics Research Center, Shanghai Maritime University, Shanghai 200135, China
highlights • NaSch model was applied to study impacts of congestion on the fuel and emission. • Three different aspects of traffic conditions were considered separately. • The impacts have been study both globally (whole lane) and locally (road sections).
article
info
Article history: Received 5 June 2017 Received in revised form 29 December 2017 Available online 4 March 2018 Keywords: Particle emission Fuel rate Dissipation NaSch model Traffic congestion
a b s t r a c t This paper presents simulation results of Traffic emitted particle modeling based on NaSch Model of a single lane. Three parts are constituted to the proposed model: traffic component (NaSch Model), fuel rate and dissipation component, and particle emission component. Impacts of speed limit, injection rate and extinction rate of the lane on the fuel cost and PM emission are disused in the periodic boundary condition and open boundary condition, respectively. Results from model simulation show that the critical transition point of the traffic system could also be used as a cut-off point for the change of the fuel and emission indexes. The high-speed limit was energy conservative and environmentally friendly until congestion occurred, while the low speed limit was better for smooth flowing traffic. The overall impact from the extension rate was more significant than the injection rate on all indexes, and the closer the road section was to the exit, the more fuel was consumed and the more particles were produced. The situation got better in descending order of the distance of the section to the exit. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Particulate matter (PM) has become a vexing question and one of the most challenging global problems for air quality mitigation and for climate change policies [1]. Dealing with PM which originates from road transport constitutes an urgent task for megacities due to thousands of vehicles shuttling back and forth along every street. High frequency outbreaks of haze weather, PM related diseases and traffic congestion have once again appeared in the forefront as an inescapable obligation to safeguard the air quality of the general public. In addition, the variables that determine vehicular exhaust emissions are mainly fleet composition, speed, speed limits, acceleration and deceleration rates, queuing time in idle mode during the red phase, queue length, traffic flow rate and ambient wind conditions [2].
*
Corresponding author. E-mail address: [email protected] (W.-Z. Lu).
https://doi.org/10.1016/j.physa.2018.02.199 0378-4371/© 2018 Elsevier B.V. All rights reserved.
W. Pan et al. / Physica A 503 (2018) 154–162
155
However, the estimation of PM emissions from road traffic requires an in-depth understanding of traffic characteristics, which cannot be told by using traditional statistical methods that lack the capability to capture the dynamic process of traffic flow [3]. It is difficult to depict the relationship between traffic congestion and PM emissions by carrying out mobile measurements in a solo car. Consequently, the effects of congestion were only partially incorporated in the predictions and measurements. The effects of congestion on emitted PM are seldom incorporated in predictions and measurements. To depict the traffic system and illustrate the mechanism physically, many traffic flow model have been proposed and developed [4–8], and formed an interdisciplinary that includes by introducing the idea of social dilemma to investigate its role on the evolution of traffic flow and formation congestion [9,10]; and incorporated with environmental consideration to evaluate the cost of energy and emission under different driving modes [11] and behavior [12,13], etc. Yang et al. [14] studies the fuel consumption and gas emissions make by traffic by compared the results among three different traffic models in cellular automata, i.e., Nagel–Schreckenberg (NaSch), finite deceleration, and adaptive cruise control. Simulations suggested that keep driving smooth was the best way to reduce the expenditure of fuel and emission pollution. Madani and Moussa [15] investigated the fuel consumption and gas emissions caused by traffic in the NaSch model with closed boundary conditions, and found that the presence of a traffic light has a big effect on fuel consumption. In light of this, this paper combines the classical NaSch model and emission function based on empirical measurement, with objective is to investigate the effects of traffic congestion on the atmosphere due the emitted PMs from on-the-road vehicles, and also the impact on the fuel rate and dissipation. 2. Methodology Three components were integrated in the model of this study: (1) traffic, (2) fuel rate and dissipation consumption, and (3) particle emission. 2.1. Traffic component The aim of introducing the traffic component was to gain a speed–time profile to provide the necessary information that would enable the model with the ability to depict the macroscopic flux, fuel consumption, and particle emission of the traffic flow by simulating every individual vehicle movement microscopically. Among multiple traffic models [16], cellular automaton (CA) ones, microscopically, were most popular for their simple algorithm, high generalization and rich phenomena. The adopted CA model in this study was the NaSch model [17], which was able to reproduce the spontaneous emergence of traffic jams and was known as the first stochastic traffic cellular automaton model. Generally, the NaSch model was defined on a one-dimensional array L in a dimensionless manner, in which each site may either be empty or occupied by one vehicle that has an integer speed in the range between zero and a maximum speed (smax ). For an arbitrary configuration, the NaSch model followed four consecutive steps, which were performed in parallel for all vehicles [18]: Step 1. Acceleration: s (i, t + 1/3) → min (s (i, t ) + 1, smax )
(1)
Step 2. Deceleration: s (i, t + 2/3) → min (s (i, t + 1/3) , gapn )
(2)
Step 3. Randomization with probability p: s (i, t + 1) → max (s (i, t + 2/3) − 1, 0)
(3)
Step 4. Car motion: x (i, t + 1) → x (i, t ) + s (i, t + 1)
(4)
where s (i, t ) and x (i, t ) are the speed and position of the vehicle i on the road at time step t. Before the determination of its motion for the next time step t + 1, the vehicle i should go through three steps (i.e. acceleration, deceleration and randomization). These steps represent three common situations during the driving process. The randomization probability p is a stochastic braking noise that makes the vehicles decelerate without backing. In general, there were two boundary conditions for CA simulation, i.e., periodic boundary condition and open boundary condition. The periodic boundary condition indicated that the number of vehicles in the system was conserved (conservation), determined by the occupation rate ρ ; the lane was similar to a closed loop. While the open boundary condition meant that vehicles could move into or get out of the lane with certain probability, determined by two adjustable parameters (i.e., injection rate α and extinction rate β ), and the number of vehicles was not conserved (non-conservation) in the simulation system. Compared to realistic traffic, it was easy to rescale the model and make comparisons with a realistic scenario by converting the length of one site and a simulation time step into 5 m of place and one second of time in a real road scenario, respectively. For example, the smax = 5 in the simulation system and was equivalent to the speed of 90 km/h. This conversion laid the foundation for the subsequent fuel and emission estimation.
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W. Pan et al. / Physica A 503 (2018) 154–162 Table 1 Parameters for Eq. (5). Notation
Description
Selected values
ξ κ ψ
Fuel to air mass ratio Heating value of a typical diesel fuel (kJ/g) Conversion factor (g/s to L/s) Engine friction factor (kJ/rev/liter) Engine speed (rev/s) Engine displacement (liters) Efficiency parameter for diesel engines Curb weight (kg) Payload (kg) Instantaneous acceleration (m/s2 ) Road gradient (%) Coefficient of aerodynamic drag Air density (kg/m3 ) Frontal surface area (m2 ) Gravitational constant (m/s2 ) Coefficient of rolling resistance Vehicle drive train efficiency Engine power demand for accessories
1 44 737 0.25 40 7 0.9 11 250 5850 0 0 0.7 1.2041 3.912 9.81 0.01 0.4 0
k N V
η w q
χ θ Cd
ρ
A g Cr ntf Pacc
Table 2 Parameters for Eq. (7). E0
f1
f2
f3
f4
f5
f6
0
2.14 × 10−4
3.35 × 10−4
−2.22 × 10−5
2.07 × 10−3
1.80 × 10−3
2.27×10−4
2.2. Fuel rate and dissipation component Energy cost should be the optimum balance between economic and environmental factors [19,20]. Fuel consumption is the relationship between the distance traveled and the amount of fuel consumed by the vehicle, while the fuel rate is defined by the time traveled instead of distance traveled, according to the protocol set for this study. Dissipation was considered only in the deceleration scenario since speed down (i.e., rolling resistance and brake) caused energy (fuel) to dissipate, which was generally not expected. The fuel rate (f ) [21] in liters per second and its dissipation rate (d) for an arbitrary vehicle i at time step t are defined as:
ξ f (i, t ) = κψ (
{ kNV +
1000ηtf
d (i, t ) =
{
)−1
1 (((
η
) ) (w + q) (χ + gsnθ + gCr cosθ) + 0.5Cd ρ As(i, t )2 s (i, t ) · )}
+ Pacc b
f (i, t − 1) − fc (i, t ) , 0
for s (i, t ) < s (i, t − 1) other .
(5)
(6)
All parameters along with typical values used in the simulation are provided in Table 1. The fuel dissipation ratio is the result of the dissipation rate over the fuel rate, which could be used to quantify the proportion of the dissipated fuel in the total fuel consumption. 2.3. Particle emission component The estimation modeling of pollutants must use emission factors obtained from in-situ vehicle tracing measurements. Generally, the required ‘factor’ information can be categorized into two types: distance-based (g/km) and time-based (g/s). In light of the NaSch model, distance-dimensionless with its simulation time step is equivalent to the real time, time-based (g/s) emission factor would be the priority choice. Hence, a general emission function proposed by using nonlinear multiple regression techniques based on empirical measurements was given as [22]: e (i, t ) = max E0 , f1 + f2 s (i, t ) + f3 s2 (i, t ) + f4 a (i, t ) + f5 a2 (i, t ) + f6 s (i, t ) a (i, t )
[
]
(7)
where E0 was a lower limit emission specified for both pollutant types and vehicle catology, and f1 to f6 were emission constants determined by the regression analysis. Table 2 only shows related values to be used in a later simulation. The simulation of the traffic behavior and related fuel rate (f ), dissipation (d) and particle emission (e) were performed in periodic boundary condition and open boundary condition, respectively. The length of the lane was set to be L = 105
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Fig. 1. Periodic boundary results of the general case with p = 0.2, smax = 5.
cells L = 1 × 105 × L, which amounts to 50 km. The averages per vehicle were obtained by averaging over 30 independent initial realizations up to 3 × 105 iteration steps for each run and by discarding the first 2 × 105 iteration steps as transient time.
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3. Results and discussion 3.1. A general case According to classical traffic theory, the estimation of the capability of vehicles moving on the road is based on the flux or mean speed which we consider to be fundamental diagrams. The fundamental diagrams and relevant results (fuel consumption, dissipation and PM emissions) for a general case with probability p = 0.2 and maximum speed smax = 5 are shown in Fig. 1(a)–(b) and (c)–(h). The occupation rate (ρ ) indicated the proportion of lattices that had been occupied, which amounted to the lane usage rate under periodic boundary condition. The increasing ρ made the global flow of the lane (Fig. 1(a)) straight climbs to peak value (i.e., ρ ≈ 0.29) at first, which was called critical transition point, then collapsed after that, until there was no more space for a vehicle when global congestion happened (i.e., ρ ≈ 1.00). This presents a first phase transition process from free flow (i.e., increasing flow rate) into jamming phase (i.e., declining flow rate), which corresponded to the mean speed that kept maximum level at first (i.e., platform in Fig. 1(b)) and gradually declined until it approached zero. In Fig. 1(c), the average ratio of vehicle states (i.e., acceleration, deceleration, following the frontal car, and jamming or stopping where speed equals zero) were provided according to the increasing occupancy ρ . Before reaching the critical point, most cars followed each other at the prescribed speed, and did not encounter congestion. Moreover, vehicles in the state of acceleration and deceleration underwent the same conditions. When reaching the critical point, stopped cars emerged with most of participants following slowing down at the same time, until time to accelerate and then the acceleration ratio began to exceed the deceleration. Two cross points are noted in Fig. 1(c): One is the intersection point between following and stopping (P1 ), the other is the intersection point between acceleration and stopping (P2 ), discussed later. Since speed was the only independent variable of Eq. (5), it is no surprise that the fuel rate had the same pattern relationship to the speed as shown in Fig. 1(d). But the dissipation due to deceleration had a unique change style, described as staircase-like as indicated in Fig. 1(e), which meant that although the fuel rate declined continuously, after a critical point, the net dissipation rate changed stage by stage. Meanwhile, the fuel dissipation ratio (Fig. 1(f)), the PM emission rate (Fig. 1(g)) and the PM emission of unit fuel consumption (Fig. 1(h)) shared a similar trend curve, as the lane became more occupied. The peak position of the PM emission rate was ρ ≈ 0.55, which was different from that of the dissipation ratio and PM emission per fuel consumption (i.e. , ρ ≈ 0.66). The corresponding values of the two occupation rates (free flow and jamming) of the two intersection points (P1 and P2 ) in Fig. 1(c) remained the same by not exceeding the two peaks set for fuel dissipation ratio (or PM per fuel consumption) and PM emission rate, respectively. This general case indicated that the critical transition points of the traffic system were not only the index that determined the traffic phases, but also helped identify the trend of fuel cost and particle emissions. As the lane became jammed, three events occurred: (1) the critical transition point of the fundamental diagram also served as the transition point to all fuel and emission indexes; (2) when the PM emission rate was the highest, the unit combustion generated PM and dissipated ratios were not in their worst situation; (3) the ratio of vehicle states could be used to identify the behavior of fuel dissipation and its PM emission. 3.2. Impact of the speed limit The speed limit was the maximum allowed to legally travel on a public road, mostly for safety reasons and could vary from region to region. In Fig. 2, simulations were performed under three different speed limits (i.e., smax = 3, 4 and 5) with randomization probability p = 0.3 to compare the effects of speed with concerns relating to fuel and the emission. The fuel rate plot in Fig. 2(a) shows that more fuel was needed for a vehicle to travel on the lane with a higher speed limit, which aligned with general knowledge. Influence from speed limits was getting smaller and smaller after the occupation rate increased, which had drivers enjoying the maximum legal speed in the free-flow phase, but then reached its respective critical points (congestion slowing traffic down to the jamming phase), which meant that the lower speed limit for fuel saving only worked in the phase of free flow, and the advantage would be more and more insignificant as traffic became more and more congested. In Fig. 2(b), the fuel dissipation ratios for three speed limits were almost the same in the phases of free flow and the last stage of congestion. The major differences happened in the first stage of the congestion phase (i.e., ρ in the range of 0.2–0.8), where peak value emerged and the higher speed limit represented a bigger proportion of dissipated fuel. As for the particle emission, the emission rate and unit fuel combustion produced PM were all in their lower level in the free flow ranges, but changed conversely at the first stage of the congestion phase when they reached their peak, and gradually leveled off until the end, as indicated in Fig. 2(c) and (d). For a lower speed limit, the emission rate and unit fuel-generated particles (exhaust emissions) were lower in the free flow phase compared with the jammed flow, From here on, the impact of speed limit on the fuel and particle emission depended on phases and stages of the traffic system involved in (1) the free flow phase, where a lower speed limit needed fewer fuel and produced less particle to the ambient; (2) in the jamming phase, although the fuel rate was the same, high speed limit was a better choice for the control of PM emission.
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Fig. 2. The impact of speed limit smax with p = 0.3.
Fig. 3. Schematic of the lane with open boundary condition.
3.3. Impact of the extinction rate and injection rate The schematic of the lane with an open boundary condition is illustrated in Fig. 3. Vehicles could access the lane at the entrance on the left side with the injection rate α , and get out of the lane at the exit on the right side with the extinction rate β . The whole lane was divided into five sections (S1 –S5 ) with the same interval length. The aim of performing the simulation under open boundary conditions was to investigate the influence of inflow and outflow on the fuel rate and PM emission counts from different lane sections. First, the influence of extension rate β on traffic behavior, fuel and PM emissions based on the average results of the whole land per vehicle data is discussed and results are exhibited in Fig. 4. As the injection probability (α ) increased, the vehicle was more likely to drive at maximum speed and take less time and fuel to pass through at the same time as when the extension rate was high enough, as shown in Fig. 4(a)–(c). However, as the β increased (i.e., β = 0.1, 0.3, and 0.5), corresponding velocity plots shared a very interesting transient trend that declined first and rose thereafter. It indicated that even when achieving some level of injection rate with little outside interference (i.e., p = 0.2), the bigger β does not guarantee higher mobility (i.e., speed). This also influenced the performance of the total fuel dissipation, PM emission and emission rate per fuel consumption in Fig. 4(d)–(f), which was largely due to the strong interaction between vehicles on the lane when β was not big enough (0.3 and 0.5 here), and the effect of synchronization became more significant compared to small extinction rate (i.e., 0.1). In addition, the subtotals of the fuel cost and PM emissions for the five sections of the lane were different. For a giving extension rate shown in Fig. 5(a) (i.e., β = 0.5), the general trend of the total fuel consumption per vehicle passing through sections was uniform at the low injection rate (i.e., β < 0.2), then went up to reach the peak point (or a platform) at the medium injection rate range of (0.4, 0.8), and gradually recovered to the same level of the low injection rate. But in different sections, the fuel costs varied and were highest for S5 , which was the nearest to the exit of the lane. Moreover, the consumption became smaller successively in a descending order of section number from S4 to S1 . This was also reflected in
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Fig. 4. The impact of extinction rate β on the average results of the whole land with p = 0.2, smax = 5.
Fig. 5. Impact on different segments with p = 0.2, smax = 5, β = 0.5.
W. Pan et al. / Physica A 503 (2018) 154–162
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Fig. 6. The impact of injection rate α on the average results of the whole land with p = 0.2, v max = 5.
relevance to the total PM emissions, as indicated in Fig. 5(b), which means that when the outbound probability was fixed, the emission problem was more serious in the exit included section, at least to the ones near an entrance. Meanwhile, circumstances related to the injection rate were simpler, as indicated in Figs. 6 and 7. Results of injection rate under the simulation condition of p = 0.2, smax = 5 for the lane average per car shown in Fig. 6(a)–(f) reflected that, when α < 0.5, the smaller of the injection rate the better and bigger the injection rate was preferably when α > 0.5, and all indexes were all worse when α = 0.5. This meant that for fixed extinction rate, the impact of increasing injection rate on all indexes (i.e., fuel cost, dissipation, particle emission and its emission per fuel cost) was identified by the speed plot. Similar to Fig. 5, the section curved in Fig. 7 showing that for fixed injection rates, S5 still produced the most PM emissions and consumed more fuel compared to other sections. Results became better in the descending order of the section numbers. Hence, simulations based on open boundary conditions provided here suggest that: (1) ensuring a smooth export (i.e., sufficient large β ) will always help cut the fuel cost and mitigate the PM polluted levels; (2) the fuel cost and traffic-made particulate pollution in the road section close to the exit was always severe compared to those sections closer to the entrance. 4. Conclusion In this paper, a model was successfully integrated and applied to depict the dynamics of traffic flow, and its relation to the fuel rate, dissipation, and particle emissions on a single lane. This traffic component was NaSch based, and simulations
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Fig. 7. Impact on different segments with p = 0.2, smax = 5, α = 0.5.
were performed in a periodic boundary condition and an open boundary condition, respectively. The general case proved the applicability of this model, and there was a shift between the peak location of the fuel dissipated ratio (or unit fuel produced particle) and particle emission rate. Moreover, impact from the speed limit, injection rate and extinction rate were estimated respectively. Major concluding remarks are (1) in the free flow phase, low speed limit was more energy conservative and environmentally friendly, while the high speed limit was better when the traffic system became jammed; (2) the extinction rate of the lane was more influential to the fuel and emission indexes than injection rate; (3) the closer the road section to the exit, the more serious the fuel cost and emission problems, which supports the importance of research on road intersections. Acknowledgments The work was partially supported by Strategic Research Grant, City University of Hong Kong Grant (SRG 7004867), Innovation and Technology (ITF) Hong Kong (ITS/410/16FP), National Natural Science Foundation of China (No. 11302125 & 11672176), and Innovation Foundation of Shanghai Municipal Ministry of Education (No. 13YZ085). References [1] S. Fuzzi, U. Baltensperger, K. Carslaw, S. Decesari, H. Denier Van Der Gon, M.C. Facchini, D. Fowler, I. Koren, B. Langford, U. Lohmann, E. Nemitz, Particulate matter, air quality and climate: lessons learned and future needs, Atmos. Chem. Phys. 15 (14) (2015) 8217–8299. [2] R. Smit, An examination of congestion in road traffic emission models and their application to urban road networks (Doctoral dissertation), Griffith University, 2006. [3] A. Goel, P. Kumar, A review of fundamental drivers governing the emissions, dispersion and exposure to vehicle-emitted nanoparticles at signalised traffic intersections, Atmos. Environ. 97 (2014) 316–331. [4] P.G. Gipps, A behavioural car-following model for computer simulation, Transp. Res. B 15 (2) (1981) 105–111. [5] O. Biham, A.A. Middleton, D. Levine, Self-organization and a dynamical transition in traffic-flow models, Phys. Rev. A 46 (10) (1992) R6124. [6] B.S. Kerner, S.L. Klenov, D.E. Wolf, Cellular automata approach to three-phase traffic theory, J. Phys. A 35 (2002) 9971–10013. [7] T. Tang, Y. Wang, X. Yang, Y. Wu, A new car-following model accounting for varying road condition, Nonlinear Dynam. 70 (2) (2012) 1397–1405. [8] H.X. Ge, Y.X. Liu, R.J. Cheng, S.M. Lo, A modified coupled map car following model and its traffic congestion analysis, Commun. Nonlinear Sci. Numer. Simul. 17 (11) (2012) 4439–4445. [9] M. Perc, Premature seizure of traffic flow due to the introduction of evolutionary games, New J. Phys. 9 (1) (2007) 3. [10] M. Perc, J.J. Jordan, D.G. Rand, Z. Wang, S. Boccaletti, A. Szolnoki, Statistical physics of human cooperation, Phys. Rep. 687 (2017) 1–55. [11] P. Hemmerle, M. Koller, H. Rehborn, B.S. Kerner, M. Schreckenberg, Fuel consumption in empirical synchronised flow in urban traffic, IET Intel. Transport Syst. 10 (2) (2016) 122–129; B.S. Kerner, S.L. Klenov, D.E. Wolf, Cellular automata approach to three-phase traffic theory, J. Phys. A: Math. Gen. 35 (47) (2002) 9971. [12] R. Ando, Y. Nishihori, How does driving behavior change when following an eco-driving car? Procedia-Soc. Behav. Sci. 20 (2011) 577–587. [13] J. Nègre, P. Delhomme, Drivers’ self-perceptions about being an eco-driver according to their concern for the environment, beliefs on eco-driving, and driving behavior, Transp. Res. Part A: Policy Pract. 105 (2017) 95–105. [14] M.L. Yang, Y.G. Liu, Z.S. You, Investigation of fuel consumption and pollution emissions in cellular automata, Chinese J. Phys. 47 (5) (2009) 589–597. [15] A. Madani, N. Moussa, Simulation of fuel consumption and engine pollutant in cellular automaton, J. Theoret. Appl. Inf. Technol. 35 (2) (2012). [16] D. Chowdhury, L. Santen, A. Schadschneider, Statistical physics of vehicular traffic and some related systems, Phys. Rep. 329 (4) (2000) 199–329. [17] K. Nagel, M. Schreckenberg, A cellular automaton model for freeway traffic, J. Physique I 2 (12) (1992) 2221–2229. [18] S. Maerivoet, B. De Moor, Cellular automata models of road traffic, Phys. Rep. 419 (1) (2005) 1–64. [19] U. Lucia, Econophysics and bio-chemical engineering thermodynamics: The exergetic analysis of a municipality, Physica A 462 (2016) 421–430. [20] U. Lucia, G. Grisolia, Unavailability percentage as energy planning and economic choice parameter, Renewable Sustainable Energy Rev. 75 (2017) 197–204. [21] S. Dabia, E. Demir, T.V. Woensel, An exact approach for a variant of the pollution-routing problem, Transp. Sci. (2016) 1–22. [22] L.I. Panis, S. Broekx, R. Liu, Modelling instantaneous traffic emission and the influence of traffic speed limits, Sci. Total Environ. 371 (1) (2006) 270–285.
Contents lists available at ScienceDirect
Physica A journal homepage: www.elsevier.com/locate/physa
Impacts of traffic congestion on fuel rate, dissipation and particle emission in a single lane based on Nasch Model Wei Pan a , Yu Xue b , Hong-Di He c , Wei-Zhen Lu a, * a b c
Department of Architecture and Civil Engineering, City University of Hong Kong, Hong Kong Institute of Physical Science and Engineering, Guangxi University, Nanning 530004, China Logistics Research Center, Shanghai Maritime University, Shanghai 200135, China
highlights • NaSch model was applied to study impacts of congestion on the fuel and emission. • Three different aspects of traffic conditions were considered separately. • The impacts have been study both globally (whole lane) and locally (road sections).
article
info
Article history: Received 5 June 2017 Received in revised form 29 December 2017 Available online 4 March 2018 Keywords: Particle emission Fuel rate Dissipation NaSch model Traffic congestion
a b s t r a c t This paper presents simulation results of Traffic emitted particle modeling based on NaSch Model of a single lane. Three parts are constituted to the proposed model: traffic component (NaSch Model), fuel rate and dissipation component, and particle emission component. Impacts of speed limit, injection rate and extinction rate of the lane on the fuel cost and PM emission are disused in the periodic boundary condition and open boundary condition, respectively. Results from model simulation show that the critical transition point of the traffic system could also be used as a cut-off point for the change of the fuel and emission indexes. The high-speed limit was energy conservative and environmentally friendly until congestion occurred, while the low speed limit was better for smooth flowing traffic. The overall impact from the extension rate was more significant than the injection rate on all indexes, and the closer the road section was to the exit, the more fuel was consumed and the more particles were produced. The situation got better in descending order of the distance of the section to the exit. © 2018 Elsevier B.V. All rights reserved.
1. Introduction Particulate matter (PM) has become a vexing question and one of the most challenging global problems for air quality mitigation and for climate change policies [1]. Dealing with PM which originates from road transport constitutes an urgent task for megacities due to thousands of vehicles shuttling back and forth along every street. High frequency outbreaks of haze weather, PM related diseases and traffic congestion have once again appeared in the forefront as an inescapable obligation to safeguard the air quality of the general public. In addition, the variables that determine vehicular exhaust emissions are mainly fleet composition, speed, speed limits, acceleration and deceleration rates, queuing time in idle mode during the red phase, queue length, traffic flow rate and ambient wind conditions [2].
*
Corresponding author. E-mail address: [email protected] (W.-Z. Lu).
https://doi.org/10.1016/j.physa.2018.02.199 0378-4371/© 2018 Elsevier B.V. All rights reserved.
W. Pan et al. / Physica A 503 (2018) 154–162
155
However, the estimation of PM emissions from road traffic requires an in-depth understanding of traffic characteristics, which cannot be told by using traditional statistical methods that lack the capability to capture the dynamic process of traffic flow [3]. It is difficult to depict the relationship between traffic congestion and PM emissions by carrying out mobile measurements in a solo car. Consequently, the effects of congestion were only partially incorporated in the predictions and measurements. The effects of congestion on emitted PM are seldom incorporated in predictions and measurements. To depict the traffic system and illustrate the mechanism physically, many traffic flow model have been proposed and developed [4–8], and formed an interdisciplinary that includes by introducing the idea of social dilemma to investigate its role on the evolution of traffic flow and formation congestion [9,10]; and incorporated with environmental consideration to evaluate the cost of energy and emission under different driving modes [11] and behavior [12,13], etc. Yang et al. [14] studies the fuel consumption and gas emissions make by traffic by compared the results among three different traffic models in cellular automata, i.e., Nagel–Schreckenberg (NaSch), finite deceleration, and adaptive cruise control. Simulations suggested that keep driving smooth was the best way to reduce the expenditure of fuel and emission pollution. Madani and Moussa [15] investigated the fuel consumption and gas emissions caused by traffic in the NaSch model with closed boundary conditions, and found that the presence of a traffic light has a big effect on fuel consumption. In light of this, this paper combines the classical NaSch model and emission function based on empirical measurement, with objective is to investigate the effects of traffic congestion on the atmosphere due the emitted PMs from on-the-road vehicles, and also the impact on the fuel rate and dissipation. 2. Methodology Three components were integrated in the model of this study: (1) traffic, (2) fuel rate and dissipation consumption, and (3) particle emission. 2.1. Traffic component The aim of introducing the traffic component was to gain a speed–time profile to provide the necessary information that would enable the model with the ability to depict the macroscopic flux, fuel consumption, and particle emission of the traffic flow by simulating every individual vehicle movement microscopically. Among multiple traffic models [16], cellular automaton (CA) ones, microscopically, were most popular for their simple algorithm, high generalization and rich phenomena. The adopted CA model in this study was the NaSch model [17], which was able to reproduce the spontaneous emergence of traffic jams and was known as the first stochastic traffic cellular automaton model. Generally, the NaSch model was defined on a one-dimensional array L in a dimensionless manner, in which each site may either be empty or occupied by one vehicle that has an integer speed in the range between zero and a maximum speed (smax ). For an arbitrary configuration, the NaSch model followed four consecutive steps, which were performed in parallel for all vehicles [18]: Step 1. Acceleration: s (i, t + 1/3) → min (s (i, t ) + 1, smax )
(1)
Step 2. Deceleration: s (i, t + 2/3) → min (s (i, t + 1/3) , gapn )
(2)
Step 3. Randomization with probability p: s (i, t + 1) → max (s (i, t + 2/3) − 1, 0)
(3)
Step 4. Car motion: x (i, t + 1) → x (i, t ) + s (i, t + 1)
(4)
where s (i, t ) and x (i, t ) are the speed and position of the vehicle i on the road at time step t. Before the determination of its motion for the next time step t + 1, the vehicle i should go through three steps (i.e. acceleration, deceleration and randomization). These steps represent three common situations during the driving process. The randomization probability p is a stochastic braking noise that makes the vehicles decelerate without backing. In general, there were two boundary conditions for CA simulation, i.e., periodic boundary condition and open boundary condition. The periodic boundary condition indicated that the number of vehicles in the system was conserved (conservation), determined by the occupation rate ρ ; the lane was similar to a closed loop. While the open boundary condition meant that vehicles could move into or get out of the lane with certain probability, determined by two adjustable parameters (i.e., injection rate α and extinction rate β ), and the number of vehicles was not conserved (non-conservation) in the simulation system. Compared to realistic traffic, it was easy to rescale the model and make comparisons with a realistic scenario by converting the length of one site and a simulation time step into 5 m of place and one second of time in a real road scenario, respectively. For example, the smax = 5 in the simulation system and was equivalent to the speed of 90 km/h. This conversion laid the foundation for the subsequent fuel and emission estimation.
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W. Pan et al. / Physica A 503 (2018) 154–162 Table 1 Parameters for Eq. (5). Notation
Description
Selected values
ξ κ ψ
Fuel to air mass ratio Heating value of a typical diesel fuel (kJ/g) Conversion factor (g/s to L/s) Engine friction factor (kJ/rev/liter) Engine speed (rev/s) Engine displacement (liters) Efficiency parameter for diesel engines Curb weight (kg) Payload (kg) Instantaneous acceleration (m/s2 ) Road gradient (%) Coefficient of aerodynamic drag Air density (kg/m3 ) Frontal surface area (m2 ) Gravitational constant (m/s2 ) Coefficient of rolling resistance Vehicle drive train efficiency Engine power demand for accessories
1 44 737 0.25 40 7 0.9 11 250 5850 0 0 0.7 1.2041 3.912 9.81 0.01 0.4 0
k N V
η w q
χ θ Cd
ρ
A g Cr ntf Pacc
Table 2 Parameters for Eq. (7). E0
f1
f2
f3
f4
f5
f6
0
2.14 × 10−4
3.35 × 10−4
−2.22 × 10−5
2.07 × 10−3
1.80 × 10−3
2.27×10−4
2.2. Fuel rate and dissipation component Energy cost should be the optimum balance between economic and environmental factors [19,20]. Fuel consumption is the relationship between the distance traveled and the amount of fuel consumed by the vehicle, while the fuel rate is defined by the time traveled instead of distance traveled, according to the protocol set for this study. Dissipation was considered only in the deceleration scenario since speed down (i.e., rolling resistance and brake) caused energy (fuel) to dissipate, which was generally not expected. The fuel rate (f ) [21] in liters per second and its dissipation rate (d) for an arbitrary vehicle i at time step t are defined as:
ξ f (i, t ) = κψ (
{ kNV +
1000ηtf
d (i, t ) =
{
)−1
1 (((
η
) ) (w + q) (χ + gsnθ + gCr cosθ) + 0.5Cd ρ As(i, t )2 s (i, t ) · )}
+ Pacc b
f (i, t − 1) − fc (i, t ) , 0
for s (i, t ) < s (i, t − 1) other .
(5)
(6)
All parameters along with typical values used in the simulation are provided in Table 1. The fuel dissipation ratio is the result of the dissipation rate over the fuel rate, which could be used to quantify the proportion of the dissipated fuel in the total fuel consumption. 2.3. Particle emission component The estimation modeling of pollutants must use emission factors obtained from in-situ vehicle tracing measurements. Generally, the required ‘factor’ information can be categorized into two types: distance-based (g/km) and time-based (g/s). In light of the NaSch model, distance-dimensionless with its simulation time step is equivalent to the real time, time-based (g/s) emission factor would be the priority choice. Hence, a general emission function proposed by using nonlinear multiple regression techniques based on empirical measurements was given as [22]: e (i, t ) = max E0 , f1 + f2 s (i, t ) + f3 s2 (i, t ) + f4 a (i, t ) + f5 a2 (i, t ) + f6 s (i, t ) a (i, t )
[
]
(7)
where E0 was a lower limit emission specified for both pollutant types and vehicle catology, and f1 to f6 were emission constants determined by the regression analysis. Table 2 only shows related values to be used in a later simulation. The simulation of the traffic behavior and related fuel rate (f ), dissipation (d) and particle emission (e) were performed in periodic boundary condition and open boundary condition, respectively. The length of the lane was set to be L = 105
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Fig. 1. Periodic boundary results of the general case with p = 0.2, smax = 5.
cells L = 1 × 105 × L, which amounts to 50 km. The averages per vehicle were obtained by averaging over 30 independent initial realizations up to 3 × 105 iteration steps for each run and by discarding the first 2 × 105 iteration steps as transient time.
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3. Results and discussion 3.1. A general case According to classical traffic theory, the estimation of the capability of vehicles moving on the road is based on the flux or mean speed which we consider to be fundamental diagrams. The fundamental diagrams and relevant results (fuel consumption, dissipation and PM emissions) for a general case with probability p = 0.2 and maximum speed smax = 5 are shown in Fig. 1(a)–(b) and (c)–(h). The occupation rate (ρ ) indicated the proportion of lattices that had been occupied, which amounted to the lane usage rate under periodic boundary condition. The increasing ρ made the global flow of the lane (Fig. 1(a)) straight climbs to peak value (i.e., ρ ≈ 0.29) at first, which was called critical transition point, then collapsed after that, until there was no more space for a vehicle when global congestion happened (i.e., ρ ≈ 1.00). This presents a first phase transition process from free flow (i.e., increasing flow rate) into jamming phase (i.e., declining flow rate), which corresponded to the mean speed that kept maximum level at first (i.e., platform in Fig. 1(b)) and gradually declined until it approached zero. In Fig. 1(c), the average ratio of vehicle states (i.e., acceleration, deceleration, following the frontal car, and jamming or stopping where speed equals zero) were provided according to the increasing occupancy ρ . Before reaching the critical point, most cars followed each other at the prescribed speed, and did not encounter congestion. Moreover, vehicles in the state of acceleration and deceleration underwent the same conditions. When reaching the critical point, stopped cars emerged with most of participants following slowing down at the same time, until time to accelerate and then the acceleration ratio began to exceed the deceleration. Two cross points are noted in Fig. 1(c): One is the intersection point between following and stopping (P1 ), the other is the intersection point between acceleration and stopping (P2 ), discussed later. Since speed was the only independent variable of Eq. (5), it is no surprise that the fuel rate had the same pattern relationship to the speed as shown in Fig. 1(d). But the dissipation due to deceleration had a unique change style, described as staircase-like as indicated in Fig. 1(e), which meant that although the fuel rate declined continuously, after a critical point, the net dissipation rate changed stage by stage. Meanwhile, the fuel dissipation ratio (Fig. 1(f)), the PM emission rate (Fig. 1(g)) and the PM emission of unit fuel consumption (Fig. 1(h)) shared a similar trend curve, as the lane became more occupied. The peak position of the PM emission rate was ρ ≈ 0.55, which was different from that of the dissipation ratio and PM emission per fuel consumption (i.e. , ρ ≈ 0.66). The corresponding values of the two occupation rates (free flow and jamming) of the two intersection points (P1 and P2 ) in Fig. 1(c) remained the same by not exceeding the two peaks set for fuel dissipation ratio (or PM per fuel consumption) and PM emission rate, respectively. This general case indicated that the critical transition points of the traffic system were not only the index that determined the traffic phases, but also helped identify the trend of fuel cost and particle emissions. As the lane became jammed, three events occurred: (1) the critical transition point of the fundamental diagram also served as the transition point to all fuel and emission indexes; (2) when the PM emission rate was the highest, the unit combustion generated PM and dissipated ratios were not in their worst situation; (3) the ratio of vehicle states could be used to identify the behavior of fuel dissipation and its PM emission. 3.2. Impact of the speed limit The speed limit was the maximum allowed to legally travel on a public road, mostly for safety reasons and could vary from region to region. In Fig. 2, simulations were performed under three different speed limits (i.e., smax = 3, 4 and 5) with randomization probability p = 0.3 to compare the effects of speed with concerns relating to fuel and the emission. The fuel rate plot in Fig. 2(a) shows that more fuel was needed for a vehicle to travel on the lane with a higher speed limit, which aligned with general knowledge. Influence from speed limits was getting smaller and smaller after the occupation rate increased, which had drivers enjoying the maximum legal speed in the free-flow phase, but then reached its respective critical points (congestion slowing traffic down to the jamming phase), which meant that the lower speed limit for fuel saving only worked in the phase of free flow, and the advantage would be more and more insignificant as traffic became more and more congested. In Fig. 2(b), the fuel dissipation ratios for three speed limits were almost the same in the phases of free flow and the last stage of congestion. The major differences happened in the first stage of the congestion phase (i.e., ρ in the range of 0.2–0.8), where peak value emerged and the higher speed limit represented a bigger proportion of dissipated fuel. As for the particle emission, the emission rate and unit fuel combustion produced PM were all in their lower level in the free flow ranges, but changed conversely at the first stage of the congestion phase when they reached their peak, and gradually leveled off until the end, as indicated in Fig. 2(c) and (d). For a lower speed limit, the emission rate and unit fuel-generated particles (exhaust emissions) were lower in the free flow phase compared with the jammed flow, From here on, the impact of speed limit on the fuel and particle emission depended on phases and stages of the traffic system involved in (1) the free flow phase, where a lower speed limit needed fewer fuel and produced less particle to the ambient; (2) in the jamming phase, although the fuel rate was the same, high speed limit was a better choice for the control of PM emission.
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159
Fig. 2. The impact of speed limit smax with p = 0.3.
Fig. 3. Schematic of the lane with open boundary condition.
3.3. Impact of the extinction rate and injection rate The schematic of the lane with an open boundary condition is illustrated in Fig. 3. Vehicles could access the lane at the entrance on the left side with the injection rate α , and get out of the lane at the exit on the right side with the extinction rate β . The whole lane was divided into five sections (S1 –S5 ) with the same interval length. The aim of performing the simulation under open boundary conditions was to investigate the influence of inflow and outflow on the fuel rate and PM emission counts from different lane sections. First, the influence of extension rate β on traffic behavior, fuel and PM emissions based on the average results of the whole land per vehicle data is discussed and results are exhibited in Fig. 4. As the injection probability (α ) increased, the vehicle was more likely to drive at maximum speed and take less time and fuel to pass through at the same time as when the extension rate was high enough, as shown in Fig. 4(a)–(c). However, as the β increased (i.e., β = 0.1, 0.3, and 0.5), corresponding velocity plots shared a very interesting transient trend that declined first and rose thereafter. It indicated that even when achieving some level of injection rate with little outside interference (i.e., p = 0.2), the bigger β does not guarantee higher mobility (i.e., speed). This also influenced the performance of the total fuel dissipation, PM emission and emission rate per fuel consumption in Fig. 4(d)–(f), which was largely due to the strong interaction between vehicles on the lane when β was not big enough (0.3 and 0.5 here), and the effect of synchronization became more significant compared to small extinction rate (i.e., 0.1). In addition, the subtotals of the fuel cost and PM emissions for the five sections of the lane were different. For a giving extension rate shown in Fig. 5(a) (i.e., β = 0.5), the general trend of the total fuel consumption per vehicle passing through sections was uniform at the low injection rate (i.e., β < 0.2), then went up to reach the peak point (or a platform) at the medium injection rate range of (0.4, 0.8), and gradually recovered to the same level of the low injection rate. But in different sections, the fuel costs varied and were highest for S5 , which was the nearest to the exit of the lane. Moreover, the consumption became smaller successively in a descending order of section number from S4 to S1 . This was also reflected in
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Fig. 4. The impact of extinction rate β on the average results of the whole land with p = 0.2, smax = 5.
Fig. 5. Impact on different segments with p = 0.2, smax = 5, β = 0.5.
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Fig. 6. The impact of injection rate α on the average results of the whole land with p = 0.2, v max = 5.
relevance to the total PM emissions, as indicated in Fig. 5(b), which means that when the outbound probability was fixed, the emission problem was more serious in the exit included section, at least to the ones near an entrance. Meanwhile, circumstances related to the injection rate were simpler, as indicated in Figs. 6 and 7. Results of injection rate under the simulation condition of p = 0.2, smax = 5 for the lane average per car shown in Fig. 6(a)–(f) reflected that, when α < 0.5, the smaller of the injection rate the better and bigger the injection rate was preferably when α > 0.5, and all indexes were all worse when α = 0.5. This meant that for fixed extinction rate, the impact of increasing injection rate on all indexes (i.e., fuel cost, dissipation, particle emission and its emission per fuel cost) was identified by the speed plot. Similar to Fig. 5, the section curved in Fig. 7 showing that for fixed injection rates, S5 still produced the most PM emissions and consumed more fuel compared to other sections. Results became better in the descending order of the section numbers. Hence, simulations based on open boundary conditions provided here suggest that: (1) ensuring a smooth export (i.e., sufficient large β ) will always help cut the fuel cost and mitigate the PM polluted levels; (2) the fuel cost and traffic-made particulate pollution in the road section close to the exit was always severe compared to those sections closer to the entrance. 4. Conclusion In this paper, a model was successfully integrated and applied to depict the dynamics of traffic flow, and its relation to the fuel rate, dissipation, and particle emissions on a single lane. This traffic component was NaSch based, and simulations
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Fig. 7. Impact on different segments with p = 0.2, smax = 5, α = 0.5.
were performed in a periodic boundary condition and an open boundary condition, respectively. The general case proved the applicability of this model, and there was a shift between the peak location of the fuel dissipated ratio (or unit fuel produced particle) and particle emission rate. Moreover, impact from the speed limit, injection rate and extinction rate were estimated respectively. Major concluding remarks are (1) in the free flow phase, low speed limit was more energy conservative and environmentally friendly, while the high speed limit was better when the traffic system became jammed; (2) the extinction rate of the lane was more influential to the fuel and emission indexes than injection rate; (3) the closer the road section to the exit, the more serious the fuel cost and emission problems, which supports the importance of research on road intersections. Acknowledgments The work was partially supported by Strategic Research Grant, City University of Hong Kong Grant (SRG 7004867), Innovation and Technology (ITF) Hong Kong (ITS/410/16FP), National Natural Science Foundation of China (No. 11302125 & 11672176), and Innovation Foundation of Shanghai Municipal Ministry of Education (No. 13YZ085). References [1] S. Fuzzi, U. Baltensperger, K. Carslaw, S. Decesari, H. Denier Van Der Gon, M.C. Facchini, D. Fowler, I. Koren, B. Langford, U. Lohmann, E. Nemitz, Particulate matter, air quality and climate: lessons learned and future needs, Atmos. Chem. Phys. 15 (14) (2015) 8217–8299. [2] R. Smit, An examination of congestion in road traffic emission models and their application to urban road networks (Doctoral dissertation), Griffith University, 2006. [3] A. Goel, P. Kumar, A review of fundamental drivers governing the emissions, dispersion and exposure to vehicle-emitted nanoparticles at signalised traffic intersections, Atmos. Environ. 97 (2014) 316–331. [4] P.G. Gipps, A behavioural car-following model for computer simulation, Transp. Res. B 15 (2) (1981) 105–111. [5] O. Biham, A.A. Middleton, D. Levine, Self-organization and a dynamical transition in traffic-flow models, Phys. Rev. A 46 (10) (1992) R6124. [6] B.S. Kerner, S.L. Klenov, D.E. Wolf, Cellular automata approach to three-phase traffic theory, J. Phys. A 35 (2002) 9971–10013. [7] T. Tang, Y. Wang, X. Yang, Y. Wu, A new car-following model accounting for varying road condition, Nonlinear Dynam. 70 (2) (2012) 1397–1405. [8] H.X. Ge, Y.X. Liu, R.J. Cheng, S.M. Lo, A modified coupled map car following model and its traffic congestion analysis, Commun. Nonlinear Sci. Numer. Simul. 17 (11) (2012) 4439–4445. [9] M. Perc, Premature seizure of traffic flow due to the introduction of evolutionary games, New J. Phys. 9 (1) (2007) 3. [10] M. Perc, J.J. Jordan, D.G. Rand, Z. Wang, S. Boccaletti, A. Szolnoki, Statistical physics of human cooperation, Phys. Rep. 687 (2017) 1–55. [11] P. Hemmerle, M. Koller, H. Rehborn, B.S. Kerner, M. Schreckenberg, Fuel consumption in empirical synchronised flow in urban traffic, IET Intel. Transport Syst. 10 (2) (2016) 122–129; B.S. Kerner, S.L. Klenov, D.E. Wolf, Cellular automata approach to three-phase traffic theory, J. Phys. A: Math. Gen. 35 (47) (2002) 9971. [12] R. Ando, Y. Nishihori, How does driving behavior change when following an eco-driving car? Procedia-Soc. Behav. Sci. 20 (2011) 577–587. [13] J. Nègre, P. Delhomme, Drivers’ self-perceptions about being an eco-driver according to their concern for the environment, beliefs on eco-driving, and driving behavior, Transp. Res. Part A: Policy Pract. 105 (2017) 95–105. [14] M.L. Yang, Y.G. Liu, Z.S. You, Investigation of fuel consumption and pollution emissions in cellular automata, Chinese J. Phys. 47 (5) (2009) 589–597. [15] A. Madani, N. Moussa, Simulation of fuel consumption and engine pollutant in cellular automaton, J. Theoret. Appl. Inf. Technol. 35 (2) (2012). [16] D. Chowdhury, L. Santen, A. Schadschneider, Statistical physics of vehicular traffic and some related systems, Phys. Rep. 329 (4) (2000) 199–329. [17] K. Nagel, M. Schreckenberg, A cellular automaton model for freeway traffic, J. Physique I 2 (12) (1992) 2221–2229. [18] S. Maerivoet, B. De Moor, Cellular automata models of road traffic, Phys. Rep. 419 (1) (2005) 1–64. [19] U. Lucia, Econophysics and bio-chemical engineering thermodynamics: The exergetic analysis of a municipality, Physica A 462 (2016) 421–430. [20] U. Lucia, G. Grisolia, Unavailability percentage as energy planning and economic choice parameter, Renewable Sustainable Energy Rev. 75 (2017) 197–204. [21] S. Dabia, E. Demir, T.V. Woensel, An exact approach for a variant of the pollution-routing problem, Transp. Sci. (2016) 1–22. [22] L.I. Panis, S. Broekx, R. Liu, Modelling instantaneous traffic emission and the influence of traffic speed limits, Sci. Total Environ. 371 (1) (2006) 270–285.