Large Transit Networks Research Articles

Minimizing Energy Use of Mixed-Fleet Public Transit for Fixed-Route Service

Affordable public transit services are crucial for communities since they enable residents to access employment, education, and other services. Unfortunately, transit services that provide wide coverage tend to suffer from relatively low utilization, which results in high fuel usage per passenger per mile, leading to high operating costs and environmental impact. Electric vehicles (EVs) can reduce energy costs and environmental impact, but most public transit agencies have to employ them in combination with conventional, internal-combustion engine vehicles due to the high upfront costs of EVs. To make the best use of such a mixed fleet of vehicles, transit agencies need to optimize route assignments and charging schedules, which presents a challenging problem for large transit networks. We introduce a novel problem formulation to minimize fuel and electricity use by assigning vehicles to transit trips and scheduling them for charging, while serving an existing fixed-route transit schedule. We present an integer program for optimal assignment and scheduling, and we propose polynomial-time heuristic and meta-heuristic algorithms for larger networks. We evaluate our algorithms on the public transit service of Chattanooga, TN using operational data collected from transit vehicles. Our results show that the proposed algorithms are scalable and can reduce energy use and, hence, environmental impact and operational costs. For Chattanooga, the proposed algorithms can save $145,635 in energy costs and 576.7 metric tons of CO2 emission annually.

Efficient Large-Scale Multi-Drone Delivery using Transit Networks

We consider the problem of routing a large fleet of drones to deliver packages simultaneously across broad urban areas. Besides flying directly, drones can use public transit vehicles such as buses and trams as temporary modes of transportation to conserve energy. Adding this capability to our formulation augments effective drone travel range and the space of possible deliveries but also increases problem input size due to the large transit networks. We present a comprehensive algorithmic framework that strives to minimize the maximum time to complete any delivery and addresses the multifaceted computational challenges of our problem through a two-layer approach. First, the upper layer assigns drones to package delivery sequences with an approximately optimal polynomial time allocation algorithm. Then, the lower layer executes the allocation by periodically routing the fleet over the transit network, using efficient, bounded suboptimal multi-agent pathfinding techniques tailored to our setting. We demonstrate the efficiency of our approach on simulations with up to 200 drones, 5000 packages, and transit networks with up to 8000 stops in San Francisco and the Washington DC Metropolitan Area. Our framework computes solutions for most settings within a few seconds on commodity hardware and enables drones to extend their effective range by a factor of nearly four using transit.

A modelling platform for optimizing time-dependent transit fares in large-scale multimodal networks

With the continuous growth of urban areas around the world, overcrowding in large transit networks has become a persistent problem, with far-reaching impacts similar to those caused by congestion in large road networks. Moreover, instead of serving as a relief for large transportation systems, congested transit networks have increased delay-related traffic and transit costs. In light of these problems, cities seek cost-effective and relatively fast-to-implement strategies to mitigate transit system congestion, one of which is time-based fare structures. By implementing time-based fares, the transit demand may shift out of the congested peak periods, easing transit travel conditions. Although time-based fares are already in use in some transportation systems, their implementation is usually based on simplified what-if analyses. Such analyses of fare structures in previous studies have lacked a comprehensive evaluation of people's responses to these fares and is usually applied to simple or sometimes hypothetical transportation networks. Therefore, this paper presents a platform for analyzing and optimizing time-based transit fares in large networks, taking into consideration the effects of these fares on people's choices of mode, departure time, and route in addition to the interactions between transit vehicles and general traffic. As a case study, the largest metropolitan area in Canada, the Greater Toronto Area, is tested. The results show that the optimal time-based fares help spread the transit demand to the shoulders of the peak. However, the savings in weighted average multimodal door-to-door travel time over the whole network are slightly small compared to the large increase in peak-hour fares.

A Model and Algorithm for Passenger-oriented Train Timetabling on Urban Rail Transit Network

This paper focuses on optimizing passenger train timetable on an urban transit network with given predetermined long and short routing operation mode. A double objective integer programming model is established in order to reduce the difficulty of solving train timetabling problem of large transit network. A Lagrangian relaxation algorithm was designed to decrease the complexity of solving the problem by transforming the complicated coupling problem into two independent sub-problems of trains and agents respectively. In response to two sub-problems of Lagrangian relaxation, a time-space network was constructed to solve the shortest path problem of passengers and trains by dynamic programming. Finally, the model and algorithm are verified and analyzed by a simple example.

A heuristic method for a congested capacitated transit assignment model with strategies

This paper addresses the problem of solving the congested transit assignment problem with strict capacities. The model under consideration is the extension made by Cominetti and Correa (2001), for which the only solution method capable of resolving large transit networks is the one proposed by Cepeda et al. (2006). This transit assignment model was recently formulated by the authors as both a variational inequality problem and a fixed point inclusion problem. As a consequence of these results, this paper proposes an algorithm for solving the congested transit assignment problem with strict line capacities. The proposed method consists of using an MSA-based heuristic for finding a solution for the fixed point inclusion formulation. Additionally, it offers the advantage of always obtaining capacity-feasible flows with equal computational performance in cases of moderate congestion and with greater computational performance in cases of highly congested networks. A set of computational tests on realistic small- and large-scale transit networks under various congestion levels are reported, and the characteristics of the proposed method are analyzed.

Hybrid Modeling of Passenger and Vehicle Traffic along a Transit Line: a sub-model ready for inclusion in a model of traffic assignment to a capacitated transit network

Abstract The CapTA model of traffic assignment to a large transit network is aimed to deal with traffic phenomena, including a range of capacity constraints, as well as with passenger route choice (Leurent et al, 2014). To this end it has a 3-layer architecture that involves (i) passenger route choice on a network of transit legs and pedestrian links, (ii) line coordination of service missions, vehicle runs with their link running times and station dwelling times, track occupancy and passenger waiting at stations, (iii) vehicle running, including the alighting and boarding of passengers in relation to run dwelling time at the station, in-vehicle passenger load in relation to seat capacity and total vehicle capacity. Yet the line model is macroscopic both for passenger flows and for vehicles serving a given mission, through a frequency variable per station. The paper brings about a novel, hybrid line model that can be used on a standalone basis at the line level or by inclusion in a three-layered model such as CapTA. In the model, a macroscopic representation of passenger flows is hybridized with a microscopic simulation of vehicles. This enables us to simulate headway (ir-)regularity and derive its consequences on vehicle loads, passenger wait times and on-board comfort, track occupancy and vehicle delay for railway modes. The resulting leg generalized times will be used to better simulate optimal travel strategies for path choice in a network in traffic assignment models such as CapTA. After presenting the model and the simulation algorithm, we provide an application to a metro line under two alternative operational policies.

Impact evaluation of a mass transit fare change on demand and revenue utilizing smart card data

Transit fares are an effective tool for demand management. Transit agencies can raise revenue or relieve overcrowding via fare increases, but they are always confronted with the possibility of heavy ridership losses. Therefore, the outcome of fare changes should be evaluated before implementation. In this work, a methodology was formulated based on elasticity and exhaustive transit card data, and a network approach was proposed to assess the influence of distance-based fare increases on ridership and revenue. The approach was applied to a fare change plan for Beijing Metro. The price elasticities of demand for Beijing Metro at various fare levels and trip distances were tabulated from a stated preference survey. Trip data recorded by an automatic fare collection system was used alongside the topology of the Beijing Metro system to calculate the shortest path lengths between all station pairs, the origin–destination matrix, and trip lengths. Finally, three fare increase alternatives (high, medium, and low) were evaluated in terms of their impact on ridership and revenue. The results demonstrated that smart card data have great potential with regard to fare change evaluation. According to smart card data for a large transit network, the statistical frequency of trip lengths is more highly concentrated than that of the shortest path length. Moreover, the majority of the total trips have a length of around 15km, and these are the most sensitive to fare increases. Specific attention should be paid to this characteristic when developing fare change plans to manage demand or raise revenue.

Finding optimal hyperpaths in large transit networks with realistic headway distributions

This paper implements and tests a label-setting algorithm for finding optimal hyperpaths in large transit networks with realistic headway distributions. It has been commonly assumed in the literature that headway is exponentially distributed. To validate this assumption, the empirical headway data archived by Chicago Transit Agency are fitted into various probabilistic distributions. The results suggest that the headway data fit much better with Loglogistic, Gamma and Erlang distributions than with the exponential distribution. Accordingly, we propose to model headway using the Erlang distribution in the proposed algorithm, because it best balances realism and tractability. When headway is not exponentially distributed, finding optimal hyperpaths may require enumerating all possible line combinations at each transfer stop, which is tractable only for a small number of alternative lines. To overcome this difficulty, a greedy method is implemented as a heuristic and compared to the brute-force enumeration method. The proposed algorithm is tested on a large scale CTA bus network that has over 10,000 stops. The results show that (1) the assumption of exponentially distributed headway may lead to sub-optimal route choices and (2) the heuristic greedy method provides near optimal solutions in all tested cases.

Harry Beck's London Underground Map

After Harry Beck designed his map of the London Underground, it became an icon of the city and a model for maps in other large transit networks around the world. The map allowed its readers to see themselves as components of the large, organized structure of the metropolis but also confronted them with the possibility of losing themselves to that structure. An analysis of the post-Beck subway map tradition shows it to be a battleground between the zeal for order and the latent chaos at the heart of the urban communities that the map represents and also situates this conflict in a larger context of the emergence of a global societal structure bound together by the control of capital and of the information that enables such control.

Modeling public-transit connectivity with spatial quality-of-transfer measurements

Improving public-transit connectivity is one of the most vital tasks in transit-operations planning. A poor connection can cause some passengers to stop using the transit service. This work analyzes the performance of public-transit networks in terms of the attributes involved with coordination and connectivity. These attributes are primarily concerned with passenger transfers, and include ride, wait and walk times and type of transfers made, that is, with street-crossing, sidewalk, non-walk and one-leg trip. Based on these attributes, transit-connectivity measures are established as a tool to evaluate the pros and cons of each defined zone of transit lines from a connectivity perspective. The zone of transit lines can be associated with small or large transit networks from which two types of analyses can be made: (i) detecting the inefficiency of connectivity-related issues for the zone, and (ii) comparing the measures between different zones to arrive to the conclusion of which zone is more worthy of improvements. This will allow, for instance, the comparison between cities and between zones in the city. In this work a model is developed to integrate spatial and non-spatial data for the construction of a public-transit network spatial repository, which in turn, is used to classify transfers, and calculate the developed connectivity measures. A case study in Auckland, New Zealand, demonstrates the benefits of the model and connectivity measures.

On blind mice and the elephant

A thorough understanding of the network impact of emerging large-scale distributed systems -- where traffic flows and what it costs -- must encompass users' behavior, the traffic they generate and the topology over which that traffic flows. In the case of BitTorrent, however, previous studies have been limited by narrow perspectives that restrict such analysis. This paper presents a comprehensive view of BitTorrent, using data from a representative set of 500,000 users sampled over a two year period, located in 169 countries and 3,150 networks. This unique perspective captures unseen trends and reveals several unexpected features of the largest peer-to-peer system. For instance, over the past year total BitTorrent traffic has increased by 12% , driven by 25% increases in per-peer hourly download volume despite a 10% decrease in the average number of online peers. We also observe stronger diurnal usage patterns and, surprisingly given the bandwidth-intensive nature of the application, a close alignment between these patterns and overall traffic. Considering the aggregated traffic across access links, this has potential implications on BitTorrent-associated costs for Internet Service Providers (ISPs). Using data from a transit ISP, we find a disproportionately large impact on a commonly used burstable (95th-percentile) billing model. Last, when examining BitTorrent traffic's paths, we find that for over half its users, most network traffic never reaches large transit networks, but is instead carried by small transit ISPs. This raises questions on the effectiveness of most in-network monitoring systems to capture trends on peer-to-peer traffic and further motivates our approach.