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Study on pollutant emissions of mixed traffic flow in cellular automaton
Physica A 537 (2020) 122686
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Physica A journal homepage: www.elsevier.com/locate/physa
Study on pollutant emissions of mixed traffic flow in cellular automaton ∗
Wang Xue a , Xue Yu a,b , , Cen Bing-ling a , Zhang Peng a , He Hong-di c a
Institute of Physical Science and Technology, Guangxi University, Nanning 53004, China Key Lab Relativist Astrophys, Nanning 530004, Guangxi, People’s Republic of China c Logistics Research Center & Shanghai Engineering Research Center of Shipping Logistics Information, Shanghai Maritime University, Shanghai 200135, China b
article
info
Article history: Received 20 April 2019 Received in revised form 18 August 2019 Available online 18 September 2019 Keywords: Emission Pollutant Mixed traffic Cellular automaton
a b s t r a c t Based on mixed NaSch traffic flow model and the empirical formula of automobile exhaust emissions, emissions of particulate matter (PM), CO2 , NOx and volatile organic compounds (VOC) are investigated with consideration of the different movement conditions, mixing ratios, the maximum velocity and lengths of vehicle. Pollutant emissions are determined by traffic characteristics from free-flow to congestion. Emissions of mixed traffic increase with the mixing ratio increasing. The impact of traffic state on emissions is discussed in detail by introducing the distribution functions for three types of motion states. Results show that decelerating vehicles discharge the most pollutants even if accelerating and decelerating vehicles in the congested state have a great impact on pollutant emissions in the mixed traffic flow. The effect of the maximum velocity and the length of vehicles on emission are investigated, respectively. It is found that the maximum velocity of the short vehicles has a significant impact on emissions when the mixing ratio and length of vehicles are fixed. The larger the maximum velocity of the short vehicles, the more the emissions is, but the maximum velocity of long vehicles does not display obvious effect. When the mixing ratio is given, the longer the vehicle, the less the emissions are due to restrictions on the loop road. © 2019 Published by Elsevier B.V.
1. Introduction In recent years, air quality has become increasingly terrible. It is one of the important factors to condition global development. In the metropolises, the motor vehicle fleet and the increasing emissions of toxic pollutants by industrial sources, cause high concentrations of harmful substances that are responsible for low visibility and various respiratory problems [1,2]. The most of particulate matter (PM), CO2 , VOC and NOX pollutants are caused by thousands of vehicles emissions [3]. Moreover, recent studies have shown that the tiny particulate matter (PM) takes on multifractal property and long-range cross-correlation behavior via analyzing data of the field measure in Hong Kong and Shanghai [4–6]. Vehicles emissions have unavoidable responsibility that cause hazy weather, respiratory diseases and traffic congestion [7]. In addition, it is the most pressing problem to improve city atmosphere quality by dealing with emissions (PM, CO2 , VOC and NOX ) form transportation. The variables which determine vehicle emissions mainly are composed vehicle types and size, velocity, velocity limits, acceleration, queuing time in idle mode during red phase, queue length and traffic flow rate [8]. However, the traditional measure to calculate PM, CO2 , VOC and NOX emission observes every moment ∗ Corresponding author at: Institute of Physical Science and Technology, Guangxi University, Nanning 53004, China. E-mail address: [email protected] (Y. Xu). https://doi.org/10.1016/j.physa.2019.122686 0378-4371/© 2019 Published by Elsevier B.V.
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Table 1 Parameters for Eq. (5). Pollutant
Vehicle type
E0
f1
f2
f3
f4
f5
f6
CO2
Diesel Bus Diesel Bus Diesel Bus Diesel Bus
0 0 0 0 0 0 0 0
3.24e−01 9.04e−01 2.41e−03 2.36e−02 9.22e−05 1.55e−03 0.00e+00 2.23e−04
8.59e−02 1.13e+00 −4.11e−04 6.51e−03 9.09e−6 8.20e−04 3.13e−04 3.47e−04
4.96e−03 −4.27e−02 6.73e−05 −1.70e−04 −2.29e−07 −2.42e−05 −1.84e−05 −2.38e−05
−5.86e−02 2.81e+00 −3.07e−03 2.17e−02 −2.20e−05 1.86e−03 0.0e+00 2.08e−03
4.48e−01 3.45e+00 2.14e−03 8.94e−03 1.69e−05 3.21e−04 7.50e−04 1.76e−03
2.30e−01 1.22e+00 1.50e−03 7.57e−03 3.75e−06 1.36e−04 3.78e−04 2.23e−04
NOX VOC PM
car car car car
Fig. 1. Fundamental diagram of the mixed traffic (p1 = 0.25, p2 = 0.5).
vehicle on the roads and counts data with vehicle exhaust emission. It is difficult to describe that PM, CO2 , VOC and NOX emission from different road traffic and complex traffic composition by the traditional method. At the same time, it cannot accomplish the estimation of PM, CO2 , VOC and NOX emission from road traffic. The influence from intricate traffic structure and traffic congestion on PM, CO2 , VOC and NOX emission is hard to observe field test. There are many traffic flow models [9–14], which depicts the traffic system and investigates the mechanism of traffic flow evolution and traffic congestion [9,10,15,16]. Meanwhile, these traffic models can combine with the impact of vehicle exhaust emission on the environmental ambient air. Treiber and Kesting present a model for the instantaneous fuel consumption that includes vehicle properties, engine properties, and gear-selection schemes and implement it for different passenger car types representing the vehicle fleet under consideration. Treiber and Kesting concluded that the influence of congestions on fuel consumption is distinctly lower than that on travel time [17]. Madani and Moussa adopted cellular automaton for simulation of fuel consumption and engine pollutant [18]. Tian et al. and Wen at al respectively studied the energy consumption of the mixed traffic in cellular automaton NaSch model and FI model [19,20]. Results manifest the length of vehicles, the maximum velocity and the mixing ratio of mixed traffic have a great impact on the energy dissipation. Tang et al. proposes an extended car-following model to study the influences of the driver’s bounded rationality on his/her micro driving behavior. The numerical results indicated that considering the driver’s bounded rationality will reduce his/her velocity during the starting process and improve the stability of the traffic flow during the evolution of the small perturbation [21]. Tang et al. used the car-following model to study the impacts of fuel consumption and emissions on the trip cost without late arrival at the equilibrium state and the effect if signal light on fuel consumption and emissions [22,23], the relation of the trip cost with fuel consumption of vehicles in single-lane traffic and two-lane traffic were also analyzed [24–26]. Zhu et al. investigated delay-feedback control strategy for reducing CO2 emission of traffic flow system [27] and an original traffic additional emission model and numerical simulation on a signalized road [28]. Pan et al. carried out the simulations for homogeneous traffic PM emissions by using cellular automaton Nagel–Schreckenberg (NaSch) model. The simulation results indicated that in the free flow, low velocity limit was more energy conservative and environmentally friendly, while the high velocity limit was better when the traffic system became jammed [29]. In this paper, we will study on pollutant emissions of mixed traffic flow which is composed of vehicles with the different length and the maximum velocity. In Section 2 the cellular automaton model of mixed traffic flow is proposed
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Fig. 2. PM emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
based on NaSch model and corresponding empirical emission model is given. In Section 3 we devoted to the effects of the different mixing ratio, pollutant type and vehicles in the different state of motion on pollutant discharge by numerical simulation and theoretical analysis. Finally, this paper is concluded. 2. Methodology 2.1. Traffic models Among many traffic models, cellular automation (CA) traffic model is one of the most popular ones due to its simple algorithm and highly applicability. NaSch model [30] is able to reproduce the spontaneous phenomenon of traffic congestion and is known as the stochastic traffic cellular automaton model. In what follows, we assumed a closed-loop lattice of L cells forms a mixed traffic flow. A typical discretization scheme assumes ∆t = 1 s and ∆L = 7.5 m corresponding to velocity increments of ∆v = ∆L/∆t = 7.5 m/s [31]. At every moment each cell may be occupied by a vehicle with the different length and the different velocity in the range of zero
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Fig. 3. CO2 emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
and a maximum velocity or without vehicles. The short vehicle and the long vehicle respectively take up LS cells and LL (LL > LS ) cells. In the initial moment all of vehicles are distributed in the cells according to the mixing ratios Cn , where long vehicle with length LL at first occupies LL cells and each short vehicle occupies LS cell. When the number of long vehicle is small, long vehicles are randomly distributed in the L cells. The long vehicle gradually increasing leads to its uniformly distributed in the L cells and then each short vehicle with unit length is randomly distributed in the rest of cells. The velocity of each vehicle on single-lane is distributed randomly. At each evolutionary time step t → t + 1, all vehicle states are updated in parallel according to the evolution rules of NaSch model. The update rules of each vehicle state evolution in mixed traffic flow are [31]: Step 1. Acceleration: 1
v (i, t + ) → min(v (i, t) + 1, vmax )
3 Step 2. Deceleration: 2
1
3
3
v (i, t + ) → min(v (i, t + ), gapi (t))
(1)
(2)
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Fig. 4. NOx emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
Step 3. Randomization with probability p: 2
v (i, t + 1) → max(v (i, t + ) − 1, 0) 3
(3)
Step 4. motion: x(i, t + 1) → x(i, t) + v (i, t + 1)
(4)
where v (i, t) and x(i, t) denote as the velocity and position of the ith vehicle on the road at time step t. If the vehicle is short, the headway between the ith and the (i + 1)th in front of it at time t is gapi (t) = x(i + 1, t) − x(i, t) − LS . Similarly, the gap of long vehicle between the ith and the (i + 1)th is gapi (t) = x(i + 1, t) − x(i, t) − LL . The number of vehicles in the system is conserved and their distribution on road is given by the occupation rate C. The mixed traffic flow composed of vehicles with the different lengths is determined by the mixing ratio Cn . That is to say, the mixing ratio Cn yields the number of long vehicle and short one on road. The conservation of number of vehicles is easy to calculate the subsequent fuel and emission estimation.
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Fig. 5. VOC emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
2.2. Emission models
Panis et al. [32] have studied traffic emissions under the influence of instantaneous velocity and acceleration. They used nonlinear multivariate regression techniques to establish an emission model. The model is based on the measurement results of real urban driving conditions. Later, this model was extended to the exhaust emission of vehicles when driving on high ways [33]. En (t) is pollutant emission for the nth vehicle in unit time. En (t) = max[E0 , f1 + f2 vn (t) + f3 vn (t)2 + f4 an (t) + f5 an (t)2 + f6 vn (t)an (t)]
(5)
where E0 is a lower limit of emission (g/s) specified for each vehicle and pollutant type, and f1 to f6 are emission parameter specific for each vehicle and pollutant type determined by the regression analysis. All of specified parameters value is given in Table 1 [32].
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Fig. 6. PM emission of accelerating vehicles for different mixing ratio (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
3. Simulation and analysis
Number of vehicles on the road is denoted as N and the global density is ρ = NL . The number of long vehicle is denoted as N L and correspondingly the number of short one is expressed as N S . Long vehicle with length LL occupies LL cells and short one occupies a unit cell. The occupancy of long vehicles is the ratio of the number of long vehicle times its length to the length of lane (C L = N L × LL /L) and accordingly the occupancy of short one equals to C S = N S × LS /L. Therefore, the total occupancy is expressed as C = (N S × LS + N L × LL )/L. The mixing ratio Cn is defined as Cn = C L /C, which is to measure the proportion of long vehicles in mixed traffic flow. The relation of the occupancy of long and short vehicles to the total occupancy is obtained as C L = Cn C and C S = (1 − Cn ) C , respectively. The global density is represented as
[ ] ρ = C (1 − Cn ) /LS + Cn /LL [19].
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Fig. 7. Fraction of accelerating vehicles vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
Road is a closed-loop lattice consisting of L = 104 cells. The periodic boundary condition is adopted for simulation. The average velocity v of traffic flow is defined as follows.
v=
t0 + T N 1 1 ∑ ∑
T N
v (i, t)
(6)
t =t0 +1 i=1
where t0 is the relaxation time to reach steady state. The fundamental diagram (flow vs. occupancy rate) of mixed traffic flow is obtained for different mixing ratio Cn by numerical simulations. In order to determine overall vehicle emissions, the average vehicle emission based on Eq. (5) is defined as follows. E=
t0 +T N 1 1 ∑ ∑
T N
Ei (t)
(7)
t =t0 +1 i=1
where Ei (t) represents the pollutant emission of the ith vehicle at time t. The average vehicle emission reflects pollutant emissions of traffic flow on the whole. The average vehicle emission and the averages velocity are obtained in the process of simulations by averaging over 50 independent initial realizations up to 3 × 105 iteration steps for each run and by discarding the first 2 × 105 iteration steps as transient time. Exhaust emissions of the short vehicle refer to the emission
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Fig. 8. PM emission of decelerating vehicles for different mixing ratios (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
parameters of the diesel cars. Similarly, emission of the long vehicle corresponds to the parameters of the bus or heavy vehicle. In order to consider the influence of vehicle motion state on mixed traffic exhaust emission, we first study the fundamental diagram (flow vs. occupancy rate) of mixed traffic flow for different mixing ratio Cn . The mixed traffic flow on road is composed of vehicles with different lengths and velocities in terms of the mixing ratio Cn . The long vehicle with L the maximum velocity vmax = 40 cells/timestep occupies 10 cells at initial moment. For simplicity, each short vehicle as S a unit occupies a cell and its maximum velocity vmax equals to 5 cells/timestep. Randomization probability p1 for short car and long vehicle is selected as p1 = 0.25 and p2 = 0.5, respectively. The fundamental diagram (flow vs. occupancy rate) of mixed traffic flow with mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0 are shown in Fig. 1. Fig. 1 shows that the fundamental diagram of mixed traffic flow is divided into two regions: free-flow and congested area. When the mixing ratio Cn = 0.2, 0.4, 0.8, the peak of curve decreases with the increase of mixing ratio and critical point increases. When the mixing ratio Cn = 1.0, it implies that all of vehicles on road are made up of long vehicle. The
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Fig. 9. Fraction of decelerating vehicles vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
curve in the fundamental diagram shows discontinuity at occupancy rate C ≈ 0.12, which indicates the occurrence of traffic congestion. The curve with a occupancy rate C greater than 0.12(>0.12) represents traffic jamming. 3.1. Emissions under different occupancy rates In this section, the average PM CO2 NOx and VOC emissions of mixed traffic flow are investigated for the mixing ratio Cn = 0.2, 0.4, 0.8 and 1.0. Fig. 2(a) shows the average emission of PM for mixing ratios Cn = 0.2, 0.4 and 0.8. Comparing with the fundamental diagram of mixed traffic flow in Fig. 1, PM emissions gradually rise to a peak and then go down to 0 g/s, which just corresponds to the state of traffic flow from free-flow to congestion. PM emission reaches a peak of 5.03 g/s at the occupancy rate C ≈ 0.28 for the mixing ratio of 0.2. Similarly, the maximum value of PM emission respectively reaches 5.14 g/s at occupancy rate C = 0.32 for mixing ratio Cn = 0.4 and 6.15 g/s at occupancy rate C = 0.44 for mixing ratio Cn = 0.8. It indicates that PM emissions increase as the mixing ratio Cn increasing. For the mixing ratio Cn = 1.0, Fig. 2(b)
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Fig. 10. Emission of PM of following vehicle for different mixing ratios (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
exhibits PM emissions for the vehicle length LL = 2, 5, 10 and 20 cells, respectively. Similar to change trend in the fundamental diagram of mixed traffic flow in Fig. 1, PM emissions in Fig. 2(b) reveal the discontinuity from free-flow to congestion and transition point corresponds to the maximum emission. Simulation shows the emission peak emerges in the state of stop&go traffic. The maximum emission respectively equals to 0.32 g/s, 0.33 g/s, 0.33 g/s and 0.35 g/s corresponding to the occupancy C ≈ 0.06, 0.16, 0.18 and 0.32 for vehicle length LL = 2, 5, 10 and 20 cells. Fig. 2(b) indicates that the longer the vehicle is, the more the PM emission will be. It is confirmed that the PM emission of bus is more than one of Diesel car when bus and Diesel car are mixed. CO2 emission for mixing ratios Cn = 0.2, 0.4 and 0.8 is shown in Fig. 3(a). Similar to change trend in PM emission of mixed traffic flow in Fig. 2, CO2 emission has a peak and then go down to 0 g/s for mixing ratios Cn = 0.2, 0.4 and 0.8. It indicates that traffic flow varies from free-flow to congestion. Moreover, Fig. 3(b) exhibits CO2 emission for mixing ratios Cn = 1.0 with the discontinuity from free-flow to congestion and reaches the maximum emission at transition point and the longer the vehicle is, the more the PM emissions. As can be seen from Figs. 4 and 5, NOx and VOC emissions have similar behaviors like CO2 emission for mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0. The change trends in NOx and VOC emissions for mixing ratios Cn = 0.2, 0.4 and 0.8 in Figs. 4(a) and 5(a) indicate that traffic flow varies from free-flow to congestion. NOx and VOC emissions for mixing ratios Cn = 1.0 in
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Fig. 11. Fraction of following vehicles vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
Figs. 4(b) and 5(b) emerge the discontinuity from free-flow to congestion, which is determined the fundamental diagram in Fig. 1. From the average emissions of PM, CO2 , NOx and VOC, it is found that pollutant emissions increase as the mixing ratio Cn increasing. The more the number of the long vehicle increases, the more the emissions. Meanwhile, traffic characteristics from free-flow to congestion determine pollutant emissions as a whole. 3.2. Effect of vehicle motion state on emission In order to further study the emission characteristics of mixed traffic flow in detail, we classify the motion state of vehicle into three types: acceleration (vi (t + 1) > vi (t)), deceleration (vi (t + 1) < vi (t)) and follow or uniform motion (vi (t + 1) = vi (t)). The emission characteristic in the state of the three types is explored. Meanwhile, the number distribution function by introducing for three types of motion states gives a reasonable explanation for these emission characteristics.
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Fig. 12. PM emission vs. occupation rate for the maximum velocity of vehicles (p1 = 0.25, p2 = 0.5, vL max = 40). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
The fraction of vehicle number in the state of acceleration, deceleration and follow is defined as follows. fs =
t0 1 1 ∑
T N
ns
t =t0 +1
where ns represents the number of vehicles accelerating (na ), decelerating (nd ) or following (nf ) in time t [20]. Fig. 6(a) and (b) corresponds to PM emission of accelerating vehicle for different mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. In contrast to the fundamental diagram of mixed traffic flow in Fig. 1, it is found that PM emission of acceleration vehicle in free-flow is unchanged and begins to continuously decay at transition point of formation of congested traffic. Amount of emissions approximately reaches ranges from 0.07–0.14 (g/s) in Fig. 6(a). The increase of the mixing ratio Cn leads to PM emissions increasing, which imply the long vehicle determines emissions. Fig. 6(b) reflects PM emission of acceleration vehicle in free-flow and congested traffic from different long vehicles. It is very clear that accelerated long vehicles in free-flow do not discharge PM, but emit a large number of PM in congested traffic. In order to give a reasonable explanation for these emission characteristics, we compute the fraction of accelerated vehicles in traffic flow for the mixing ratio Cn . Fig. 7(a) and (b) denote the fraction of accelerated vehicles in traffic flow
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Fig. 13. PM emission vs. occupancy rates (p1 = 0.25, p2 = 0.5, vL max = 40, vs max = 40, Ls = 1, Cn = 0.4).
for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. Fig. 7(a) shows that fraction of accelerated vehicles in free-flow has not clearly increase, but substantially increases at transition point of formation of congested traffic for the mixing ratios Cn = 0.2, 0.4 and 0.8, sharply increases for the mixing ratios Cn = 1.0 by comparing with the fundamental diagram in Fig. 1. After fraction of accelerated vehicles continuously achieve to the maximum value, and then the number of accelerated vehicles gradually decreases and approaches to 0. PM emissions of decelerated vehicle for different mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0 are respectively yielded in Fig. 8(a) and (b). In contrast to PM emissions of accelerated vehicle, it is found that PM emission of deceleration vehicle in free-flow is gradually increased and begins to drastically rise at transition point of formation of congested traffic and then reaches a maximum value. The maximum value corresponding to amount of emission is 0.09, 0.10 and 0.14 (g/s) for different mixing ratios Cn = 0.2, 0.4 and 0.8 in Fig. 8(a), respectively. The increase of the mixing ratio Cn increases the number of long vehicles, which leads to PM emissions increase. Fig. 8(b) reflects PM emission of deceleration vehicles in free-flow and congested traffic from different long vehicles. It is very clear that decelerated long vehicles in free-flow do not discharge PM, but emit a large number of PM from 0 jumping to 2.0 ∼ 2.5 (g/s) in congested traffic. Comparing with acceleration case, the order of PM emissions of decelerated vehicles is larger than one of accelerated vehicles. It indicates that the decelerated vehicles mainly determine PM emissions. Fig. 9(a) and (b) exhibit the fraction of decelerated vehicles in traffic flow for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. Fig. 9(a) shows that fraction of decelerated vehicles in free-flow has a large value about 20% even for small occupancy C, but dramatically decays when the occupancy C exceeds to about 0.8 for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0. Fig. 9(b) shows a strange behaviors: the fraction of single decelerated vehicles with different lengths in free-flow is unchanged and sharply decays at transition point of formation of congested traffic in contrast to the fundamental diagram in Fig. 1, and then gradually rises to peak, finally drop down to zero. It indicates that the fraction of single decelerated vehicles with different lengths occupies a bigger proportion to determine PM emissions of traffic flow. Fig. 10(a) and (b) reveal PM emissions of following vehicles for different mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. In contrast to PM emissions of accelerated vehicles and decelerated vehicles, it shows that amount of PM emission of following vehicle has a small value and begins to monotonously rise at transition point of formation of congested traffic and then reaches a maximum value, drop down to zero at occupancy C = 1.0. Fig. 10(b) reflects PM emission of single following vehicles for different long vehicles. It is very clear that following long vehicles in free-flow do not discharge PM, but emit a small amount of PM in congested traffic, but the increases the number of long vehicles do not significantly increase PM emissions. Fig. 11(a) and (b) exhibit the fraction of following vehicles in traffic flow for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. Fig. 11(a) and (b) show that fraction of following vehicles in free-flow has an changeless value, but gradually decreases in congested traffic for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0. It indicates that the fraction of single following vehicles with different lengths occupies a bigger proportion in free-flow, but the fraction in congested traffic quickly decays and leads to reduction of PM emissions.
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3.3. Impact of the maximum velocity on emissions In order to investigate the influence of the maximum velocity of vehicles on the emissions of mixed traffic, we choose the mixture ratio Cn = 0.4, the randomization probability pL = 0.5 for long vehicles and correspondingly ps = 0.25 for the short vehicles. Fig. 12(a) shows PM emissions for the different maximum velocity of short vehicles when the mixture ratio Cn = 0.4 and long vehicles maintain their maximum velocity. As can be seen on the figure, PM emission of vehicles undergoes from free-flow to congested traffic. At first, PM emission of vehicles increases to a peak in traffic congested and then decays to 0 in complete traffic congestion. Fig. 12(a) shows the maximum emission value of PM is 0.03 g/s and 0.06 g/s corresponds s s to the maximum of short vehicle increases from vmax = 1 to vmax = 7. It indicates that the maximum velocity of the short vehicles has a great impact on PM emission. As the maximum velocity of the short vehicles increases, PM emission also increases. Fig. 12(b) shows PM emissions from free-flow to congested traffic when long vehicles change the maximum velocity and short vehicles maintain their maximum velocity. PM emission of vehicles also increases to a peak and then decays to 0 from traffic congestion to complete stop. However, with the increase of the maximum velocity of long vehicles, PM emission does not significantly change. It illustrates that the increase of the maximum velocity of long vehicle cannot have a great impact on the vehicle emission of mixed traffic. 3.4. Influence of vehicle length on emissions In order to study the emission characteristics of mixed traffic caused by long vehicles, we change the length of long vehicle, fix the short vehicle LS = 1 and maintain other parameters. Fig. 13 shows PM emission for different length of long vehicles LL = 2, 5, 10 and 20. As can be seen from Fig. 13, PM emission of vehicles undergoes from increasing to a peak and then decays to 0 in complete traffic congestion. In Fig. 13, the maximum emission value of PM goes down from about 0.06 g/s to 0.05 g/s when the length of long vehicle increases from LL = 2 to 20. It indicates that emissions of vehicles reduce due to the number of vehicles decreasing on the loop road even if the length of long vehicles increases. 4. Conclusions Based on mixed NaSch traffic flow model and the empirical formula of automobile exhaust emissions, emissions of particulate matter (PM), CO2 , NOx and volatile organic compounds (VOC) are investigated with consideration of the different movement conditions, mixing ratios, the maximum velocity and lengths of vehicle. The pollutant emissions in mixed traffic are determined by traffic characteristics from free-flow to congestion. The pollutant emissions in freetraffic are almost changeless, but emissions in congestion rise to a peak and then decays to zero. Emissions of traffic flow composed of the single long vehicles discontinuously jump to a larger value at the transition point from free-flow to congestion. Emissions of mixed vehicles increase as the mixing ratio Cn increasing. It indicates that the more the number of the long vehicle increases, the more the emissions. The effect of traffic state on PM emissions is discussed in detail. The distribution function of three types of motion states is introduced to explain PM emissions. Results show that accelerating and decelerating vehicles in the congested state have a great impact on pollutant emissions in the mixed traffic flow, but decelerating vehicles discharge the most pollutants. The impact of the maximum velocity and the length of vehicles on emission are investigated, respectively. Results indicate that the maximum velocity of the short vehicles has a significant impact on emissions when the mixing ratio and length of vehicles are given. The larger the maximum velocity of the short vehicles, the more the emissions is, but the maximum velocity of long vehicles does not display obvious effect. When the mixing ratio Cn is given, the longer the vehicle, the less the emissions are due to restrictions on the loop road. Acknowledgments The project supported by the National Natural Science Foundation of China (Grant No. 11962002&11302125) and the Natural Science Foundation of Guangxi, China (Grant No. 2018GXNSFAA138205). References [1] Douglas W. Dockery, C. Arden Pope, Xiping Xu, John D. Spengler, James H. Ware, Martha E. Fay, Benjamin G. Ferris Jr., Frank E. Speizer, An association between air pollution and mortality in six U.S. cities, New England, J. Med. 329 (1993) 1753–1759. [2] C. Arden Pope III, Richard T. Burnett, Michael J. Thun, Eugenia E. 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Physica A journal homepage: www.elsevier.com/locate/physa
Study on pollutant emissions of mixed traffic flow in cellular automaton ∗
Wang Xue a , Xue Yu a,b , , Cen Bing-ling a , Zhang Peng a , He Hong-di c a
Institute of Physical Science and Technology, Guangxi University, Nanning 53004, China Key Lab Relativist Astrophys, Nanning 530004, Guangxi, People’s Republic of China c Logistics Research Center & Shanghai Engineering Research Center of Shipping Logistics Information, Shanghai Maritime University, Shanghai 200135, China b
article
info
Article history: Received 20 April 2019 Received in revised form 18 August 2019 Available online 18 September 2019 Keywords: Emission Pollutant Mixed traffic Cellular automaton
a b s t r a c t Based on mixed NaSch traffic flow model and the empirical formula of automobile exhaust emissions, emissions of particulate matter (PM), CO2 , NOx and volatile organic compounds (VOC) are investigated with consideration of the different movement conditions, mixing ratios, the maximum velocity and lengths of vehicle. Pollutant emissions are determined by traffic characteristics from free-flow to congestion. Emissions of mixed traffic increase with the mixing ratio increasing. The impact of traffic state on emissions is discussed in detail by introducing the distribution functions for three types of motion states. Results show that decelerating vehicles discharge the most pollutants even if accelerating and decelerating vehicles in the congested state have a great impact on pollutant emissions in the mixed traffic flow. The effect of the maximum velocity and the length of vehicles on emission are investigated, respectively. It is found that the maximum velocity of the short vehicles has a significant impact on emissions when the mixing ratio and length of vehicles are fixed. The larger the maximum velocity of the short vehicles, the more the emissions is, but the maximum velocity of long vehicles does not display obvious effect. When the mixing ratio is given, the longer the vehicle, the less the emissions are due to restrictions on the loop road. © 2019 Published by Elsevier B.V.
1. Introduction In recent years, air quality has become increasingly terrible. It is one of the important factors to condition global development. In the metropolises, the motor vehicle fleet and the increasing emissions of toxic pollutants by industrial sources, cause high concentrations of harmful substances that are responsible for low visibility and various respiratory problems [1,2]. The most of particulate matter (PM), CO2 , VOC and NOX pollutants are caused by thousands of vehicles emissions [3]. Moreover, recent studies have shown that the tiny particulate matter (PM) takes on multifractal property and long-range cross-correlation behavior via analyzing data of the field measure in Hong Kong and Shanghai [4–6]. Vehicles emissions have unavoidable responsibility that cause hazy weather, respiratory diseases and traffic congestion [7]. In addition, it is the most pressing problem to improve city atmosphere quality by dealing with emissions (PM, CO2 , VOC and NOX ) form transportation. The variables which determine vehicle emissions mainly are composed vehicle types and size, velocity, velocity limits, acceleration, queuing time in idle mode during red phase, queue length and traffic flow rate [8]. However, the traditional measure to calculate PM, CO2 , VOC and NOX emission observes every moment ∗ Corresponding author at: Institute of Physical Science and Technology, Guangxi University, Nanning 53004, China. E-mail address: [email protected] (Y. Xu). https://doi.org/10.1016/j.physa.2019.122686 0378-4371/© 2019 Published by Elsevier B.V.
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Table 1 Parameters for Eq. (5). Pollutant
Vehicle type
E0
f1
f2
f3
f4
f5
f6
CO2
Diesel Bus Diesel Bus Diesel Bus Diesel Bus
0 0 0 0 0 0 0 0
3.24e−01 9.04e−01 2.41e−03 2.36e−02 9.22e−05 1.55e−03 0.00e+00 2.23e−04
8.59e−02 1.13e+00 −4.11e−04 6.51e−03 9.09e−6 8.20e−04 3.13e−04 3.47e−04
4.96e−03 −4.27e−02 6.73e−05 −1.70e−04 −2.29e−07 −2.42e−05 −1.84e−05 −2.38e−05
−5.86e−02 2.81e+00 −3.07e−03 2.17e−02 −2.20e−05 1.86e−03 0.0e+00 2.08e−03
4.48e−01 3.45e+00 2.14e−03 8.94e−03 1.69e−05 3.21e−04 7.50e−04 1.76e−03
2.30e−01 1.22e+00 1.50e−03 7.57e−03 3.75e−06 1.36e−04 3.78e−04 2.23e−04
NOX VOC PM
car car car car
Fig. 1. Fundamental diagram of the mixed traffic (p1 = 0.25, p2 = 0.5).
vehicle on the roads and counts data with vehicle exhaust emission. It is difficult to describe that PM, CO2 , VOC and NOX emission from different road traffic and complex traffic composition by the traditional method. At the same time, it cannot accomplish the estimation of PM, CO2 , VOC and NOX emission from road traffic. The influence from intricate traffic structure and traffic congestion on PM, CO2 , VOC and NOX emission is hard to observe field test. There are many traffic flow models [9–14], which depicts the traffic system and investigates the mechanism of traffic flow evolution and traffic congestion [9,10,15,16]. Meanwhile, these traffic models can combine with the impact of vehicle exhaust emission on the environmental ambient air. Treiber and Kesting present a model for the instantaneous fuel consumption that includes vehicle properties, engine properties, and gear-selection schemes and implement it for different passenger car types representing the vehicle fleet under consideration. Treiber and Kesting concluded that the influence of congestions on fuel consumption is distinctly lower than that on travel time [17]. Madani and Moussa adopted cellular automaton for simulation of fuel consumption and engine pollutant [18]. Tian et al. and Wen at al respectively studied the energy consumption of the mixed traffic in cellular automaton NaSch model and FI model [19,20]. Results manifest the length of vehicles, the maximum velocity and the mixing ratio of mixed traffic have a great impact on the energy dissipation. Tang et al. proposes an extended car-following model to study the influences of the driver’s bounded rationality on his/her micro driving behavior. The numerical results indicated that considering the driver’s bounded rationality will reduce his/her velocity during the starting process and improve the stability of the traffic flow during the evolution of the small perturbation [21]. Tang et al. used the car-following model to study the impacts of fuel consumption and emissions on the trip cost without late arrival at the equilibrium state and the effect if signal light on fuel consumption and emissions [22,23], the relation of the trip cost with fuel consumption of vehicles in single-lane traffic and two-lane traffic were also analyzed [24–26]. Zhu et al. investigated delay-feedback control strategy for reducing CO2 emission of traffic flow system [27] and an original traffic additional emission model and numerical simulation on a signalized road [28]. Pan et al. carried out the simulations for homogeneous traffic PM emissions by using cellular automaton Nagel–Schreckenberg (NaSch) model. The simulation results indicated that in the free flow, low velocity limit was more energy conservative and environmentally friendly, while the high velocity limit was better when the traffic system became jammed [29]. In this paper, we will study on pollutant emissions of mixed traffic flow which is composed of vehicles with the different length and the maximum velocity. In Section 2 the cellular automaton model of mixed traffic flow is proposed
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Fig. 2. PM emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
based on NaSch model and corresponding empirical emission model is given. In Section 3 we devoted to the effects of the different mixing ratio, pollutant type and vehicles in the different state of motion on pollutant discharge by numerical simulation and theoretical analysis. Finally, this paper is concluded. 2. Methodology 2.1. Traffic models Among many traffic models, cellular automation (CA) traffic model is one of the most popular ones due to its simple algorithm and highly applicability. NaSch model [30] is able to reproduce the spontaneous phenomenon of traffic congestion and is known as the stochastic traffic cellular automaton model. In what follows, we assumed a closed-loop lattice of L cells forms a mixed traffic flow. A typical discretization scheme assumes ∆t = 1 s and ∆L = 7.5 m corresponding to velocity increments of ∆v = ∆L/∆t = 7.5 m/s [31]. At every moment each cell may be occupied by a vehicle with the different length and the different velocity in the range of zero
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Fig. 3. CO2 emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
and a maximum velocity or without vehicles. The short vehicle and the long vehicle respectively take up LS cells and LL (LL > LS ) cells. In the initial moment all of vehicles are distributed in the cells according to the mixing ratios Cn , where long vehicle with length LL at first occupies LL cells and each short vehicle occupies LS cell. When the number of long vehicle is small, long vehicles are randomly distributed in the L cells. The long vehicle gradually increasing leads to its uniformly distributed in the L cells and then each short vehicle with unit length is randomly distributed in the rest of cells. The velocity of each vehicle on single-lane is distributed randomly. At each evolutionary time step t → t + 1, all vehicle states are updated in parallel according to the evolution rules of NaSch model. The update rules of each vehicle state evolution in mixed traffic flow are [31]: Step 1. Acceleration: 1
v (i, t + ) → min(v (i, t) + 1, vmax )
3 Step 2. Deceleration: 2
1
3
3
v (i, t + ) → min(v (i, t + ), gapi (t))
(1)
(2)
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Fig. 4. NOx emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
Step 3. Randomization with probability p: 2
v (i, t + 1) → max(v (i, t + ) − 1, 0) 3
(3)
Step 4. motion: x(i, t + 1) → x(i, t) + v (i, t + 1)
(4)
where v (i, t) and x(i, t) denote as the velocity and position of the ith vehicle on the road at time step t. If the vehicle is short, the headway between the ith and the (i + 1)th in front of it at time t is gapi (t) = x(i + 1, t) − x(i, t) − LS . Similarly, the gap of long vehicle between the ith and the (i + 1)th is gapi (t) = x(i + 1, t) − x(i, t) − LL . The number of vehicles in the system is conserved and their distribution on road is given by the occupation rate C. The mixed traffic flow composed of vehicles with the different lengths is determined by the mixing ratio Cn . That is to say, the mixing ratio Cn yields the number of long vehicle and short one on road. The conservation of number of vehicles is easy to calculate the subsequent fuel and emission estimation.
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Fig. 5. VOC emission rate vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
2.2. Emission models
Panis et al. [32] have studied traffic emissions under the influence of instantaneous velocity and acceleration. They used nonlinear multivariate regression techniques to establish an emission model. The model is based on the measurement results of real urban driving conditions. Later, this model was extended to the exhaust emission of vehicles when driving on high ways [33]. En (t) is pollutant emission for the nth vehicle in unit time. En (t) = max[E0 , f1 + f2 vn (t) + f3 vn (t)2 + f4 an (t) + f5 an (t)2 + f6 vn (t)an (t)]
(5)
where E0 is a lower limit of emission (g/s) specified for each vehicle and pollutant type, and f1 to f6 are emission parameter specific for each vehicle and pollutant type determined by the regression analysis. All of specified parameters value is given in Table 1 [32].
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Fig. 6. PM emission of accelerating vehicles for different mixing ratio (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
3. Simulation and analysis
Number of vehicles on the road is denoted as N and the global density is ρ = NL . The number of long vehicle is denoted as N L and correspondingly the number of short one is expressed as N S . Long vehicle with length LL occupies LL cells and short one occupies a unit cell. The occupancy of long vehicles is the ratio of the number of long vehicle times its length to the length of lane (C L = N L × LL /L) and accordingly the occupancy of short one equals to C S = N S × LS /L. Therefore, the total occupancy is expressed as C = (N S × LS + N L × LL )/L. The mixing ratio Cn is defined as Cn = C L /C, which is to measure the proportion of long vehicles in mixed traffic flow. The relation of the occupancy of long and short vehicles to the total occupancy is obtained as C L = Cn C and C S = (1 − Cn ) C , respectively. The global density is represented as
[ ] ρ = C (1 − Cn ) /LS + Cn /LL [19].
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Fig. 7. Fraction of accelerating vehicles vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
Road is a closed-loop lattice consisting of L = 104 cells. The periodic boundary condition is adopted for simulation. The average velocity v of traffic flow is defined as follows.
v=
t0 + T N 1 1 ∑ ∑
T N
v (i, t)
(6)
t =t0 +1 i=1
where t0 is the relaxation time to reach steady state. The fundamental diagram (flow vs. occupancy rate) of mixed traffic flow is obtained for different mixing ratio Cn by numerical simulations. In order to determine overall vehicle emissions, the average vehicle emission based on Eq. (5) is defined as follows. E=
t0 +T N 1 1 ∑ ∑
T N
Ei (t)
(7)
t =t0 +1 i=1
where Ei (t) represents the pollutant emission of the ith vehicle at time t. The average vehicle emission reflects pollutant emissions of traffic flow on the whole. The average vehicle emission and the averages velocity are obtained in the process of simulations by averaging over 50 independent initial realizations up to 3 × 105 iteration steps for each run and by discarding the first 2 × 105 iteration steps as transient time. Exhaust emissions of the short vehicle refer to the emission
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Fig. 8. PM emission of decelerating vehicles for different mixing ratios (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
parameters of the diesel cars. Similarly, emission of the long vehicle corresponds to the parameters of the bus or heavy vehicle. In order to consider the influence of vehicle motion state on mixed traffic exhaust emission, we first study the fundamental diagram (flow vs. occupancy rate) of mixed traffic flow for different mixing ratio Cn . The mixed traffic flow on road is composed of vehicles with different lengths and velocities in terms of the mixing ratio Cn . The long vehicle with L the maximum velocity vmax = 40 cells/timestep occupies 10 cells at initial moment. For simplicity, each short vehicle as S a unit occupies a cell and its maximum velocity vmax equals to 5 cells/timestep. Randomization probability p1 for short car and long vehicle is selected as p1 = 0.25 and p2 = 0.5, respectively. The fundamental diagram (flow vs. occupancy rate) of mixed traffic flow with mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0 are shown in Fig. 1. Fig. 1 shows that the fundamental diagram of mixed traffic flow is divided into two regions: free-flow and congested area. When the mixing ratio Cn = 0.2, 0.4, 0.8, the peak of curve decreases with the increase of mixing ratio and critical point increases. When the mixing ratio Cn = 1.0, it implies that all of vehicles on road are made up of long vehicle. The
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Fig. 9. Fraction of decelerating vehicles vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
curve in the fundamental diagram shows discontinuity at occupancy rate C ≈ 0.12, which indicates the occurrence of traffic congestion. The curve with a occupancy rate C greater than 0.12(>0.12) represents traffic jamming. 3.1. Emissions under different occupancy rates In this section, the average PM CO2 NOx and VOC emissions of mixed traffic flow are investigated for the mixing ratio Cn = 0.2, 0.4, 0.8 and 1.0. Fig. 2(a) shows the average emission of PM for mixing ratios Cn = 0.2, 0.4 and 0.8. Comparing with the fundamental diagram of mixed traffic flow in Fig. 1, PM emissions gradually rise to a peak and then go down to 0 g/s, which just corresponds to the state of traffic flow from free-flow to congestion. PM emission reaches a peak of 5.03 g/s at the occupancy rate C ≈ 0.28 for the mixing ratio of 0.2. Similarly, the maximum value of PM emission respectively reaches 5.14 g/s at occupancy rate C = 0.32 for mixing ratio Cn = 0.4 and 6.15 g/s at occupancy rate C = 0.44 for mixing ratio Cn = 0.8. It indicates that PM emissions increase as the mixing ratio Cn increasing. For the mixing ratio Cn = 1.0, Fig. 2(b)
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Fig. 10. Emission of PM of following vehicle for different mixing ratios (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
exhibits PM emissions for the vehicle length LL = 2, 5, 10 and 20 cells, respectively. Similar to change trend in the fundamental diagram of mixed traffic flow in Fig. 1, PM emissions in Fig. 2(b) reveal the discontinuity from free-flow to congestion and transition point corresponds to the maximum emission. Simulation shows the emission peak emerges in the state of stop&go traffic. The maximum emission respectively equals to 0.32 g/s, 0.33 g/s, 0.33 g/s and 0.35 g/s corresponding to the occupancy C ≈ 0.06, 0.16, 0.18 and 0.32 for vehicle length LL = 2, 5, 10 and 20 cells. Fig. 2(b) indicates that the longer the vehicle is, the more the PM emission will be. It is confirmed that the PM emission of bus is more than one of Diesel car when bus and Diesel car are mixed. CO2 emission for mixing ratios Cn = 0.2, 0.4 and 0.8 is shown in Fig. 3(a). Similar to change trend in PM emission of mixed traffic flow in Fig. 2, CO2 emission has a peak and then go down to 0 g/s for mixing ratios Cn = 0.2, 0.4 and 0.8. It indicates that traffic flow varies from free-flow to congestion. Moreover, Fig. 3(b) exhibits CO2 emission for mixing ratios Cn = 1.0 with the discontinuity from free-flow to congestion and reaches the maximum emission at transition point and the longer the vehicle is, the more the PM emissions. As can be seen from Figs. 4 and 5, NOx and VOC emissions have similar behaviors like CO2 emission for mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0. The change trends in NOx and VOC emissions for mixing ratios Cn = 0.2, 0.4 and 0.8 in Figs. 4(a) and 5(a) indicate that traffic flow varies from free-flow to congestion. NOx and VOC emissions for mixing ratios Cn = 1.0 in
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Fig. 11. Fraction of following vehicles vs. occupancy rate (p1 = 0.25, p2 = 0.5, vL max = 40, vS max = 5). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
Figs. 4(b) and 5(b) emerge the discontinuity from free-flow to congestion, which is determined the fundamental diagram in Fig. 1. From the average emissions of PM, CO2 , NOx and VOC, it is found that pollutant emissions increase as the mixing ratio Cn increasing. The more the number of the long vehicle increases, the more the emissions. Meanwhile, traffic characteristics from free-flow to congestion determine pollutant emissions as a whole. 3.2. Effect of vehicle motion state on emission In order to further study the emission characteristics of mixed traffic flow in detail, we classify the motion state of vehicle into three types: acceleration (vi (t + 1) > vi (t)), deceleration (vi (t + 1) < vi (t)) and follow or uniform motion (vi (t + 1) = vi (t)). The emission characteristic in the state of the three types is explored. Meanwhile, the number distribution function by introducing for three types of motion states gives a reasonable explanation for these emission characteristics.
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Fig. 12. PM emission vs. occupation rate for the maximum velocity of vehicles (p1 = 0.25, p2 = 0.5, vL max = 40). (a) LL = 10 cells, LS = 1 cells (b) Cn = 1.0.
The fraction of vehicle number in the state of acceleration, deceleration and follow is defined as follows. fs =
t0 1 1 ∑
T N
ns
t =t0 +1
where ns represents the number of vehicles accelerating (na ), decelerating (nd ) or following (nf ) in time t [20]. Fig. 6(a) and (b) corresponds to PM emission of accelerating vehicle for different mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. In contrast to the fundamental diagram of mixed traffic flow in Fig. 1, it is found that PM emission of acceleration vehicle in free-flow is unchanged and begins to continuously decay at transition point of formation of congested traffic. Amount of emissions approximately reaches ranges from 0.07–0.14 (g/s) in Fig. 6(a). The increase of the mixing ratio Cn leads to PM emissions increasing, which imply the long vehicle determines emissions. Fig. 6(b) reflects PM emission of acceleration vehicle in free-flow and congested traffic from different long vehicles. It is very clear that accelerated long vehicles in free-flow do not discharge PM, but emit a large number of PM in congested traffic. In order to give a reasonable explanation for these emission characteristics, we compute the fraction of accelerated vehicles in traffic flow for the mixing ratio Cn . Fig. 7(a) and (b) denote the fraction of accelerated vehicles in traffic flow
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Fig. 13. PM emission vs. occupancy rates (p1 = 0.25, p2 = 0.5, vL max = 40, vs max = 40, Ls = 1, Cn = 0.4).
for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. Fig. 7(a) shows that fraction of accelerated vehicles in free-flow has not clearly increase, but substantially increases at transition point of formation of congested traffic for the mixing ratios Cn = 0.2, 0.4 and 0.8, sharply increases for the mixing ratios Cn = 1.0 by comparing with the fundamental diagram in Fig. 1. After fraction of accelerated vehicles continuously achieve to the maximum value, and then the number of accelerated vehicles gradually decreases and approaches to 0. PM emissions of decelerated vehicle for different mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0 are respectively yielded in Fig. 8(a) and (b). In contrast to PM emissions of accelerated vehicle, it is found that PM emission of deceleration vehicle in free-flow is gradually increased and begins to drastically rise at transition point of formation of congested traffic and then reaches a maximum value. The maximum value corresponding to amount of emission is 0.09, 0.10 and 0.14 (g/s) for different mixing ratios Cn = 0.2, 0.4 and 0.8 in Fig. 8(a), respectively. The increase of the mixing ratio Cn increases the number of long vehicles, which leads to PM emissions increase. Fig. 8(b) reflects PM emission of deceleration vehicles in free-flow and congested traffic from different long vehicles. It is very clear that decelerated long vehicles in free-flow do not discharge PM, but emit a large number of PM from 0 jumping to 2.0 ∼ 2.5 (g/s) in congested traffic. Comparing with acceleration case, the order of PM emissions of decelerated vehicles is larger than one of accelerated vehicles. It indicates that the decelerated vehicles mainly determine PM emissions. Fig. 9(a) and (b) exhibit the fraction of decelerated vehicles in traffic flow for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. Fig. 9(a) shows that fraction of decelerated vehicles in free-flow has a large value about 20% even for small occupancy C, but dramatically decays when the occupancy C exceeds to about 0.8 for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0. Fig. 9(b) shows a strange behaviors: the fraction of single decelerated vehicles with different lengths in free-flow is unchanged and sharply decays at transition point of formation of congested traffic in contrast to the fundamental diagram in Fig. 1, and then gradually rises to peak, finally drop down to zero. It indicates that the fraction of single decelerated vehicles with different lengths occupies a bigger proportion to determine PM emissions of traffic flow. Fig. 10(a) and (b) reveal PM emissions of following vehicles for different mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. In contrast to PM emissions of accelerated vehicles and decelerated vehicles, it shows that amount of PM emission of following vehicle has a small value and begins to monotonously rise at transition point of formation of congested traffic and then reaches a maximum value, drop down to zero at occupancy C = 1.0. Fig. 10(b) reflects PM emission of single following vehicles for different long vehicles. It is very clear that following long vehicles in free-flow do not discharge PM, but emit a small amount of PM in congested traffic, but the increases the number of long vehicles do not significantly increase PM emissions. Fig. 11(a) and (b) exhibit the fraction of following vehicles in traffic flow for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0, respectively. Fig. 11(a) and (b) show that fraction of following vehicles in free-flow has an changeless value, but gradually decreases in congested traffic for the mixing ratios Cn = 0.2, 0.4, 0.8 and 1.0. It indicates that the fraction of single following vehicles with different lengths occupies a bigger proportion in free-flow, but the fraction in congested traffic quickly decays and leads to reduction of PM emissions.
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3.3. Impact of the maximum velocity on emissions In order to investigate the influence of the maximum velocity of vehicles on the emissions of mixed traffic, we choose the mixture ratio Cn = 0.4, the randomization probability pL = 0.5 for long vehicles and correspondingly ps = 0.25 for the short vehicles. Fig. 12(a) shows PM emissions for the different maximum velocity of short vehicles when the mixture ratio Cn = 0.4 and long vehicles maintain their maximum velocity. As can be seen on the figure, PM emission of vehicles undergoes from free-flow to congested traffic. At first, PM emission of vehicles increases to a peak in traffic congested and then decays to 0 in complete traffic congestion. Fig. 12(a) shows the maximum emission value of PM is 0.03 g/s and 0.06 g/s corresponds s s to the maximum of short vehicle increases from vmax = 1 to vmax = 7. It indicates that the maximum velocity of the short vehicles has a great impact on PM emission. As the maximum velocity of the short vehicles increases, PM emission also increases. Fig. 12(b) shows PM emissions from free-flow to congested traffic when long vehicles change the maximum velocity and short vehicles maintain their maximum velocity. PM emission of vehicles also increases to a peak and then decays to 0 from traffic congestion to complete stop. However, with the increase of the maximum velocity of long vehicles, PM emission does not significantly change. It illustrates that the increase of the maximum velocity of long vehicle cannot have a great impact on the vehicle emission of mixed traffic. 3.4. Influence of vehicle length on emissions In order to study the emission characteristics of mixed traffic caused by long vehicles, we change the length of long vehicle, fix the short vehicle LS = 1 and maintain other parameters. Fig. 13 shows PM emission for different length of long vehicles LL = 2, 5, 10 and 20. As can be seen from Fig. 13, PM emission of vehicles undergoes from increasing to a peak and then decays to 0 in complete traffic congestion. In Fig. 13, the maximum emission value of PM goes down from about 0.06 g/s to 0.05 g/s when the length of long vehicle increases from LL = 2 to 20. It indicates that emissions of vehicles reduce due to the number of vehicles decreasing on the loop road even if the length of long vehicles increases. 4. Conclusions Based on mixed NaSch traffic flow model and the empirical formula of automobile exhaust emissions, emissions of particulate matter (PM), CO2 , NOx and volatile organic compounds (VOC) are investigated with consideration of the different movement conditions, mixing ratios, the maximum velocity and lengths of vehicle. The pollutant emissions in mixed traffic are determined by traffic characteristics from free-flow to congestion. The pollutant emissions in freetraffic are almost changeless, but emissions in congestion rise to a peak and then decays to zero. Emissions of traffic flow composed of the single long vehicles discontinuously jump to a larger value at the transition point from free-flow to congestion. Emissions of mixed vehicles increase as the mixing ratio Cn increasing. It indicates that the more the number of the long vehicle increases, the more the emissions. The effect of traffic state on PM emissions is discussed in detail. The distribution function of three types of motion states is introduced to explain PM emissions. Results show that accelerating and decelerating vehicles in the congested state have a great impact on pollutant emissions in the mixed traffic flow, but decelerating vehicles discharge the most pollutants. The impact of the maximum velocity and the length of vehicles on emission are investigated, respectively. Results indicate that the maximum velocity of the short vehicles has a significant impact on emissions when the mixing ratio and length of vehicles are given. The larger the maximum velocity of the short vehicles, the more the emissions is, but the maximum velocity of long vehicles does not display obvious effect. When the mixing ratio Cn is given, the longer the vehicle, the less the emissions are due to restrictions on the loop road. Acknowledgments The project supported by the National Natural Science Foundation of China (Grant No. 11962002&11302125) and the Natural Science Foundation of Guangxi, China (Grant No. 2018GXNSFAA138205). References [1] Douglas W. Dockery, C. Arden Pope, Xiping Xu, John D. Spengler, James H. Ware, Martha E. Fay, Benjamin G. Ferris Jr., Frank E. Speizer, An association between air pollution and mortality in six U.S. cities, New England, J. Med. 329 (1993) 1753–1759. [2] C. Arden Pope III, Richard T. Burnett, Michael J. Thun, Eugenia E. 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