Research on Congestion Pricing in Multimode Traffic considering Delay and Emission

1MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing 100044, China 2Shandong Provincial Transport Scientific Research Institute, Jinan 250031, China 3Center of Cooperative Innovation for Beijing Metropolitan Transportation, Beijing 100044, China 4School of Traffic and Transportation, Beijing Jiaotong University, Beijing 100044, China 5Changchun Municipal Engineering Design and Research Institute, Changchun 130033, China


Introduction
With the development of urbanization and automation, the supply and demand contradiction of urban traffic has become increasingly prominent as well as traffic jam, which has resulted in a series of problems, such as increasing travel delays and traffic emissions, more frequent traffic accidents, and reducing transportation efficiency. The primary reason of urban traffic congestion is the sharp contradiction between urban transport developing and land use. To ease this problem effectively, thousands miles of urban roads have been built in many Chinese cities recently, but this is not the feasible solution to mitigate congestion. For a few decades, congestion pricing has been considered to be an effective way for traffic demand management and revenue regeneration in many cities worldwide. It can balance the spatiotemporal distribution of travel demand by making travelers readjust their travel modes and routes to avoid congested roads. Thus, t h et r a ffi cc o n g e s t i o nc a nb ea l l e v i a t e da n du r b a nt r a ffi c system-wide operation efficiency can be improved.
The original motivation of congestion pricing is to reduce traffic congestion [1][2][3][4][5]. Now these corresponding models can generally be classified into two categories, namely, static and dynamic. Waiters proposed an optimal static congestion pricing model according to marginal cost pricing theory, and this model firstly defined that toll charge on each road section was the difference of marginal social cost and marginal individual cost [6]. Dafermos and Sparrow established a road charging model based on marginal charging theory [7], which was applied in multiclass-user transportation network subsequently [8]. Yang and Huang extended to study marginal cost pricing with the constraint of road traffic capacity [9]. In the field of dynamic congestion pricing, Vickrey built a congestion pricing model, considering the departure time of 2 Discrete Dynamics in Nature and Society the travelers at the bottleneck, to make toll pricing equal to queue time cost for system equilibrium [10]. Wie and Tobin developed two types of dynamic congestion pricing models based on the marginal cost pricing theory, and two dynamic charging models were appropriate for a network with stable travel demand and fluctuant travel demand, respectively [11]. Arnott et al. researched the bottleneck charging problem under the condition of random travel capacity and demand for further study [12]. Yang and Huang formulated a timevaryingpricingmodelofaroadbottleneckwithelastictraffic demand based on optimal control theory [13]. Liu et al. proposed a mathematical programming with equilibrium constraint model for the speed-based toll design [1 ].
In recent years, given the ever-increasing concern on the sustainability of transportation, travel environments have received much attention and have been comprehensively considered in the travel mode choice. Nowadays, both emissions and other environmental factors are often taken into account in road pricing. It is believed that congestion pricing c o u l dl e a dt oe m i s s i o nr e d u c t i o na n du r b a ne n v i r o n m e n t improvement. In this field, Johansson discussed how to apply marginal cost pricing theory to obtain the maximal net social benefit by internalizing marginal emissions and fuel consumption costs [15]. Nagurney et al. carried out a series of pioneering work on market-based policies and proposed a novel charging strategy to keep traffic emission within the limi to fanen vir o nmen talq uali tystandar d [16][17][18]. Yin and Lawphongpanich showed that a traffic flow distribution on a network with minimum emissions can always be induced by a toll charging scheme if link emission functions are increasing [19]. Chen and Yang studied nonnegative link toll schemes and cum rebate schemes for Pareto system optimum of congestion and emissions on a road network using a biobjective optimization approach [20]. Almodóvar et al. proposed a bilevel approach for estimating pollution tax to meet environmental goals [21]. Li et al. designed a road toll model considering congestion and environmental externalities on a congested network with uncertain demand [22]. Yang et al. presented an optimal toll approach for linkbasedemissionpricing [23].
These aforementioned methods of urban road pricing mainly focus on single-mode transportation system, which consider environmental factors such as emission. However, few articles have been devoted to focusing on multimode transportation system, particularly on environment and congestion. Hence, a comprehensive congestion pricing approach, under multimode and environmental condition, should be developed to reduce travel delay and pollution emission, for the efficiency and sustainability of entire urban transportation system. The rest of the paper is organized as follows: Section 2 constructs a bilevel programming model of dual-mode urban traffic congestion pricing considering delay and emissions a n dt h e np r o p o s e st h ea l g o r i t h mc o m b i n i n gt h es u c c e s s i v e average method with the genetic algorithm. Section 3 performs a numerical simulation to test the applicability of the congestion pricing method on system operation and performance. Section concludes the paper with a summary of the general findings.

Model Construction and Algorithm Solution
2.1. Model Construction. Firstly, the dual-mode pricing model in the paper assumes that the car and bus network are completely separated, and commuters could only transfer within the bus network. Secondly, the ultra-network theory, discussed by Nagurney and Dong [2 ], is applied in the urban multimode traffic network according to adding virtual nodes and links [25]. In the following network, traveler's cost perceptual psychology is described by proportional expansion and absolute expansion and extended to links and sections [26]. Finally, the Logit-SUE model is applied to analyze route choice behavior in the multimode traffic network. (1) In this paper, buses and cars are regarded as heavy vehicles and light vehicles, respectively, and their emissions are calculated by (2). In the calculation, the specific parameter values of carbon dioxide, as the only emission gas, are described by Yao and Song [27]. Therefore, in which, is the average passengers number by car; is the length of link ; ℎ is the frequency of bus line ; is the toll charge of link ; + is the upper bound of toll charges on link ; is the set for car routes; is the set for bus paths; 1 , 2 , 3 ,and 4 are the parameters of emission function by car; 1 , 2 ,a n d 3 are the parameters of emission function by bus; when ∈ , 0 is the freeflow travel time on link ;w h e n ∈ , 0 is the average travel time of bus on link ; , are the parameters of BPR function; V is the average travel speed on link . Besides, is a 0-1 variable; if bus line goes through path ,then =1; otherwise =0.

The Lower-Level Model.
In the lower-level model, (5) is the probabilistic loading equation for Logit-SUE model. Equation (6) is the constraint for travel demand equilibrium. Equation (7) is the nonnegative flow constraint. Equation (8) is link flow conservation constraint. Equation (9) reflects commuters' travel variance of each mode in the relative cost structure and perceived cost: where is the commuters' flow for path between OD pair ; is the travel demand between OD pair ; is the parameter for Logit-SUE model; is the total cost on path between OD pair ; is the set of OD pairs; is the valid path set between OD pair ,and = ∪ ; is the incidence matrix of link ,i fl i n k is on the path , =1 ,otherwise =0 ; V is the monetary cost of fuel consumption per kilometer; is the travel time perception expansion by car, and assume that >1 ; is the travel time perception expansion on the bus, and we have that > ; V is the monetary cost per comfortable degree loss by bus; ℎ ( ) is the function of comfort cost on link ;w h e n ∈ , is the traffic capacity on link ;w h e n ∈ , is the average traffic capacity of bus line ; is the sum of bus replacement fare and transfer time cost on path between OD pair ; is the replacement fare on path ; is the perceived transfer time cost, which has an inverse relationship with the transferred bus frequency.
V a l i dp a t hs e t ,a st h eb a s i cc o m p o n e n to fL o g i t -S U E assignment model, has important implications for traffic assignment results. There are a variety of effective path set methods proposed for SUE, such as Dial algorithm [28], full path set [29], and cumulative path set under user-equilibrium condition [30]. For simplicity, the efficient path set of absolute cost constraints is adopted to filter the feasible path. Based on multimode cost function in (9), commuters' preferences, and travel habits, we can obtain valid paths of each mode: where is the path set between OD pair on car network; is the path set between OD pair on bus network; − and − are the total monetary cost (RMB) of any link between OD pair by car and bus under free-flow state, respectively; is the total cost (RMB) of path between OD pair under free-flow state.
2.2. The Algorithm. In the paper, the algorithm combining the successive average method (MSA) with the genetic algorithm (GA) is developed to solve the proposed bilevel programming pricing model. It aims to solve the lower Logit-SUEmodelandthentoaccuratelyevaluatetheapplicability of each chromosome in GA. The detail algorithm solution is shown as follows.
Step 1. According to (12), find the valid path set between OD pair .
Step 2. Enter the predetermined model parameters and set the initial path flow =0,∀ , .
Step 3. Update the link flow and travel cost and calculate and substitute the generalized travel cost of each path in the set based on (8).
Step 6. Examine the astringency, if

Experimental Results
3.1. Experimental Road Network. The hypothetical network for numerical test, as shown in Figure 1,consistsoftwotraffic modes: car and bus (c and b, resp.). The label of each link has a unique two-part name, mode-symbols and serial-codes. It is important to note, however, that the serial codes of bus network are the number combination of line and section, for example, b12 represents the second link on bus line 1.
In Figure 1, there are 8 nodes (including grey internal transfer stations of bus) and 21 links. There are 11 links (c1∼c11) for the car subnetwork and 2 lines, 11 sections (b11∼b15 and b21∼b25) for bus subnetwork. The net information is listed in Tables 1, 2, 3,and and all the parameters remain fixed in the following schemes.

Experimental Parameters and Schemes.
The normal values of all parameters in the congestion pricing model are given in Table 5. Suppose the other parameters are fixed when carrying out a parameter sensitivity analysis.
Based on the standard parameter values and (12),t h e effective path set of the dual-mode network is obtained in Table 6.
As shown in Table 6, there are 12 effective paths between OD pairs, including 6 paths of car network and 6 paths (including transferred paths, which are number 8, number 9, number 11, and number 12) of bus network. Based on the above assumptions and results, two simulated test schemes in Table 7 are set up in this paper, which are the basic test analysis under charge and the analysis under charging or nocharging. Additionally, the corresponding model is the lower Logit-SUE model of the bilevel programming under the nocharging condition.

Test Scheme 1.
To simplify the representation, the additional units are omitted in the following analysis. The results of test Scheme 1 in Table 7 contain two parts. On the one hand, the commuters' flow proportion change of each mode a n dc h a n g eo ft o t a ld e l a ya n dt o t a le m i s s i o na r es h o w ni n Figure 2, when the travel demand under charging increases from 500 to 5000. On the other hand, when the delay weight of the upper objective function increases from 0 to 1, the variations in commuters' flow proportion for each mode are    Figure 3(a), and the variations of total delay and total emission are depicted in Figure 3(b),respectively .
In Figure 2, it shows that (i) commuters' flow proportion of the car has an increasing tendency with the travel demand, but oppositely bus share decreases, particularly when the total travel demand is over 3000. It indicates that the growth of comfort loss cost, due to bus crowding, is higher than growth of car travel time cost, particularly at a high travel demand (Figure 2(a)) and (ii) the total delay and the total emission increase gradually with the travel demand, and the growth rate of the total delay is slightly higher than that of total emissions. It demonstrates that the growth of travel demand, as compared to charging, leads to the deterioration of transportation system performance in Figure 2(b).
In Figure 3, it concludes that when the delay weight of objective function ≤ 0.4, the growth of the target delay weight has no significant influence on the commuters' Discrete Dynamics in Nature and Society 5    reduced total delay, and the increased total emission, and these effects will be smaller and smaller until disappearing along with increasing .Thoseindicatethat(i)althoughthe increase of delay weight is of benefit for reducing system-wide total delay, it leads to the decline of bus share and increasing total emissions and (ii) to promote low-carbon travel, bus service level also should be improved to reduce travel cost and further to promote system efficiency and travelers' benefits.
In addition to the improvement of bus performance, the measures, including increasing bus frequency and reducing transfer cost, also should be taken in time by the authorities.
3. . Test Scheme 2. In this section, the results of test Scheme 2 in Table 7 contain two parts. Firstly, when the travel demand increases from 500 to 5000, the commuters' flow proportion change of each mode and the change of the total delay and the total emissions between pricing and no-pricing can be shown in Figure . Secondly, when the delay weight of the upper objective function increases from 0 to 1, the commuters' flow proportion change of each mode and the change of total delay and total emission between pricing and no-pricing are shown in Figure 5. (iii) when the travel demand is equal to 3500, road pricing reaches to the maximum; (iv) with the travel demand over 3000, congestion pricing can effectively reduce the total delay of network and gradually increase with the growth of travel demands; and (v) no matter how much travel demand is, the implementation of road congestion pricing can reduce the total emission.
The aforementioned test addresses that, when the delay weight is equal to the emission weight, congestion pricing at medium travel demands can effectively affect commuters' travel mode choices and improve the bus share. The reason can be explained as that road pricing is the most conducive to exert the cost advantages of bus at medium travel demands. Meantime, road pricing promotes the increasing of bus users   and plays a key role in sustained environmental improvement. However, it should not be implemented from the perspective of relieving congestion when travel demand is at a low level, because the average travel time of bus is longer than that of car. Instead, when travel demand is at a high level, pricing can significantly improve network performance due to apparent cost advantages of car. According to Figure 5, it deduces that (i) no matter how much the target delay weight is, congestion pricing can not only improve the bus share and reduce the total emissions but also increase the total delay; (ii) when ≤0.4, pricing has maximum effects on each parameter, and this effect has small relevance to the target delay weight in this range; and (iii) when ≥0 . 4 ,w i t ht h ei n c r e a s eo fd e l a y weight, the congestion pricing decreases positive effect for car commuters' proportions and the total emissions and weakens t h en e g a t i v ei m p a c to ft h et o t a ld e l a y .Th ea b o v er e s u l t s indicate that, when the traffic demand is at the medium level (travel demand is equal to 2500), there is a significant conflict between the optimization of travel mode share and relieving traffic congestion, even through congestion pricing.

Conclusions
Compared with the existing studies, this paper investigates theco n g estio np ricin gf o rd ual-modeurba ntra fficnetw o rk (car mode and bus mode) at first. Second, a traffic congestion pricing model based on bilevel programming with Logit-SUE is established for the bimode traffic network considering delay and emission. Third, an improved GA embedded MSA is presented to resolve the optimal pricing strategy. Finally, a numerical example is presented to illustrate the capabilities of the methodology and further indicates that (i) congestion pricing can increase the mode share of bus and thus contributes to reduce the total network emission and improve urban environment; (ii) when the travel demand is at a low level, it is difficult to make a tradeoff between reducing emission and relieving congestion; (iii) when the travel demand is at a high level, congestion pricing could raise bus share and reduce total emission.