ATIS与收费策略下多用户随机均衡的效率损失

Bounding the Efficiency Loss of Multi-class Stochastic User Equilibrium under ATIS and Road Tolling

考虑ATIS作用的交通网络,用户具有交通信息接受程度的异质性;进一步,考虑实施道路收费策略情形下,用户具有时间价值的异质性;基于这两类异质性,研究了ATIS下异质性交通网络的效率损失问题。用户对ATIS系统的响应程度,亦即ATIS信息遵从率,是影响ATIS系统运行效率的关键因素。因此,通过ATIS信息遵从率参数的引入,将用户分为不同类型。假设用户均按照随机方式进行择路,建立了基于时间准则与基于费用准则的多用户Logit-随机均衡变分不等式。当系统总出行成本包含收费时,建立了多用户双准则系统最优模型,界定了多用户Logit-随机均衡相对于多用户系统最优的效率损失,推导出效率损失上界;进一步分析了当路段阻抗函数为多项式情形时,引入了自由流出行时间参数,给出了双准则下效率损失上界的解析式,分析了效率损失上界与各参数之间的关系。研究结论表明,双准则下效率损失上界为ATIS信息遵从率的减函数;此外,效率损失上界与路段阻抗函数、用户时间价值及其对路网的熟悉程度、路网本身复杂程度等因素有关。最后,通过算例验证了结论的有效性。

With the dramatical increasement of the motor vehicles,many complex traffic problems have emerged.Information induction and congestion tolling strategy are two common and effective traffic management and control methods,guiding or inducing travelers’route choices to improve system efficiency.Traffic managers often combine the Advanced Traveler Information Systems(ATIS)with the congestion tolling strategy,fully utilizing the advantages of both to form an integrated demand management model.As an important part of Intelligent Transportation Systems,ATIS enables the sharing and utilization of traffic information,guiding travelers to make correct route choices.Congestion tolling strategy influences travelers’decisions by charging road tolls.Regarding the efficiency loss of the heterogeneous traffic network under ATIS,relevant research only considers the impact of the ATIS penetration rate.However,the influence of the information compliance rate is often ignored on the efficiency loss of ATIS.Scholars have already examined the efficiency loss of road tolling strategy.How the efficiency loss of the traffic network changes under the combined effect of ATIS and tolling strategy is an important issue for traffic managers.Therefore,it is necessary to theoretically explore the impact of ATIS and tolling strategy on the efficiency of the traffic network.In this paper,based on different heterogeneities,the efficiency loss of heterogeneous traffic network under ATIS and tolling strategy is discussed.Considering that users are heterogeneous in the value of time(VOT)under the road tolling strategy,users have heterogeneity in terms of different information received in a transportation network under ATIS.Based on the two heterogeneities,the efficiency loss of the heterogeneous network is investigated.Firstly,all users are classified into different groups based on the VOT heterogeneity.Then,considering that ATIS essentially depends on the travelers’response to the traffic information,the information compliance rate is introduced.Taking into account the impact of the ATIS penetration rate and the information compliance rate,users are divided into three classes in each group,i.e.,users with ATIS and in compliance with ATIS advice,users with ATIS but not in compliance with ATIS advice,and users without ATIS.Due to the high complexity of heterogeneous traffic networks under ATIS,travelers only have imperfect information about the network and often choose their travel routes with stochastic uncertainty.Therefore,all users are assumed to follow the stochastic user equilibrium(SUE).Under the assumptions of the logit path choice model,a multi-class SUE model and its equivalent variational inequalities based on the time units and monetary units under ATIS and road tolling strategy are presented.While tolls are considered as part of the total system cost,multi-class system optimum(SO)models under two criteria are constructed.Then the efficiency loss of multi-class SUE against the multi-class SO under both criteria is investigated,and then the upper bounds are presented.Furthermore,for the polynomial travel time function,considering the effect of free flow travel time,the analytic expressions of the tighter upper bound of efficiency loss are derived,and further analysis is made on the parameters influencing the upper bounds,focusing on the influence of the ATIS penetration rate and the information compliance rate on the upper bounds of efficiency loss.The results show that the upper bounds of the efficiency loss decrease with an increase of ATIS penetration rate and the information compliance rate.Besides,the upper bounds are also related to the link cost functions,the users’VOT and familiarity with the network,and the complexity of the network.Finally,the conclusions are validated through a numerical example.The results provide theoretical and technical supports for ATIS and road tolling strategy design,and then achieves optimal control of traffic system.The next step will extend our research from a deterministic network to a stochastic network,aiming to investigate the efficiency loss of multi-class equilibrium in a stochastic heterogeneous network.