Transportation Research Part B-Methodological最新文献

{"title":"A game-theoretical model of road pricing with an endogenized user-equilibrium with multiple user classes","authors":"Gaurav Malik ,&nbsp;Stef Proost ,&nbsp;Chris M․J․ Tampère","doi":"10.1016/j.trb.2025.103211","DOIUrl":"10.1016/j.trb.2025.103211","url":null,"abstract":"<div><div>This paper presents a game-theoretical model of road pricing. The model incorporates an endogenized demand and path-choice user-equilibrium with variable user demand and multiple user classes. Different to most of the literature, the proposed model allows to compute in a direct way the optimal tolls, rather than by trial and error of exogenous toll values and tackles the problem of inactive paths that can become active (and vice-versa). Additionally, games with multiple government in different settings can be solved. We proceed in four stages. Firstly, the user-equilibrium model is developed to predict the response of general users to toll instruments of the government(s). Modelling of multiple user classes allows to differentiate users who have different Value of Time and Willingness-To-Pay for their trips. Further, it allows such users to be targeted by different toll instruments. Secondly, a single-player optimization problem is formulated to find optimal toll values for a government acting as a Stackelberg leader over the users. Thirdly, to handle the non-uniqueness of user-equilibrium path flows, a heuristic-based post-processing method is presented that helps in identifying suitable access restrictions necessary to avoid the suboptimal user responses. Fourthly, the single-player optimization problem is used as a building block to develop a general game-theoretical framework that can be applied to different competition scenarios between different types of governments with each, possibly, tolling a different part of the network or the society. The model is, then, applied to four illustrative case-studies. The first case-study involves a single-player optimization problem and ends with a comparison of three solution methods. Mixed Integer Quadratic Program is shown to be the fastest as well as the most consistent. The second case-study involves a game-theoretical problem with two governments and two user classes, and four competition scenarios are elaborated. It is demonstrated how the central objective function can only be worsened by any type of competition between players, and that players have an incentive to take leadership to convert a Nash game to a Stackelberg game. The third case study specifically addresses the non-uniqueness of user-equilibrium path flows, and two different levels of access restrictions are assessed in the post-processing. Finally, the fourth case study shows an application of the single-player optimization problem to a real-world urban mobility problem.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103211"},"PeriodicalIF":5.8,"publicationDate":"2025-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143783891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Conflict-free optimal control of connected automated vehicles at unsignalized intersections: A condition-based computational framework with constrained terminal position and speed","authors":"Yongjie Xue ,&nbsp;Li Zhang ,&nbsp;Yuxuan Sun ,&nbsp;Yu Zhou ,&nbsp;Zhiyuan Liu ,&nbsp;Bin Yu","doi":"10.1016/j.trb.2025.103209","DOIUrl":"10.1016/j.trb.2025.103209","url":null,"abstract":"<div><div>Conventional intersection management relies on traffic signals to coordinate conflicting traffic flows and distribute right-of-way. However, delays caused by traffic signals remain a major burden on urban transportation systems. Emerging connected automated vehicles (CAVs) are expected to improve the intersection management by coordinating vehicle movements without relying on traffic signals. Hence, this paper primarily focuses on coordinating CAVs at unsignalized intersections, especially common unsignalized intersections composed of major and minor roads, which exhibit inherent asymmetries such as higher speed limits and vehicle arrival rates on major roads compared to minor roads. We propose a conflict-free optimal control method to achieve highly efficient coordination of CAVs at these unsignalized intersections. The method employs a hierarchical coordination framework, in which an upper layer optimizes the passing order for CAVs through the intersection, and a lower layer designs a second-order optimal control model with constrained terminal position and speed for trajectory planning. Specifically, the upper layer adopts an improved Incremental Learning Monte Carlo Tree Search to efficiently generate a nearly global-optimal passing order for CAVs within a very short planning time. The lower layer introduces a condition-based computational framework that enhances the standard iterative solution procedure used in the constrained Hamiltonian analysis, and derives a closed-form analytical solution for the constrained optimal control problem without any recursive steps. The results of numerical experiments show that the proposed method can achieve real-time conflict-free optimal trajectory planning for all CAVs. Compared with fully-actuated signal control, the proposed method reduces the average delay for all CAVs by <span><math><mrow><mn>19</mn><mo>.</mo><mn>92</mn><mi>s</mi></mrow></math></span>, <span><math><mrow><mn>16</mn><mo>.</mo><mn>46</mn><mi>s</mi></mrow></math></span>, and <span><math><mrow><mn>15</mn><mo>.</mo><mn>47</mn><mi>s</mi></mrow></math></span> under both symmetric and asymmetric traffic demands (i.e., the ratios of CAV arrival rates on the major to minor roads are 1:1, 2:1, and 3:1, respectively).</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103209"},"PeriodicalIF":5.8,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143759600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computational investigations of a multi-class traffic flow model: Mean-field and microscopic dynamics","authors":"A. Machtalay ,&nbsp;A. Habbal ,&nbsp;A. Ratnani ,&nbsp;I. Kissami","doi":"10.1016/j.trb.2025.103196","DOIUrl":"10.1016/j.trb.2025.103196","url":null,"abstract":"<div><div>We address a multi-class traffic model, for which we computationally assess the ability of mean-field games (MFGs) to yield approximate Nash equilibria for traffic flow games of intractable large finite-players. We introduce <em>ad hoc</em> numerical methodologies, with recourse to techniques such as High-Performance Computing (HPC) and regularization of Loose Generalized Minimal Residual (LGMRES) solvers. The developed apparatus allows us to perform simulations at significantly larger space and time discretization scales. For three generic scenarios of cars and trucks, and three cost functionals, we provide numerous numerical results related to the autonomous vehicles (AVs) traffic dynamics, which corroborate for the multi-class case the effectiveness of the approach emphasized in Huang et al. (2020). We additionally provide several original comparisons of macroscopic Nash mean-field speeds with their microscopic versions, allowing us to computationally validate the so-called <span><math><mrow><mi>ϵ</mi><mo>−</mo></mrow></math></span>Nash approximation, with a rate slightly better than theoretically expected.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103196"},"PeriodicalIF":5.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143695910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"There is something more fundamental than fundamental diagram","authors":"Daiheng Ni","doi":"10.1016/j.trb.2025.103206","DOIUrl":"10.1016/j.trb.2025.103206","url":null,"abstract":"<div><div>Revealing the inherent relationships among traffic flow characteristics, fundamental diagram has long been regarded as one of the pillars of traffic flow theory since Greenshields seminal work. When it is combined with the law of (mass/vehicle) conservation, dynamic modelling of traffic flow at the macroscopic level such as LWR and others have thrived. This paper shows that fundamental diagram is only a shadow of something more fundamental, i.e., phase diagram, which is originated from first principles of physics. At the microscopic level, traffic flow can be analyzed by examining the relative motion of two vehicles in car following. When the coordinate system is fixed on the leading vehicle, the Hamiltonian of this system can be defined as the total energy of the system. Conservation of total energy is established by incorporating physical entities (vehicles) and non-physical entities (drivers), the latter of which is enabled by the field theory of traffic flow. Consequently, the Hamilton's equations stipulate a vector field that constitutes the phase diagram of the system which, in turn, specifies Hamiltonian flow swirling around some equilibrium points. When focusing on the equilibrium points, the phase diagram reduces to the fundamental diagram, during which process much information is lost. Consequently, the lost information obscures the origin of the equilibrium points and further the fundamental diagram. This research roots traffic flow theory in first principles of physics and offers an example to address the dynamics of similar systems that involve human intelligence.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103206"},"PeriodicalIF":5.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143637759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A flexible non-normal random coefficient multinomial probit model: Application to investigating commuter's mode choice behavior in a developing economy context","authors":"Chandra R. Bhat ,&nbsp;Aupal Mondal ,&nbsp;Abdul Rawoof Pinjari","doi":"10.1016/j.trb.2025.103186","DOIUrl":"10.1016/j.trb.2025.103186","url":null,"abstract":"<div><div>There is growing interest in employing non-normal parameter distributions on covariates to account for random taste heterogeneity in multinomial choice models. In this study, we propose a flexible, computationally tractable, structurally simple, and parsimonious-in-specification random coefficients multinomial probit (MNP) model that can accommodate non-normality in the random coefficients. Our proposed methodology subsumes the normally distributed random coefficient MNP model as a special case, thus eliminating the need to a priori decide on the distributional assumption for each coefficient. The approach employs an implicit Gaussian copula to combine the univariate coefficient distributions into a multivariate distribution with a flexible dependence structure. Using our new flexible MNP framework, we investigate the commute mode choice behavior for workers in the city of Bengaluru, a metropolitan city in southern India. Results from our analysis indicate that sociodemographic variables, commute characteristics, and mode-related attributes significantly impact the commute mode choice decision. Importantly, our results indicate the presence of unobserved taste heterogeneity in the sensitivities to the travel time and travel cost variables; moreover, the distribution of the travel time coefficient is found to be significantly non-normal. In terms of data fit, our proposed model statistically outperforms the traditional MNP model as well as an MNP model that imposes normality on the travel time coefficient. The pitfalls of ignoring non-normality in the distribution of parameters are also discussed, as are several policies to promote a shift from private modes of transportation to more sustainable public transportation/walk modes.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103186"},"PeriodicalIF":5.8,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143627570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bounding the efficiency of vehicle automation in general transportation networks","authors":"Fang Zhang ,&nbsp;Qiang Meng ,&nbsp;Araz Taeihagh","doi":"10.1016/j.trb.2025.103204","DOIUrl":"10.1016/j.trb.2025.103204","url":null,"abstract":"<div><div>Emerging autonomous vehicle (AV) technology is expected to bring substantive benefits to the transportation systems. This study focuses on the improvement of travel efficiency in transportation networks with AVs. Inspired by the concept of price of anarchy (PoA), we introduce a novel indicator, the benefit of vehicle automation (BVA), to quantify the efficiency benefit brought by AVs. The BVA is defined as the ratio of the transportation network performances under the two user equilibrium states before and after the penetration of AVs. In characterizing the BVA, both the AV market penetration rates and the automation levels are used to describe AV deployment, and the impact of AVs in terms of capacity improvement and value-of-travel-time (VOTT) compensation are explicitly considered. Under mild assumptions, we derive a family of bounds of BVA that are independent of the network topology, including two types of lower bounds and four types of upper bounds. These bounds have different degrees of generality and effectiveness in distinct scenarios. Properties including tightness, monotonicity and generality of the bounds are discussed. Numerical experiments on general networks are conducted to verify the effectiveness and applicability of them. Furthermore, we also propose two bicriteria bounds of BVA. The first specifies the maximum level of rising demand whose induced efficiency loss can be offset by the benefit of AV penetration, while the second provides an upper bound on the worse-off degree of the performance due to non-uniform AV penetration across origin-destination pairs. This work is expected to deepen our understanding of the efficiency benefit of AVs in general transportation networks, and to provide a guideline for policymakers to navigate the integration of AVs.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103204"},"PeriodicalIF":5.8,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143628274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rapid post-disruption assessment of capacity reduction and demand distribution for transportation network under limited information","authors":"S. Travis Waller ,&nbsp;Qingying He ,&nbsp;Wei Liu","doi":"10.1016/j.trb.2025.103194","DOIUrl":"10.1016/j.trb.2025.103194","url":null,"abstract":"<div><div>Transportation networks are crucial for social and economic activities but are susceptible to disruptions. Rapid quantification of the impacts of network disruptions can assist in planning recovery efforts. However, gathering timely and comprehensive information for assessing transportation network state is often challenging and not always possible. This study introduces a network assessment strategy to estimate total link capacity reduction and origin–destination (OD) demand matrix (CRDM) for disrupted transportation networks subject to limited information, i.e., link travel time accessible from smartphone-based trajectory data. The CRDM problem can be formulated as a bi-level model, optimizing estimates of externally caused capacity reduction and OD demand matrix in the upper level while solving the user-equilibrium-based traffic assignment in the lower level. The proposed bi-level model with a generalized least squares (GLS) objective (to minimize the discrepancy between observed and estimated travel times) does not yield a unique solution. Therefore, we further employ the maximum entropy principle to develop a maximum entropy-least squares (MELS) model, which has a unique solution. To solve the MELS model, we develop a tailored augmented Lagrangian algorithm and conduct numerical studies on different transportation networks (i.e., a two-link single-OD network, the Sioux-Falls network and a real-world regional transportation network). The proposed approach is able to provide a rapid post-disruption evaluation of the overall link capacity loss in transportation network under limited information, i.e., without OD demand information and with limited information on link travel time.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103194"},"PeriodicalIF":5.8,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143619369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modeling the effects of new airport on a multi-airport system with air-rail integration service and heterogeneous passengers","authors":"Wen-Jing Liu ,&nbsp;Zhi-Chun Li ,&nbsp;Xiaowen Fu","doi":"10.1016/j.trb.2025.103195","DOIUrl":"10.1016/j.trb.2025.103195","url":null,"abstract":"<div><div>This paper investigates the effects of new airport on a multi-airport system (MAS) with air-rail integration service and heterogeneous passengers. Vertical structure models are proposed to capture the interactions among the stakeholders: passengers, airlines, and rail operator. In the proposed models, passenger heterogeneity is reflected by a continuous value-of-time (VOT) distribution, and the total passenger demand is given. The critical VOTs dividing the passengers into different groups by travel mode are identified, and the distributional effects of new airport and air-rail cooperation on the heterogeneous passengers are examined. The findings show that the new airport and air-rail cooperation can benefit all passengers, and these benefits vary significantly across passengers. The poorest passengers gain the most from the air-rail cooperation. However, who gains the most from the new airport depends on the transfer time and cost for the new airport service. For a relatively low transfer time and cost, the mid-income passengers gain the most. Otherwise, the low-income passengers gain the most. At a high congestion level of the hub airport, introducing a new airport is more efficient in decreasing the social cost of the system than introducing the air-rail cooperation. Conversely, at a low congestion level of the hub airport, introducing a new airport may cause an increase in the social cost of the system instead. Consequently, the decision of investing in a new airport in an MAS should be carefully made.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103195"},"PeriodicalIF":5.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Airport's optimal decisions considering non-aeronautical business, terminal capacity and alternative regulatory regimes","authors":"Yue Huai ,&nbsp;Enoch Lee ,&nbsp;Hong K. Lo ,&nbsp;Anming Zhang","doi":"10.1016/j.trb.2025.103192","DOIUrl":"10.1016/j.trb.2025.103192","url":null,"abstract":"<div><div>This study explores the optimal decisions of airports on charge, capacity, and suggested passengers’ arrival time at the airport under various regulatory regimes (e.g., single- or dual-till regulation). By considering both aeronautical- and non-aeronautical businesses and further incorporating the non-linear relationship between queuing time in the check-in zone and shopping time in the retail zone, we find that unlike runway capacity expansion, where single-till regulation leads to underinvestment (as compared to the unregulated case), terminal capacity expansion is contingent upon traffic volumes. Under higher traffic volumes, terminal capacity expansion becomes less efficient in reducing the terminal congestion delay, thereby reducing the effect on expanding passengers’ shopping time and concession revenue. As the revenue loss is disregarded under single-till regulation, airports would overinvest in terminal capacity under higher traffic volumes, which reverses the underinvestment tendency under lower traffic volumes. Also, single-till regulation results in a later airport arrival time suggested to passengers, for which the excess concession revenue from an earlier arrival time is overlooked. By contrast, dual-till regulation tends to attract more passengers to the airport by reducing terminal and runway delays, therefore leading to lower airport charge, shorter terminal time and higher capacity. The increased ridership and enhanced utility thus improve the overall social welfare.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103192"},"PeriodicalIF":5.8,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143611243","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the morning commute problem with mixed autonomous and human-driven traffic under stochastic bottleneck capacity","authors":"Qiumin Liu ,&nbsp;Wei Liu ,&nbsp;Rui Jiang ,&nbsp;Xiao Han","doi":"10.1016/j.trb.2025.103203","DOIUrl":"10.1016/j.trb.2025.103203","url":null,"abstract":"<div><div>This paper investigates the impact of external uncertainty on morning commute behavior when autonomous vehicles (AVs) are introduced and interact with human-driven vehicles (HVs). We adopt the bottleneck model to study the morning commuting dynamics. In this context, we consider two potential benefits for AVs, i.e., value-of-time (VOT) compensation/reduction and capacity enhancement. We develop an extension-elimination-verification-supplement approach to simplify the equilibrium analysis process to obtain the equilibrium departure flow patterns. We find that the external uncertainty makes the equilibrium departure flow patterns more complicated than those under the deterministic setting, yielding three basic departure flow pattern types, i.e., AVs travel inside HVs, AVs travel after HVs, and HVs and AVs depart alternatively. If AVs are able to reduce VOT, their ability to improve bottleneck capacity does not qualitatively change the equilibrium departure flow patterns. Moreover, although increasing the penetration of AVs can improve the system performance to some degree, the total travel costs may not be monotonically decreasing with respect to AV penetration when AVs cannot significantly enhance bottleneck capacity. The optimal penetration rate of AVs minimizing the total travel costs is no less than 50% and the total travel costs reach the minimum in the situation with mixed HVs and AVs rather than in the 100% AV penetration if the bottleneck capacity enhancement caused by AVs is not significant enough. Furthermore, increasing the penetration of AVs may indeed increase traffic congestion when compared to that under 100% HVs if AVs cannot enhance bottleneck capacity sufficiently. To reduce total travel costs by increasing AV penetration, it is necessary to ensure that AVs can enhance bottleneck capacity sufficiently as the penetration rate of AVs increases when the adverse effects of VOT compensation on traffic congestion are dominated. When the penetration rate of AVs reaches 100%, the capacity enhancement from AVs should be sufficiently large to ensure that AVs can simultaneously improve the system performance and reduce traffic congestion.</div></div>","PeriodicalId":54418,"journal":{"name":"Transportation Research Part B-Methodological","volume":"195 ","pages":"Article 103203"},"PeriodicalIF":5.8,"publicationDate":"2025-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143592452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}