Design of a Bike–Bus Network for a City of Half a Million Citizens
Publication: Journal of Urban Planning and Development
Volume 147, Issue 3
Abstract
This work develops a mathematical model for designing bikeway networks that integrate into public bus transport services in urban areas using concepts from network multiobjective optimization and mixed-integer linear programming (MILP). The proposed model maximizes 14 objectives and 14 constraints by referring in a generalized way to lane comfort, safety, path objectivity, network connectivity, intermodality with bus service, and monetary budgets. In the context of a developing country, we believe that this model can address the transit network design problem (TNDP) as an innovative proposal for integration between alternative modes of transport and buses. A case study in Sao Jose dos Campos city, Sao Paulo state, Brazil, is conducted, and exact solutions are obtained with partially connected networks (first approach) and fully connected networks (second approach). A scenario analysis enables verification of the integrated transportation system performance and, for the case study, prioritizes the least expensive bikeway type. Therefore, the results from the proposed model can contribute to urban planning in testing alternative scenarios for bike–bus networks.
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Acknowledgments
This research was partially supported by the National Council for Scientific and Technological Development (CNPq—302730/2018; CNPq—303350/2018-0) and the São Paulo State Research Foundation (FAPESP—2018/06858-0; FAPESP—2018/14433-0).
Notation
The following symbols are used in this paper:
Indexes
- i,j
- nodes that define the candidate link; i corresponds to the origin node, and j corresponds to the destination node, with (i, j) ∈ G | G ={(1, …, I), (1, …, J)};
- k
- bikeway type, including a one-way bike path (k = 1), two one-way bike paths (k = 2), a two-way bike path (k = 3), a one-way bike lane (k = 4), two one-way bike lanes (k = 5), a two-way bike lane (k = 6), a bike route (k = 7), two bike routes (k = 8), and a shared sidewalk (k = 9);
- l
- bus lines, with l ∈ {1, …, l}; and
- p
- bus stop points, with p ∈ {1, …, P}.
Sets
- Aij
- traffic lane existence matrix candidate for the node in the lane of link (i, j), if Aij = 1, link (i, j) presents a traffic lane candidate for the model, otherwise Aij = 0;
- Bij
- sidewalk existence matrix candidate for the node in the lane of link (i, j), if Bij = 1, link (i, j) presents a sidewalk candidate for the model, otherwise Bij = 0;
- Gij
- link existence matrix formed by nodes (i, j), with G = {(1, …, I), (1, …, J)}; and for each link (i, j).
Parameters
- BTk
- preferred weight for each type of bikeway k-type (pts);
- CBk
- bikeway k-type construction cost (BRL/m);
- ICj
- connectivity index at node j;
- LDij
- lane declivity of link (i, j) (pts);
- LLij
- lane length in link (i, j) (m);
- LOpl
- indicates if bus line l is attended by bus stop point p;
- NIij
- number of intersections in link (i, j) (units);
- NPij
- number of origin and destination points in link (i, j) (pts);
- NSij
- number of stop signals in link (i, j) (units);
- PAij
- perceived afforestation in link (i, j) (pts);
- PCij
- perceived conservation status on the lane of link (i, j) (pts);
- PLij
- perceived lane lighting in link (i, j) (pts);
- PPijp
- indicates if bus stop point p exists on link (i, j);
- PRi
- location of preferred regions that have access over the network by nodes i (pts);
- SLij
- speed limit of motor vehicles in link (i, j) (pts);
- WLij
- candidate lane width in link (i, j) (m);
- WBSij
- candidate sidewalk width contained in link (i, j) (m);
- total sidewalk width in link (i, j) (m);
- disregarded sidewalk width in link (i, j) (m);
- WBTk
- bikeway width k-type, k ≤ 8 (m); and
- WLTij
- candidate traffic lane width in link (i, j) (m).
Decision Variables
- BLl
- if BLl = 1, bus line l will be attended on the model result by some bus stop point p. Otherwise, BLl = 0, bus line l will not be attended in the model result by any bus stop point p
- Xijk
- if Xijk = 1, bikeway k-type will be implemented, according to the model result, in link (i, j). Otherwise, Xijk = 0, link (i, j) will not be implemented; and
- Yi
- if Yi = 1, node i will be implemented, according to the result of the model. Otherwise, Yi = 0, node i will not be implemented.
Constants
- AB
- available budget limit to build the bike–bus network (BRL);
- DIV
- divided constant that represents how much the lane traffic width (WLTij) in the link (i, j) must be greater than the width of the bikeway k-type, k ≤ 8 (WBTk);
- h
- constant used to aid in obtaining the value of BLl, where 0 < h < 1; and
- m
- constant used to aid in obtaining the value of Yi, where 0 < m < 1.
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Published In
Journal of Urban Planning and Development
Volume 147 • Issue 3 • September 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jun 11, 2020
Accepted: Jan 29, 2021
Published online: Apr 28, 2021
Published in print: Sep 1, 2021
Discussion open until: Sep 28, 2021
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