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Edited by: Sakdirat Kaewunruen, University of Birmingham, UK

Reviewed by: Cheul Kyu Lee, Korea Railroad Research Institute, South Korea; Steve Krezo, Western Sydney University, Australia

Specialty section: This article was submitted to Transportation and Transit Systems, a section of the journal Frontiers in Built Environment

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

The high contribution of greenhouse gas (GHG) emissions by the transportation sector calls for the development of emission reduction efforts. In this paper, we examine how efficient bus transit networks can contribute to these reduction measures. Utilizing continuum approximation methods and a case study in Barcelona, we show that efforts to decrease the costs of a transit system can lead to GHG emission reductions as well. We demonstrate GHG emission comparisons between an optimized bus network design in Barcelona and the existing system. The optimization of the system network design involves minimizing system costs and thereby determining optimal network layout and transit frequency. In this case study, not only does the cost-optimal design lead to a 17% reduction in total costs, but even more notably, the optimal design leads to a 50% reduction in GHG emissions. Furthermore, the level of service to the user is not detrimentally affected and, in fact, it is slightly improved. We, therefore, extrapolate and hypothesize that the optimization of transit networks in many cities would result in significant GHG emission reductions. The analysis in this paper specifically focuses on the effects of bus technology with fixed ridership corresponding to the Barcelona case study, but the methods implemented could be easily applied to other transit modes in different cities.

With the increasing concern about global climate change, greenhouse gas (GHG) emission levels of the transportation sector have gained significant interest among researchers and policy makers. Transportation contributes 28% of all greenhouse gas emissions in the United States and 23% worldwide (Kahn Ribeiro et al.,

Griswold et al. (

Existing transit systems are not designed to optimize for costs, so it is likely that most systems are operating above the Pareto frontier, with both higher costs and emissions. This paper addresses the unexplored question of how much GHG emissions can be reduced by moving an existing transit system to the cost-optimal point on the Pareto curve. Unlike the emissions reductions identified in Griswold et al. (

Much of the literature related to transit emissions focuses on operating emissions and does not account for total life-cycle emissions (Herndon et al.,

In this paper, we estimate the level of GHG emission reductions that can occur as a result of designing a transit network for optimal societal costs. We hypothesize that user and agency costs are minimized in the design of a network, both costs and GHG emissions will be reduced. The following section describes the CA methods that are used to develop a model of the transit network to optimize. Section “

Continuum approximation methods have been developed and utilized in order to optimize transit networks with the objective of minimizing user and agency costs. That is, minimizing the time spent by users accessing, waiting, transferring, and riding (and the corresponding costs associated with these times) and the costs required to maintain and operate the system. CA methods provide decision makers with insights on optimal system design by making generalizations that simplify the analysis. Utilizing CA models yields decision variables that can be implemented in design, such as stop spacing, service frequencies (headways), and line spacing. Of course, the generated decision variables may need to be slightly modified in order to appropriately fit geographic and pre-existing infrastructure conditions of the design region. The need for these adjustments will be discussed further in the following section.

There has been a variety of work examining different transit network structures. While Holroyd (

Equation _{x}_{y}_{x}_{y}_{x}_{x}/D_{x}_{y}_{y}/D_{y.}_{x}_{y}_{.} Utilizing the aforementioned CA methods, an objective function was developed based on total system costs. This was minimized subject to a number of constraints including the maximum number of allowable corridors and the minimum headways,

As was previously mentioned, the objective function in Eq. _{i}_{w}_{T}

In this section, we will present our findings regarding the change in both cost and GHG emissions that can result when optimizing a transit network. Specifically, we will be looking at a case study of Barcelona. First, we present the parameters that were determined by Estrada et al. (

The Barcelona optimization model employed by Estrada et al. (

Parameter | Current | Model |
---|---|---|

One-way infrastructure length—2 |
891 | 220 |

Vehicles— |
659 | 266 |

Vehicle-km/h— |
7,579 | 3,990 |

Average travel time (min) | 31.7 | 30.9 |

Total user costs (per hour) | $487,806 | $475,476 |

Agency costs (per hour) | $157,170 | $62,419 |

Total costs (per hour) | $644,976 | $537,894 |

The optimization and design modification described above produce a 17% reduction in costs from the current system to the proposed model. Detailed cost calculations can be found in the Section “

While much effort in understanding transportation-related GHG emissions has typically been placed on tailpipe emissions, we are focused on life-cycle emissions associated with each of the aforementioned scenarios. Utilizing the emissions parameters developed by Chester and Horvath (

Factor | Units | Reference | |
---|---|---|---|

_{I} |
8.1 | CO_{2}e g/(km-h) |
Griswold ( |

_{M} |
3,400 | CO_{2}e g/(veh-h) |
Chester and Horvath ( |

_{V} |
1,500 | CO_{2}e g/(veh-km) |
Chester and Horvath ( |

The optimized model yields a network that produces much lower GHG emissions than the current network (Table

Component | Current emissions (CO_{2}e g/h) |
Model emissions (CO_{2}e g/h) |
---|---|---|

Infrastructure | 7.2 × 10^{3} |
1.7 × 10^{3} |

Vehicles | 2.2 × 10^{6} |
9.0 × 10^{5} |

Vehicle-km/h | 1.1 × 10^{7} |
6.1 × 10^{6} |

Total | 1.4 × 10^{7} |
7.0 × 10^{6} |

Our analysis shows that the optimization of the Barcelona transit network would not only lead to cost reductions, but would have a large effect on the potential level of GHG emissions. While system costs are reduced by 17%, the GHG emissions are reduced by 50%. The set of design parameters associated with this analysis comprise the cost-optimal point with regards to emissions. That is, costs are being minimized without any emission-based constraints. As decision makers become more concerned with specific emission standards in the future, additional constraints regarding emission levels may be implemented in the optimization. This will allow network designs to be based on the trade-offs between costs and GHG emissions. In the following section, we will discuss implications and suggestions for future work regarding these findings.

The findings presented in the previous section offer insights for transit agency decision makers. The optimization of a transit network—with the intention of making it a competitive alternative to the automobile—can lead to drastic reductions in both costs and emissions. The case study of Barcelona showed that applying this optimization process not only led to cost and emission reductions but maintained the level of service provided to the users. The approach taken in the examination of Barcelona can be applied to many cities in the world that utilize a transit system.

The constraints that were in place for the Barcelona case study would be paralleled by similar design restrictions in other cities, and could easily be accounted for in the optimization and analysis process. In Barcelona, as previously stated, there were design constraints set forth by the city regarding the minimum allowable headways and the maximum number of available corridors. Restrictions similar to these exist in other cities and must be taken into consideration when developing a model. Furthermore, once a model is created and decision variables are yielded, additional modifications must be considered to fit the geography and demand centers of the city, as was done by Estrada et al. (

The reductions achieved in this case study did not have an effect on ridership. Since level of service was not altered, demand elasticity was not addressed in this paper. In future work, as models yield varying levels of service to users, demand elasticity should be considered. While we hypothesize that a correlation between GHG emissions reduction and transit network optimization exists, more city scenarios must be examined to further support this claim. To better understand the effect on GHG emission reductions, cities with different layouts, demand densities, and wage rates could be studied. The focus of this paper has been to address cost-optimal network design, which assumes that no costs are associated with GHG emission reductions. Griswold et al. (

Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work: JG*, TS*, SM, AH, and JL. Drafting the work or revising it critically for important intellectual content: JG, TS, SM*, AH*, and JL. Final approval of the version to be published: JG, TS, SM*, AH, and JL*. Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved: JG, TS, SM, AH, and JL. *Leading author who made crucial contributions to the corresponding criterion.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The following mathematical program was presented in Estrada et al. (

Most variables are defined within the paper; those which have not been previously presented are defined here.

The objective function is based on total system cost and is subject to several constraints: the spacing value must be greater than zero, the horizontal and vertical spacings, _{x}_{y}_{x}_{y}

The length,

The average vehicular distance traveled per hour of operation is a function of the geometric layout of the network as well as the service frequency.

The occupancies of the vehicles are determined by the catchment area of bus routes, service frequency, and the trip generation rate during rush periods, Λ (passengers/hr).

The number of vehicles required in the fleet is a function of the vehicle-km/h traveled _{c}

The following formulas address the values concerned with user costs. That is, the various components that contribute to the time users spend in the system. The access time _{w}

The average waiting time that users experience _{1}_{2}

The expected number of transfers _{T}

Finally, the in-vehicle travel time _{c}

_{i} |
Current | Model | |
---|---|---|---|

One-way infrastructure length (2 |
80 | 891 | 220 |

Vehicles ( |
60.2 | 659 | 266 |

Vehicle-km/h ( |
5.2 | 7,579 | 3,990 |

Total cost (Euros/h) | € 114,723 | € 45,561 | |

Total cost (US dollars/h) | $157,170 | $62,419 |

Per person (min) | Per person cost (Euros) | Total cost (Euros/h) | Total cost (USD/h) | |
---|---|---|---|---|

Access and egress | 12.64 | 3.16 | € 142,200 | $194,814 |

Waiting time | 3.02 | 0.76 | € 33,975 | $46,546 |

In vehicle time | 15.19 | 3.80 | € 170,888 | $234,116 |

Total travel time | 30.85 | 7.71 | € 347,063 | $475,476 |

Per person (min) | Per person cost (Euros) | Total cost (Euros/h) | Total cost (USD/h) | |
---|---|---|---|---|

Access and egress | 10.44 | 2.61 | € 117,450 | $160,907 |

Waiting time | 4.59 | 1.15 | € 51,638 | $70,743 |

In vehicle time | 16.62 | 4.16 | € 186,975 | $256,156 |

Total travel time | 31.65 | 7.91 | € 356,063 | $487,806 |

Current | Model | |
---|---|---|

Total cost (Euros/h) | € 470,785 | € 392,623 |

Total cost (US dollars/h) | $644,976 | $537,894 |

% Change | −16.60% |