Mathematical Modeling Study on Carbon Emission Control by Green Transportation Network Planning in Urban Agglomerations

In recent years, urban agglomerations have developed rapidly, becoming an important direction for exploring forms of economic development in the new era. However, the economic development of urban agglomerations is often accompanied by huge carbon emissions, which seriously affect the environment and human health. In order to realize the win-win situation of economic development and environmental protection, it is necessary to take effective measures to decouple the economic development of city clusters from carbon emissions [1-4]. Therefore, the importance of building a green transportation network becomes more and more prominent. Green transportation network refers to the transportation network oriented to low-carbon travel, aiming to reduce carbon emissions, improve air quality, and enhance transportation efficiency [5-7].

First of all, the core of urban green transportation network is public transportation. Public transportation is an important way for urban residents to travel, and its degree of development directly affects the degree of green urban transportation. In some international metropolis, subway has become the main public transportation, which can accommodate a large number of passengers and reduce the pressure of road traffic [8-11], of course, the construction of bicycle paths and other green transportation routes is also an important part of the construction of green transportation network. In addition, the publicity and education of green transportation is also a crucial part. The government and related organizations should popularize the knowledge of green travel to the public through various media channels and provide practical suggestions for low-carbon travel [12-15]. Through publicity and education, the environmental awareness of the public can be improved, so that more people can participate in the ranks of low-carbon travel. Finally, the government plays a key role in building a green transportation network. The government should increase the investment in green transportation system [16-18].

Literature [19] proposed two models of urban spatial structure oriented to low-carbon transportation based on literature review: traditional pedestrian city and modern transportation metropolis, and mentioned the improved GTOD model. The integration of land use and green transportation system is emphasized. It forms the basis of the proposed urban structure model and helps to promote low-carbon transportation and sustainable urban growth management. Literature [20] calculated the coupled coordination between pollution, carbon reduction and economic quality in three major urban agglomerations in China. The modified gravity model and social network were adopted to analyze the overall correlation and network structure among cities. Conclusions are drawn that the spatial distribution of the three urban agglomerations is moving towards centralization and the inter-city connections are increasing, and suggestions are made to reduce carbon emissions. Literature [21] constructed a carbon emission reduction capacity evaluation system. The social network analysis method was used to characterize the spatially relevant network structure of carbon emission reduction capacity. The quadratic assignment method was used to describe its driving factors. The effectiveness of the system is demonstrated by taking a city cluster as an example, revealing the deficiencies of the city cluster and proposing countermeasures to improve the synergistic management of carbon emission reduction in the city cluster. Literature [22] combined the modified gravity model and social network analysis to measure the network structure characteristics of carbon emission spatial correlation of several city clusters as a whole and each city cluster, and discussed the influencing factors of carbon emission spatial correlation based on QAP. It was concluded that “the influencing factors and the degree of spatial correlation of carbon emissions in each city cluster are different”. Literature [23] quantified the carbon metabolism profile and spatial distribution evolution of the Beijing-Tianjin-Hebei urban agglomeration by combining carbon emission and ecological network analysis. It emphasizes that land use planning, arable land protection policy and ecological compensation mechanism are feasible measures to promote the sustainable development of urban agglomerations.

Literature [24] takes the Yangtze River Delta urban agglomeration as the research object, uses the extended Kaya identity model to explore the impact of industrial transformation, life consumption and spatial expansion on consumption efficiency, and draws the conclusion that the reduction of carbon emissions is mainly concentrated in the core cities. And based on its existing problems, targeted countermeasures such as the development of low-carbon public transportation are proposed. Literature [25] calculated the spatial structure indices of six city clusters in China from the demographic and economic perspectives by applying the rank-size rule. The GTWR model was used to analyze the spatial and temporal differences in the impact of the spatial structure of different urban agglomerations on carbon emissions. Conclusions such as relatively higher carbon emissions in the Yangtze River Delta, Beijing-Tianjin-Hebei and Central Plains urban agglomerations were obtained. It is recommended to optimize the spatial structure appropriately based on the temporal evolution and internal characteristics of the city clusters. Literature [26] conducted an empirical study on the example of Shandong Peninsula city cluster. The spatial structure of the urban agglomeration was measured in the dimensions of concentration and diffusion, and transportation accessibility. Based on regression analysis, the impact of spatial structure of urban agglomeration on carbon emission was evaluated. The study concluded that “concentration and transportation accessibility have a positive impact on carbon emission”. Literature [27] developed the GDEMATEL model, which combines a λ-order gravity model with decision-making experiments and evaluation laboratory methods. By applying it to different sizes of UAVs, several results were obtained, such as “the urban agglomeration transportation network is characterized by too many independent cities and insufficient functional differentiation between cities”. Literature [28] classifies the impact of urbanization on carbon emission efficiency into four aspects and proposes the IPCE model to avoid the shortcomings of the “self-evaluation” method. The carbon emission efficiency of several typical urban agglomerations was analyzed with the help of this model. The results show that the carbon emission efficiency of urban agglomerations has not been improved, and the difference in efficiency between the “self-assessment” method and the IPCE method is more obvious. Suggestions for improving the carbon emission efficiency are also put forward.

Determine the mathematical model for calculating the carbon emissions of fuel and electric transportation, the model contains internal and external traffic, transit traffic is not in the scope of consideration, in order to meet the travel needs of residents, as far as possible, synchronize the realization of the green transportation network planning of the urban agglomeration oriented to the demand for carbon-control, in this regard, the construction of carbon emission model based on the CE-ALINEA algorithm, so that the carbon emissions converge to the road is in the carbon emission model based on the CE-ALINEA algorithm is constructed so that the carbon emission converges to the emission level when the road is at the maximum weighted flow. In order to verify the superiority of the CE-ALINEA control designed in this paper in the control of road network emission reduction, a total of four simulation scenarios are designed, which cover no control, timing control, ALINEA control and CE-ALINEA control scenarios, and then the four simulation scenarios are compared and analyzed. The four planning scenarios are presented as single variable influencing factors, and the CE-ALINEA control model is used to explore the comparison of carbon emissions of major transportation modes in a city under the four planning scenarios.

2

Transportation network planning study for carbon emission control

2.1

Green Transportation Theory and Low-Carbon Transportation Characteristics

2.1.1

Green Transportation Theory

Green transportation theory is a new concept of understanding. There is no uniform definition of green transportation. However, from the related research on green transportation, it is largely the same as the concept of sustainable development to solve the problems of environmental pollution and resource shortage. Green transportation emphasizes the “green development” of urban transportation, i.e., reducing traffic congestion, rational use of natural resources, and reducing the pollution of the natural environment caused by transportation development. The main feature of green transportation is the optimization and unification of the links and subsystems within the transportation system, and the coordination and unification between the transportation system and the resources and environment and other related systems. Its purpose is to fully satisfy people’s reasonable travel needs with minimum resource consumption, to maximize traffic efficiency with minimum cost, and to meet the requirements of socio-economic development and environmental carrying capacity of coordinated and sustainable transportation. The concept embodies the idea of “people-oriented”, meets the transportation needs of all residents, and realizes social equity to the maximum extent. Its ultimate goal is to achieve coordination between transportation, the natural environment, economic development, social needs, and energy.

2.1.2

Low-carbon transportation characteristics

Carbon emission is the abbreviation for greenhouse gas emission, and the so-called greenhouse gas (abbreviated as GHG) refers to any gas that absorbs and emits infrared radiation and exists in the atmosphere, playing a role similar to that of a greenhouse in trapping solar radiation and heating the air [29-30]. Carbon dioxide (CO₂) accounts for the largest share of anthropogenic greenhouse gases, and thus CO₂ emissions are generally used to represent the level of greenhouse gas emissions in general studies. Low-carbon transportation characteristics are mainly reflected in systematic, two-way and relative. The details are summarized below:

1)

Systemic

Low-carbon transportation is, first of all, an integrated system, in which any one or several modes of transportation cannot replace other modes of transportation, and it is necessary to give full play to the respective advantages of various modes of transportation as well as to the dynamic coordination between them in the process of transportation operation. Under this integrated system, there are different systems within it, such as the transportation vehicle system and the transportation energy system. In the transportation means system, it is necessary to develop new low-carbon transportation means as well as to continuously improve the technological content of traditional transportation means. In the transportation energy system, it is necessary to develop new low-carbon energy sources, innovate energy technology, and improve the efficiency of traditional energy use, both of which are complementary and indispensable.

2)

Bidirectionality

Low-carbon transportation includes both “supply” and “demand” aspects. On the supply side, it is necessary to provide a low-carbon transportation service system, which is the foundation. On the demand side, it is necessary to update the public’s traditional transportation concepts and choose reasonable transportation means, which is an important supplement. Therefore, only by realizing the “balance of supply and demand” in the transportation system can we really make urban transportation move forward in the direction of low-carbon transportation.

3)

Relativity

If we only consider the stage of transportation operation, many modes of transportation can achieve a huge carbon reduction target from “high carbon” to “low carbon” or even “zero carbon”. Therefore, in terms of the relative carbon emissions of many modes of transportation, private cars do not necessarily mean high carbon emissions, and electric vehicles definitely emit low carbon emissions. At present, public transport vehicles fueled by fossil resources also have enormous carbon reduction potential and can gradually achieve the objective of a low-carbon public transport system.

2.2

Urban Transportation Scale Carbon Emission Measurement

2.2.1

Overall calculation methodology

Summarizing the advantages and disadvantages of the existing methods, combining the ownership method with the turnover method, taking into account the upstream energy consumption of electric transportation vehicles, establishing a carbon emission accounting model for fuel-fired transportation vehicles and electric transportation vehicles, and proposing a carbon emission calculation method adapted to the scale of urban transportation and taking into account the whole life cycle, so as to provide the basis for scientific assessment of the current situation and reasonable prediction of the future and make a quantitative assessment. The method only considers the carbon emissions that have a strong correlation with the operation stage of transportation, including the fuel tank to wheel stage of fuel vehicles and the power plant to battery stage of electric vehicles, while the carbon emissions of other fuel production and vehicle production stages are not included in the scope of this study. In terms of the study boundary, it includes both internal and external transportation in the city, and transit transportation is not considered in the scope of this study. Distinguish between different types of travel and different means of transportation, and construct the carbon emission calculation model separately. The calculation formula is: (1) $C_{General} = C_{y} + C_{d}$ (2) $C_{y} = C_{y e} + C_{y n}$ (3) $C_{d} = C_{d e} + C_{d n}$ Where: C_General is the total carbon emissions from transportation in a city/kg. C_y is the total carbon emissions from electric transportation/kg. C_d is the total carbon emissions from fuel transportation/kg. C_ye and C_yn are the total carbon emissions from external and internal transportation of electric transportation/kg, respectively. C_de and C_dn are the total carbon emissions from external and internal transportation of fuel transportation/kg, respectively.

2.2.2

Calculation of carbon emissions from oil-fired transportation vehicles

Carbon emissions from internal passenger transportation are calculated using the formula (4) $C_{d n} = \sum_{i}^{n} (V_{i} * L_{i} * e_{i})$ Where: V_i is the number of ownership/vehicle of the i type of fuel transportation, and the ownership data can be obtained through the local environmental protection department or traffic control department. L_i is the average mileage/km of the ith type of fuel transportation vehicle. Information on the activity level of operating vehicles can be obtained from the statistical data of operating units, and information on the activity level of non-operating vehicles can be obtained from the traffic control department or the urban traffic operation model. e_i is the emission factor/(kg·vehicle^-1·km^-1) of the ith fuel transportation vehicle, which can be obtained from the local environmental protection department or traffic control department.

In order to measure carbon emissions, passenger turnover data from different transportation modes’ operating sectors are needed. Due to the objective conditions such as numerous transportation modes, diverse travel terminals, and non-uniform management departments, the urban traffic sharing rate and travel characteristics can be obtained by using the resident travel survey or the urban traffic operation model to further obtain passenger-related travel information. The formula for calculating carbon emissions from external transportation trips is: (5) $C_{d e} = C_{d e p} + C_{d e f}$ (6) $C_{d e p} = \sum_{i}^{n} (\frac{T_{i}}{z_{i}} \times e_{i})$ (7) $C_{d e f} = \sum_{i}^{n} (\frac{F_{i}}{c_{i}} \times f_{i})$ Where: C_dep and C_def are the carbon emissions/kg from external passenger and freight traffic of the oil-fired vehicle, respectively. T_i is the passenger turnover/(person·km) of external traffic of the ith oil-fired vehicle, which is obtained from the statistical data of the transportation sector. Z_i is the average passenger load/(person·vehicle^-1) of the ith fuel mode, obtained from the statistical data of the transportation department: e_i is the emission factor/(kg·vehicle^-1·km^-1) of the ith fuel mode in the state of carrying passengers. F_i is the freight turnover/(t·km⁻¹) of the ith oil-fired mode of transportation, obtained from the statistical data of the transportation sector: C_i is the average tonnage of freight carried by the ith oil-fired mode of transportation/(t·vehicle^-1), obtained from the statistical data of the transportation sector: f_i is the emission factor of freight transported by the ith oil-fired mode of transportation/(kg·vehicle^-1·km^-1).

2.2.3

Calculation of Carbon Emissions from Electric Vehicles

The carbon emission calculation for the travel process of electric transportation adds parameters related to the energy consumption of electric vehicles, including the charging and discharging efficiency and the line loss of electric power transmission. The internal transportation carbon emission calculation formula is: (8) $C_{y n} = \frac{\sum_{l}^{n} \frac{v_{1} \times l_{i} \times α_{i} \times P_{i}}{J_{i} \times 100}}{1 - y}$ Where: v_i for the ind type of electric transportation vehicle ownership/vehicle: l_i for the ith type of electric transportation vehicle average mileage/km. α_i for the i th type of electric transportation vehicle carbon emission factor/(kg·kW⁻¹·h⁻¹), that is, the carbon emission factor of the power generation process, which can be calculated according to the energy structure of the carbon emission factor of electricity in different distribution regions. P_i is the power consumption per unit distance/(kWh·100km^-1·vehicle^-1) of the ith type of electric transportation vehicle, which usually refers to the 100km energy consumption of the vehicle, and this indicator has a large impact on the vehicle driving process, which can be obtained from the vehicle enterprises, but usually changes according to the different models, seasons, and traffic, and it can be determined to launch the actual situation. Analysis. J_i is the charging efficiency/% of the i th type of electric transportation, charging efficiency is affected by multiple parameters such as vehicle power, battery performance, charging pile performance, ambient temperature, and so on, the actual calculation should be combined with the charging pile construction and layout to determine the charging pile performance, according to the type of vehicle to determine the power of the vehicle, the performance of the battery, which can be obtained from the vehicle enterprises, the ambient temperature can be obtained from the meteorological department, and the comprehensive evaluation to determine the charging efficiency parameter finally. Efficiency parameters. y is the transmission and distribution loss/%, which can be obtained from the power sector. The formula for calculating carbon emissions from external transportation trips is: (9) $C_{y e} = C_{y e p} + C_{y e f}$ (10) $C_{y e p} = \frac{\sum_{i}^{n} \frac{k_{i} \times α_{i} \times P_{i}}{z_{i} \times l_{i} \times 100}}{1 - y}$ (11) $C_{y e f} = \frac{\sum_{i}^{n} \frac{h_{i} \times α_{i} \times P_{i}}{c_{i} \times l_{i} \times 100}}{1 - y}$ Where: C_yep and C_yef are the carbon emissions/kg from external passenger and freight traffic of electric vehicles respectively. t_i is the passenger turnover/(person·km) of external traffic of the i th electric vehicle. z_i is the average passenger load/(person·vehicle^-1) of the ith type of electric transportation h_i is the freight turnover of the ith type of electric transportation/(t·km⁻¹) . c_i is the average cargo tonnage/(t·vehicle^-1) of the ith type of electric transportation.

2.3

Carbon emission model based on CE-ALINEA algorithm

2.3.1

Principles of model construction

In the context of the current “dual-carbon” goal, the carbon control path of “travel mode optimization” is an inevitable choice for the low-carbon development of urban road transport.Let more low fuel consumption, low emission public transport motorized travel mode can not only meet the travel needs of residents, but also to achieve the “energy consumption side” to control the demand for transport carbon emissions.The desire of large cities to optimize their transport modes and move to zero or low carbon transport modes is a response to today’s urgent need for carbon control.Transportation mode is to complete the displacement of people or things. Under the guiding ideology of low-carbon road transport development, on the basis of meeting the travel needs of residents, the simultaneous realization of the demand for environmental protection as far as possible is the basic value of the travel structure optimization oriented to the demand for carbon control. Therefore, the basic principle of the carbon emission model based on the CE-ALINEA algorithm should simultaneously meet the residents’ travel and carbon control demands.

2.3.2

ALINEA algorithm

ALINEA model is the most widely used and stable feedback control algorithm in ramp control, widely used in Europe, America and other developed countries in urban road control links, ALINEA algorithm basic principle is shown in Fig. 1. ALINEA is a classical single-point control algorithm, is also a kind of closed-loop feedback control algorithm, whose parameters can be selected or calibrated, and the idea comes from the automatic control theory of the PID algorithm, the algorithm to maintain the downstream occupancy of the main line to set the desired value as the goal, to achieve the main line capacity maximization [31]. In one control cycle, the regulation rate is: (12) $γ (k) = γ (k - 1) + K [\hat{O} - {\hat{O}}_{1} (k - 1)]$ Where: γ(k) is the ramp regulation rate calculated for the k nd control cycle. γ (k – 1) is the ramp regulation rate for the k – 1th control cycle, and the regulation rate is the length of green light in one control cycle. K is the fixed calibration parameter. $\overset{⌢}{O}$ is the desired occupancy rate downstream of the mainline, which is usually set to the optimal occupancy rate. ${\overset{⌢}{O}}_{1} (k - 1)$ is the measured occupancy downstream of the mainline in the k – 1th control cycle.

In the ALINEA model algorithm, K3 parameters of the main line downstream expected occupancy $\overset{⌢}{O}$ , regulation period, and calibration parameters need to be set in advance. The paper deals with the selection of ALINEA model parameters according to the existing research results as follows:

1) the existing research and engineering practice using a wide range of regulation period, generally 20 ~ 300 s. Considering the ramp and mainline flow, occupancy detector data acquisition frequency of 20s / time, the paper will be set to 40s control period, the minimum number of control cycles for 6, that is, a single control at least 4min.

2) In general, the control result is not sensitive to the calibration parameter K_R, the value range is generally 70 ~ 200veh / h, and the study shows that the control effect is better when K_R = 70veh / h.

3) The desired occupancy rate is generally the best occupancy rate (flow rate and capacity are equal or similar), and the value is generally 0.18~0.31. This paper sets the occupancy rate slightly less than the capacity, and sets it at 0.3.

2.3.3

Real-time carbon emissions measurement indicators

1)

Real-time carbon emissions from fuel vehicles

The real-time carbon emission measurement model is constructed by combining the microscopic single-vehicle emission model with the MFD, which is between the macro model and the microscopic model, aiming at dynamically observing the changes of aggregated emissions in the road network. The real-time carbon emission measurement model can reflect the real-time macroscopic carbon emission of the road network, and is also easy to calculate and calibrate, so this work introduces this index into the carbon measurement calculation in the ramp control model. The carbon emission measurement index of fuel automobile is: (13) $\begin{array}{l} E_{t, C O_{2}}^{I C E V} = \sum_{i} 3 .18 e^{- 3} \\ \times \frac{217 + 0.253 \times v_{t}^{w} + 9.65 e^{- 3} \times v_{t}^{w^{2}}}{1 + 9.6 e^{- 2} \times v_{t}^{w} - 4.12 e^{- 4} \times v_{t}^{w^{2}}} \times v_{t}^{w} k_{t}^{w} n_{i} \times l_{i} \end{array}$ where: $E_{t, C O_{2}}^{I C E V}$ denotes the CO₂ emissions (kg·h⁻¹) from fuel vehicles on the road network during time period t. $v_{t}^{w}$ and $k_{t}^{w}$ denote the weighted speed (km·h⁻¹) and weighted density (veh·km⁻¹) obtained based on MFD during time period t, respectively. n_i denotes the number of lanes of the road section i. l_i denotes the length (km) of the road section i. The constant term parameters are obtained based on the microscopic emission model COPERT-III. The MFD-based weighted flow $q_{t}^{w}$ , weighted speed $v_{t}^{w}$ and weighted density $k_{t}^{w}$ 3 macroscopic parameters are: (14) ${\begin{array}{l} q_{t}^{w} = \frac{\sum q_{i, t} \times l_{i}}{\sum l_{i}} \\ k_{t}^{w} = \frac{\sum k_{i, t} \times l_{i}}{\sum l_{i}} \\ v_{t}^{w} = \frac{\sum v_{i, t} \times l_{i}}{\sum l_{i}} \end{array}$ Where: q_i,t represents the volume of traffic on the roadway i passing through during time period t. k_i,t denotes the average density of each lane on section i during time period t. v_i,t denotes the average speed of vehicles passing each lane on section i during time period t. l_i is the length of the road section i.

2)

Real-time carbon emissions of electric vehicles

The carbon emissions of electric vehicles consider the indirect emissions of their electricity consumption during the production phase, i.e., the electricity consumed by the electric vehicle while driving is multiplied by the electricity emission factor. The carbon emissions of electric vehicles (EVs) are measured as: (15) $\begin{array}{l} E_{t, C O_{2}}^{E V} = \sum_{i} 0 .704 \\ \times (2.287 e^{- 5} \times v_{t}^{w^{2}} - 0.1913 e^{- 2} \times v_{t}^{w} + 0.1436) \times v_{t}^{w} k_{t}^{w} n_{i} \times l_{i} \end{array}$

Assuming a penetration rate of α for electric vehicles on the road, the total road carbon emissions are: (16) $E_{t, C O_{2}} = (1 - α) \times E_{t, C O_{2}}^{I C E V} + α \times E_{t, C O_{2}}^{E V}$

2.3.4

CE-ALINEA construction

In this work, the ALINEA control algorithm is improved with the control objective of emission reduction optimization so that the carbon emissions converge to the emission level when the road is at the maximum weighted flow rate. Figure 2 shows a schematic diagram of the macro carbon emission threshold for expressways. Namely: (17) $k^{*} = f^{- 1} (q^{max})$ (18) $E_{C R} = s ([k^{*}])$ Where: k^* represents the weighted density corresponding to the maximum weighted flow of the mainline. f is the relationship function between flow and density. $[k^{*}]$ denotes the value of the scatter density closest to k^*. E_CR is the carbon emission value corresponding to this scatter density, i.e., the macro carbon emission threshold.

This work constructs an on-ramp control algorithm that takes into account the carbon emission factor, i.e., the CE-ALINEA control algorithm, which is based on the following principle, viz: (19) $r (t) = k_{R} \cdot \int_{0}^{t} [\frac{E_{C R} - E_{(t - 1), C O_{2}}}{E_{C R}}] d t$

Deriving and discretizing the above equation yields: (20) $r (t) = r (t - 1) + k_{R} \cdot [\frac{E_{C R} - E_{(t - 1), C O_{2}}}{E_{C R}}]$ Where: E_{(t–1),CO₂} is the emission on the expressway mainline in cycle (t – 1). Carbon emission threshold E_CR is the emission corresponding to when the road network reaches the maximum weighted flow rate.

It is considered that ramp control will result in increased ramp queuing and thus increased ramp carbon emissions. In order to avoid the scenarios of excessive ramp queuing and excessive increase in ramp carbon emissions, this work adds a queuing control model that considers ramp carbon emissions to the CE-ALINEA control, i.e: (21) $r (t) = r (t - 1) + k_{Q} \cdot [\frac{E_{(t - 1), q}}{{\hat{E}}_{q}} - 1]$ Where: ${\hat{E}}_{q}$ is the threshold value for ramp queuing emissions. The ramp queuing carbon emissions E_t,q in cycle t are: (22) $E_{t, q} = 3.18 e^{- 3} \times \frac{217 + 0.253 \times v_{t}^{q} + 9.65 e^{- 3} \times v_{t}^{q^{2}}}{1 + 9.6 e^{- 2} \times v_{t}^{q} - 4.12 e^{- 4} \times v_{t}^{q^{2}}} \times l_{q} \times l_{o n}$ Where: $v_{t}^{q}$ is the speed of the ramp vehicles in the queue. l_p and l_on are the ramp queue length and ramp length, respectively. Meanwhile, in order to avoid the situation of greatly increasing the ramp regulation rate affecting the mainline traffic, this work constructs a hierarchical control model based on Eq. (20) for the queuing carbon emission of the ramp: (23) $r (t) = r (t - 1) + k_{R} \cdot [\frac{E_{C R} - E_{(t - 1), C O_{2}}}{E_{C R}}], l (t) \leq 0.6 l_{max}$ (24) $\begin{array}{l} r (t) = r (t - 1) + ω k_{R} \cdot [\frac{E_{C R} - E_{(t - 1), C O_{2}}}{E_{C R}}] \\ + (1 - ω) k_{Q} \cdot [\frac{E_{(t - 1), q}}{{\hat{E}}_{q}} - 1] 0.6 l_{max} < l (t) \leq 0.9 l_{max} \end{array}$ (25) $r (t) = r (t - 1) + k_{Q} \cdot [\frac{E_{(t - 1), q}}{{\hat{E}}_{q}} - 1], l (t) > 0.9 l_{max}$ (26) $g (t) = T \cdot \frac{r (t)}{S},$ (27) $g_{min} \leq g (t) \leq g_{max}$ Where: ω is the weight parameter. l_max is the maximum queue length. g is the green phase time. T is the signal control period. S is the entrance ramp saturation flow rate. g_min and g_max denote the minimum and maximum green light time, respectively. Models (23), (24) and (25) represent the use of CE-ALINEA considering only mainline carbon emissions when the ramp queue does not exceed 0.6l_max, the use of CE-ALINEA control considering both mainline and ramp carbon emissions when the ramp queue length exceeds 0.6l_max, and the use of ramp regulation rate considering only ramp queue emissions when the ramp queue length exceeds 0.9l_max, respectively. Eq. g(t) is the green phase time of the signal in the tth control cycle, and Eq. (27) is the constraint on the green phase time.

3

Example analysis of transportation planning for low-carbon needs

3.1

Model simulation analysis

3.1.1

Simulation experiment program design

A simulation experiment program is designed based on the interweaving area of an entrance/exit ramp and the mainline in the selected north-south elevated area. In order to compare the control effects of different control methods, a total of four simulation scenarios are designed, namely, no control, timed control, ALINEA control and CE-ALINEA control scenarios, and the control experiments are conducted to demonstrate the superiority of the CE-ALINEA control proposed in this paper in the control of road network emission reduction, and in order to validate the applicability of the CE-ALINEA control proposed in this paper in the case of traffic demand change. In order to verify the applicability of the proposed CE-ALINEA control when the traffic demand changes, two scenarios of traffic demand reduction and traffic demand increase are further considered in the experimental design, corresponding to the mainline traffic flow of 4000 veh/h and 6000 veh/h, respectively.

3.1.2

Comparative analysis of traffic emission optimization

The emission reductions from adopting the three different ramp control schemes are shown in Fig. 3 compared to not adopting the ramp control scheme. It can be seen that among the three control schemes, the emission reduction effect of adopting timed control is the worst, and even an increase in emissions occurs under the 2min and 3min control cycles. Comparing the two dynamic control algorithms, the ALINEA control algorithm, although it is not aimed at emission reduction as the control objective, but it makes the emissions of the main line reduced by reducing the congestion of the main line as well, and the average emission reduction under the five control cycles when using the ALINEA control is 31.57kg, and the emission reduction under the 1-min control cycle is the best, with an emission reduction of 57.83kg.The CE-ALINEA control algorithm performs better in terms of emission reduction, and brings higher emission reduction under different control cycles. When using CE-ALINEA control, the average emission reduction under five control cycles is 44.66kg, and the same is the best emission reduction under the 1min control cycle, with an emission reduction of 61.38kg.Overall, the CE-ALINEA control algorithm shows more stable control in achieving carbon reduction on mainline roads.

Taking the 3-minute control cycle as an example, the mainline carbon emissions under different control algorithms are shown in Fig. 4. Since the road network flow is in the loading state in the first hour, the difference in the mainline emissions under each control scheme is very small, so Fig. 4 only plots the emission changes in the last two simulation hours. It can be clearly seen that when the timed control scheme is used, there are some hours of emissions more than the no-control scheme, while the two dynamic control schemes are able to make the emissions have a more obvious reduction, indicating that the timed control is not able to be used as an effective means of control for road emission reduction.Continuing to compare the two dynamic control scenarios, the control effect of CE-ALINEA is better than that of ALINEA algorithm, starting from 1h23min, the emissions of the mainline under the control of CE-ALINEA are at a lower level compared with several other control scenarios, and although the emissions of the mainline at individual time periods show some oscillations, the overall is maintained below 883kgCO₂/h, which is better than the other scenarios, indicating that CE-ALINEA has a better optimization effect in reducing mainline carbon emissions.

3.1.3

Comparative analysis of operational efficiency optimization

The weighted speed of the main line is used to judge the operation state, and the speed comparison between different control schemes is shown in Fig. 5. In the no-control state, the weighted speed of the mainline is the same as that in the measured data, which is approximately 49.75 km/h. After adopting the timed control, the average speed of the mainline is increased by 4.92% and 6.77% when the control period is 1min and 5min, respectively, and the operation efficiency can be improved, but in the rest of the three control periods, the operation speed of the mainline is reduced, which is because the timed control is not able to make timely adjustments according to the real-time operating conditions of the road network, so it is also not an effective control means in improving the road access efficiency. Next, comparing the two dynamic control algorithms, both the ALINEA control algorithm and the CE-ALINEA control algorithm are able to effectively improve the running speed of the mainline. With ALINEA control, the speed of the mainline is increased by 6.52% on average under five different control cycles, and the most obvious speed increase is 11.99% when the control cycle is 1 min. The CE-ALINEA control algorithm improves the operating efficiency of the mainline even more obviously, and it can bring a higher percentage of speed increase in different control cycles, and the speed of the mainline is increased by 11.99% when the control cycle is 1 min. When using CE-ALINEA control, the speed of mainline is improved by 8.57% on average under five different control cycles, and also the speed improvement under 1min control cycle is the best, which is improved by 13.27%. Overall, the CE-ALINEA control algorithm is still able to show better optimization effects in improving the operation efficiency of mainline road traffic.

Taking the 1min control cycle as an example, the speed changes of the mainline at different control algorithms are shown in Fig. 6. The average speed of the mainline is recorded every 60ms. In the first hour, because the traffic on the road network is still loading, the operating speed of the mainline in the four scenarios stays near the maximum restricted speed of 72km/h. One minute later, the traffic on the road network finishes loading, at which time the operating speed of the mainline starts to decrease and stabilizes at 00h:01min:52s. For the no-control scenario, the speed of the mainline decreases to below 32km/h after 00h:01min:52s. After taking the timed control, the operating efficiency of the mainline improves somewhat and maintains near 37km/h. For ALINEA control and CE-ALINEA control, the average speed of the mainline in the two scenarios has a more obvious difference from 00h:01min:52s. ALINEA control targets the downstream section after the ramp convergence, and takes the lead in regulating the traffic emissions of the mainline at this point in time because the vehicles in the network are already loaded and the density is at a high level, while the traffic emissions of the mainline have not yet reached the control threshold of CE-ALINEA, so the average speed of the mainline was lower than that of ALINEA control when CE-ALINEA control was used, but in the subsequent simulation periods, CE-ALINEA showed a better control effect, and the average speed of the mainline in most of the periods was higher than that of the ALINEA control scenarios, which demonstrated the fact that CE-ALINEA was able to bring better control results.

The comparison of the other two evaluation metrics, average travel time and number of vehicles passing on the mainline, for different simulation scenarios is shown in Table 1. Taken together, the results show that among the five control cycles, the CE-ALINEA control shows better performance in most cases compared to several other control scenarios in terms of realizing operational efficiency improvement as well as reducing mainline traffic emissions.

Table 1.

Simulation scene evaluation index comparison

Evaluation index	Control cycle	Uncontrolled	Timing control	Controlled by ALINEA	CE-ALINEA control
Average travel time (s)	1min	517.1	454.8	417.7	409.6
	2min	519.3	545.4	495.6	476.4
	3min	515.3	545.4	487.1	447.1
	4min	519.6	536.9	485.6	484.9
	5min	502.8	438.6	436.4	436.7
Main line traffic car Number of vehicles (veh)	1min	9008	9354	9552	9676
	2min	8997	8879	9219	9454
	3min	8989	8856	9254	9528
	4min	8968	8896	9345	9358
	5min	9244	9637	9829	9847

3.2

Analysis of Carbon Emissions from Urban Transportation under Planning Scenarios

3.2.1

Planning program design

In order to compare the carbon emission level of the current transportation in a city, it is assumed that under the new urban layout planning scheme, the fuels of city cabs and buses are natural gas, the fuels of cars and motorcycles are 93# gasoline, and the average 100-kilometer fuel consumption of each major transportation mode of buses, cabs, cars, and motorcycles remains unchanged, as well as the carbon emission factors of various fuels, the net calorific value of the fuels, and fuel density all remain unchanged. The compact multi-center cluster urban spatial layout led by public transportation can effectively guide residents to prioritize public transportation. That is to say, in this mode, private transportation travel behavior will be partially shifted to public transportation mode travel. Based on the CE-ALINEA control model, four planning scenarios are proposed by taking the transportation mode as a single variable influencing factor.

Scenario 1: All of the shifted traffic chooses public transportation trips, with 15% of trips from cars shifted to public transportation, 15% of trips from cabs shifted to public transportation, and 15% of trips from motorcycles shifted to public transportation.

Option 2: All of the shifted traffic chooses bus trips, 30% of the trips from cars are shifted to buses, 30% of the trips from cabs are shifted to buses, and 30% of the trips from motorcycles are shifted to buses.

Scenario 3: All of the shifted traffic chooses bus trips, 45% of the trips from cars are shifted to buses, 45% of the trips from cabs are shifted to buses, and 45% of the trips from motorcycles are shifted to buses.

Scenario 4: All of the shifted traffic chooses bus trips, 60% of the trips from cars are shifted to buses, 60% of the trips from cabs are shifted to buses, and 60% of the trips from motorcycles are shifted to buses.

3.2.2

Analysis of results

According to the results obtained from the CE-ALINEA control model estimation, the comparison of carbon emissions of major transportation modes in a city under the planning scheme is listed, and the comparison of carbon emissions of major transportation modes under the planning scheme and the status quo is shown in Table 2. It can be clearly seen that the status quo carbon emissions of 31.9 kg, compared with the scenarios 1, 3 and 4, the carbon emissions control effect of scenario 2 is optimal, and its reduction ratio is 13.66%. When 30% of private motorized traffic is transferred to public transportation, the total carbon emissions of urban transportation are the smallest, with a reduction of 13.66% relative to the status quo. This verifies to some extent the locking effect of urban spatial layout on urban transportation carbon emissions.

Table 2.

Comparison of carbon emissions of major modes of transportation

Type		Car	Taxi	Motorcycle	Bus	Total carbon emission	Reduction ratio (%)
Current carbon emission		19.6kg	4.06kg	5.46kg	2.78kg	31.9kg
Carbon emissions under planning	Scheme1	13.38kg	3.11kg	3.58kg	28.62kg	28.57kg	10.52%
	Scheme2	10.16kg	2.24kg	2.67kg	27.64kg	27.49kg	13.66%
	Scheme3	6.66kg	1.46kg	1.76kg	28.46kg	28.67kg	11.03%
	Scheme4	3.28kg	0.68kg	0.86kg	29.66kg	29.87kg	7.18%

From the data obtained above, the comparison of the proportion of carbon emissions from each major transportation mode to the total carbon emissions is listed, and the results of the comparison of the proportion of carbon emissions from major transportation modes to the total emissions in the planning scheme and the current situation are shown in Table 3. Based on the data in the table, it can be seen that under the public transportation-led compact multi-center city layout model, with the increase of the proportion of private transportation shifted to public transportation, the carbon emissions of public transportation and its proportion in the total amount of emissions also increased significantly, the carbon emissions of cars and its proportion decreased significantly, and the carbon emissions of cabs and motorcycles and their proportion decreased relatively slowly.

Table 3.

Comparison of the proportion of carbon emissions to the total

Type		Bus/%	Car/%	Taxi/%	Motorcycle/%
Carbon emissions as a percentage of total	Status quo	8.76	61.6	11.7	17.94
	Scheme1	31.6	46.8	9.9	11.7
	Scheme2	44.9	35.8	7.7	11.6
	Scheme3	64.5	22.7	4.7	8.1
	Scheme4	82.6	10.6	1.8	5

A comparison of the number of motor vehicles in each category under the regulated program is shown in Figure 7. The number of cars decreases by 18,400 and the number of motorcycles decreases by 27,300, totaling 45,700, while the number of buses increases by just over 1,500, with the number of private motor vehicles decreasing by 30 times the number of buses increasing. It can be seen that, due to the transfer of private motor vehicles, especially high-polluting, high-energy consumption, low-efficiency cars and motorcycles by tens of thousands of the number of reduction in the number of buses only by thousands of the number of increase in the total number of urban motor vehicle ownership, thereby significantly reducing, which greatly relieves the pressure of the urban traffic. The compact multi-center cluster urban layout led by public transportation can effectively reduce the carbon emission level of urban transportation. The carbon emissions of urban transportation in a city under this model mainly come from buses. One of the ways to achieve low-carbon transportation is to reduce energy consumption and carbon emissions per unit mileage by using energy-efficient transportation. Therefore, the use of low-carbon urban transportation vehicles with low energy consumption and high energy efficiency, especially buses, can reduce the level of carbon emissions from urban transportation under this model. At present, a small number of hybrid vehicles and pure electric vehicles are the two types of energy-efficient vehicles to be promoted at this stage. Hybrid and pure electric vehicles can save about 20% of energy consumption in a comprehensive manner, and the corresponding carbon emissions will be greatly reduced. An urban area is located on a river valley plain with flat terrain, which fully meets the driving requirements of pure electric vehicles. If a large number of pure electric public transportation vehicles (buses, cabs, etc.) are used under the new planning mode, the effect of energy saving and emission reduction in the city will be very good. In summary, the urban layout planning scheme can significantly reduce the level of carbon emissions from urban transportation, and is conducive to the shift of urban private transportation modes to public transportation, thus realizing the decarbonization of urban transportation from the level of urban layout planning.

4

Conclusion

This paper synthesizes the green transportation theory and low-carbon transportation characteristics, proposes a carbon emission model based on the CE-ALINEA algorithm, and applies the model to analyze the example of transportation planning under low-carbon demand.

1) Compared with the other three control schemes, when using CE-ALINEA control, the average emission reduction under five control cycles is 44.66 kg, also the best emission reduction effect under 1 min control cycle, with an emission reduction of 61.38 kg. On the whole, in realizing the carbon emission reduction of the main road, the CE-ALINEA control algorithm shows a more stable control effect.

2) The status quo carbon emission is 31.9kg, compared with scheme 1, 3 and 4, the carbon emission control effect of scheme 2 is the best, and its reduction ratio is 13.66%, which indicates that when 30% of private motorized transportation is transferred to public transportation, the total carbon emission of urban transportation is the smallest, and the relative status quo carbon emission is reduced by 13.66%, which confirms that the urban spatial layout has a carbon emission locking effect on urban transportation carbon emissions.

Language:: English

Publication timeframe:: 1 times per year
Journal Subjects:: Life Sciences, Life Sciences, other, Mathematics, Applied Mathematics, General Mathematics, Physics, Physics, other

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Mathematical Modeling Study on Carbon Emission Control by Green Transportation Network Planning in Urban Agglomerations

Dazhang Liu

Published Online: Mar 21, 2025

Received: Nov 06, 2024

Accepted: Feb 08, 2025

DOI: https://doi.org/10.2478/amns-2025-0644

KeywordsCE-ALINEA, Control model, Network planning, Carbon emission, Green transportation theory

© 2025 Dazhang Liu, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
CE-ALINEA, Control model, Network planning, Carbon emission, Green transportation theory