Evaluation of average travel delay caused by moving bottlenecks on highways

PLOS ONE, Nov 2019

This paper presents a modelling framework to evaluate travel delay of all vehicles influenced by moving bottlenecks on highways. During the derivation of analytical formulas, the arrival of slow vehicles was approximated by a Poisson process based on the assumption that they occupied a constant low proportion of the traffic stream. The mathematical analysis process was developed from moving bottlenecks with the same velocity to those with multiple different velocities, and the closed-form expression of expected average travel delay was obtained by utilizing kinematic-wave moving bottleneck theory, gap acceptance theory, probability theory and renewal theory. Model validation and parameters sensitive analysis were conducted by simulation relying on the open source database of US highway 10. The maximum passing rate and the macroscopic parameters of initial traffic state with maximum delay could be found by means of approximate formulas. The proposed modeling framework can be applied for evaluating impacts of slow vehicles on highway operation quantifiably, based on which traffic managements like truck prohibited period decision and speed or lane restriction could be made more scientifically.

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Evaluation of average travel delay caused by moving bottlenecks on highways

August Evaluation of average travel delay caused by moving bottlenecks on highways Xueyan Wei 0 1 Chengcheng Xu 0 1 Wei Wang 0 1 Menglin Yang 0 1 Xiaoma Ren 1 0 Jiangsu Key Laboratory of Urban ITS, Southeast University , Nanjing, Jiangsu , China , 2 Jiangsu Province Collaborative Innovation Center of Modern Urban Traffic Technologies, Southeast University , Nanjing, Jiangsu , China , 3 Department of Urban Traffic, Hisense TransTech Co., Ltd. , Qingdao, Shandong , China 1 Editor: Xiaolei Ma, Beihang University , CHINA This paper presents a modelling framework to evaluate travel delay of all vehicles influenced by moving bottlenecks on highways. During the derivation of analytical formulas, the arrival of slow vehicles was approximated by a Poisson process based on the assumption that they occupied a constant low proportion of the traffic stream. The mathematical analysis process was developed from moving bottlenecks with the same velocity to those with multiple different velocities, and the closed-form expression of expected average travel delay was obtained by utilizing kinematic-wave moving bottleneck theory, gap acceptance theory, probability theory and renewal theory. Model validation and parameters sensitive analysis were conducted by simulation relying on the open source database of US highway 10. The maximum passing rate and the macroscopic parameters of initial traffic state with maximum delay could be found by means of approximate formulas. The proposed modeling framework can be applied for evaluating impacts of slow vehicles on highway operation quantifiably, based on which traffic managements like truck prohibited period decision and speed or lane restriction could be made more scientifically. - Data Availability Statement: Data are available from the open source database of US highway 10. (Available from: http://data.dot.state.mn.us/ datatools/) and within the Supporting Information files. Funding: This work was supported by the National Natural Science Foundation of China, 51338003, to Wei Wang. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The author, Xiaoma Ren, is affiliated with Hisense TransTech Co., Ltd., a commercial company. There are no patents, Introduction In mixed-traffic flow, the presence of a slow vehicle (SV) may cause a bottleneck for traffic stream with normal travel speed, which is moving with the running of that slow vehicle. SVs can be trucks, working vehicles and even cars driving by cautious drivers. These ªmoving bottlenecks (MBs)º make great contributions to the degradation of highway capacity and level of service, which has been confirmed by experimental findings [ 1 ]. Hence, it is indispensable to incorporate the influence mechanism of MBs into practical traffic models. The existing studies on the influence mechanism of MBs can be classified into two categories. One is early studies on the exploration of characteristics of a MB and the other is subsequent studies on qualitative and quantitative influence of MBs on capacity. Early studies focused on exploring characteristics of MBs. The concept of ªmoving bottlenecks (MBs)º describing the effect of bottlenecks caused by SVs was proposed by Gazis and Herman [ 2 ] firstly and was improved by Newell [ 3 ] who introduced the kinematic wave theory to analyze the influencing process of a MB on traffic stream theoretically. Later, Muñoz and Daganzo [ 1 ] diagnosed a MB from field data by adopting the oblique coordinate system [4] and the characteristics of a MB were then presented detailedly from field observation. Meanwhile, qualitative analysis of passing rates was conducted through two freeway experiments by them. However, all these studies only focus on one single MB regardless of possible interactions between two MBs. The interactions were firstly analyzed depending on SVs' relative positions, which included arriving separately, arriving in pairs and blocking two lanes, and arriving in pairs and blocking one lane [5], with homogeneity assumption. Based on these almost complete theories of MBs, numerical analytical method of multiple MBs was introduced through modelling the time-space trajectories of MBs approximately by step functions with steps equal to the lattice spacing, and the interaction of two MBs traveling in the same lane with different speed was then firstly illustrated [ 6,7 ]. Afterwards, the effect of MBs on capacity became a prevailing research focus, which was first formulated by Laval [ 8 ] through analysis of simplified stochastic processes in one lane and was improved subsequently to multiple types of MBs in multilane [ 9 ]. As its extensive applications, Juran et al.[ 10 ] analyzed MBs at network level together with dynamic traffic assignment, and Liu [ 11 ] modified the CTM model, by using methods from the lagged CTM, to take MBs of buses into consideration by directly adop (...truncated)


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Xueyan Wei, Chengcheng Xu, Wei Wang, Menglin Yang, Xiaoma Ren. Evaluation of average travel delay caused by moving bottlenecks on highways, PLOS ONE, 2017, Volume 12, Issue 8, DOI: 10.1371/journal.pone.0183442