Heterogeneous Design for Feeder Services of Trunk Transit System Yue Su, Fan Wenbo To cite this version: Yue Su, Fan Wenbo. Heterogeneous Design for Feeder Services of Trunk Transit System. 22nd Intelligent Transportation Systems Conference (ITSC), Oct 2019, Auckland, New Zealand. 10.1109/ITSC.2019.8917013. hal-02489404 HAL Id: hal-02489404 https://hal.archives-ouvertes.fr/hal-02489404 Submitted on 26 Feb 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Heterogeneous Design for Feeder Services of Trunk Transit System Yue Su and Wenbo Fan Abstract— This paper extends the uniform design of a mode transit network. Most recently, their network was trunk-feeder system, e.g., rail-bus system, over a grid network enhanced by ref. [6] with the consideration of feeder buses’ in the literature to the heterogeneous design, where the emission cost (as a constraint into the optimization). These spacings of feeder bus lines and stops are allowed to vary two works both assumed a uniform demand over the study spatially to better serve the demand. The trunk lines are evenly domain to simplify the modelling, and all the design deployed over the study area with the line spacing to be variables (i.e., the line spacing and station spacing, service optimized. Employing the method of continuum approximation, headways) of rail and bus systems are reduced to scalar we develop a joint design model to minimize the generalized variables. The corresponding minimization problems system cost as a sum of transit patrons’ cost, agency cost, and become very easy to be solved. It is demonstrated in ref. [7] emission cost. The proposed model is applied on two types of that even under the uniform demand assumption, the feeder trunk systems (i.e., rail and Bus Rapid Transit, BRT) in small- and large-sized city scenarios. The results indicate that: (i) the services need a spatially heterogeneous design in best fit proposed model saves 31% of the system cost as compared with with the demand that perform a many-to-one pattern and the uniform-designed feeder system; (ii) large-sized cities (e.g., accumulate as approaching the trunk stations. New York City) prefer faster transit system as the trunk transit In light of above, this paper explicitly models the mode (i.e., rail), while small-sized cities welcome more heterogeneous design for the feeder bus services of trunk economical trunk transit mode (i.e., BRT); and (iii) considering transit over a grid network. The demand is still assumed to emission cost into the optimization model will lead to 9.43% follow a uniform distribution to obtain parsimonious models. reduction in actual emission cost. Emission cost is also taken into consideration to enhance the Keywords—trunk-feeder system, heterogeneous design, environmental awareness. continuum approximation, emission The remainder of this paper is organized as follows: next section formulates the system costs and the optimization I. INTRODUCTION problem of the trunk-feeder system by employing CA To fight against the increasing vehicular congestion and approach. The analytical analyses of the decision environmental problems, many cities in the world resort to variables/functions are also presented. Section three applies the high-capacity public transport systems (e.g., rail or the proposed model to various scenarios with respect to city metro) as the urban trunk transit. Due to the expensive cost sizes, demand levels, and trunk transit modes. Insightful of building and operating, these trunk transit systems are findings are obtained by comparing the results of the often limited in network scale, and thus need feeder buses to proposed model with that of the traditional uniform design, extend the demand coverage area by picking up and and with the case that ignores emission cost. The last section delivering passengers to and from rail stations [1] [2]. draws conclusions. Not surprisingly, the trunk-feeder system has been II. METHODOLOGY extensively studied in literature. The most relevant works to 2 this study dates back to Wirashinghe et al. [3]. They adopted Consider a square city of size (km ), we present a the method of Continuum Approximation (CA) in trunk-feeder system over a grid network, as illustrated in formulating parsimonious models for the optimal design of a Fig. 1a. The trunk lines and stations are evenly spaced by 2 rail-bus corridor. The design variables such as rail station �� = 2� (km), and a square service area of size � × � (km ) spacing and feeder bus line spacing are formulated as is designed for a feeder system. Without loss of generality, continuous functions of locations in the corridor. feeder buses are operated to run and visit stops along vertical Considering spatially uneven demand, they optimized the lines to pickup patrons, and upon reaching the horizontal rail station spacing and feeder bus line spacing functions as trunk line they run without stopping to the trunk station, as well as the service headways (as scalar variables). Then, ref. shown by Fig. 1b; and vice versa for the process of [4] extended to take the rail line length into the decision delivering patrons from the trunk station. In the proposed variables to be determined. A major extension to the trunk- model, the layout of feeder-bus system is allowed to be feeder corridor structure was made in Sivakumaran et al [5], spatially varying. Let ��(�) denote the bus line spacing in who established a trunk-feeder system over a grid network the neighborhood of the cross-section at x, and �(�, �) be and demonstrated their advantage over traditional single- the bus stop spacing in the neighborhood area of (x, y). To facilitate modeling, a few assumptions are made as follows: *Research supported by the National Natural Science Foundation 1. The demand is uniformly distributed over the study (Project No. 51608455). area with density � (passengers/km2/h). Yue Su is with Department of Transportation and Logistic, Southwest Jiaotong University, Chengdu 610031, China; 2. To accomplish their trips, all passengers take feeder Wenbo Fan is with Department of Transportation and Logistic, buses to access and egress from trunk stations at both Southwest Jiaotong University, Chengdu 610031, China (Corresponding trip ends, and ride trunk transit in the middle of trips. author e-mail: [email protected]). 1 Manuscript 392 submitted to 2019 22nd Intelligent Transportation Systems Conference (ITSC). Received April 14, 2019. 3. Passengers choose the nearest stop to board or alight Thus the average accessing and egressing walk distance to � (�)+�(�,�) feeder bus. They arrive at stops randomly without bus stops can be estimated by � . Dividing by the pre-trip scheduling. 2 average walking speed, �� (km/h), yields the average access and egress time per patron. The two items in RHS of (6) are waiting time at trunk B(,) x y stations and feeder bus stops, respectively. It is underscored that the average waiting time per boarding or transferring is (,)xy the half of headway, i.e., H for trunk service and ℎ(�) for S y feeder lines at cross-section x. Additionally, (6) accounts for Sxf () the transfer delay, ��−�, e.g., walking time and inconvenience O x penalty. The first RHS item of (7) is the in-vehicle time on trunk (a) Trunk system layout (b) Feeder system layout lines, of which V (km/h) is the cruising speed of trunk Fig.1. Layout of trunk-feeder system vehicle. The detailed derivation and explanation can be found in Sivakumaran et al. [5] and omitted here for sake of The generalized system cost, ��, is the weighted sum of simplification. The second item ��� denotes the in-vehicle user cost, �� , operator cost, �� , and emission cost, �� , travel time on feeder lines, which is formulated by: expressed as below: � � � ��� = ��� + ��� + ��� �� = �� + �� + �� The first time item �� represents the total in-vehicle time where � contains three cost items: the access/egress time �� � experienced by on-board passengers to overcome a unit to/from transit stops (� ), the waiting time at origin and � distance in a cruising bus, and cab be estimated by: transfer stops (��), in-vehicle time that on-board passengers 2 overcome in both trunk and feeder lines (�� ). Thus, �� is � 2 � � ��� = 2�� ∙ ∙ 2 expressed by: �� � �� = �� + �� + �� It is noted in (9) that under uniform demand, the average � travel distance per patron in feeder system is S; yields the The operator cost �� is composed by the lines �� 2 infrastructure cost (��); the stops infrastructure cost (��); the average travel time; and the total demand is 2�� per feeder vehicle-km related cost (���); the vehicle-time related cost service zone (including outbound and inbound demand). (��ℎ). � The second time item ��� is the additional time lost at �� = �� + �� + ��� + ��ℎ stops due to acceleration and deceleration, which is formulated by: Emission cost �� mainly entails: the emission cost while 2�2 � � � dwelling at stops (�1); the emission cost at cruising speed �� = ∙ �� ∙ ∫ ∫ ���� � �� �2 0 �=0 �=0 �(�,�) 2 (��). where �0 is the acceleration and deceleration time at stop (in 1 2 �� = �� + �� unit of hour). The formulation logic of (10) is that: The accumulated onboard flow of each bus line passing (�, �) is Each cost item in (2-4) will be derived by employing CA �� method for trunk and feeder systems, respectively. � ∙ ��(�) ∙ �. For the area of �� × ��, there are lines ��(�) �� �� A. User Cost and stops along each line. Thus, � ∙ ��(�) ∙ � ∙ ∙ �(�,�) ��(�) We first summarize the expressions of � , � , � as (5-7), �� � � � ∙ � yields the time lost at stops in the domain by �� × and then derive them below.