Customized bus service design for jointly optimizing passenger-to-vehicle assignment and vehicle routing

Emerging transportation network services, such as customized buses, hold the promise of expanding overall traveler accessibility in congested metropolitan areas. A number of internet-based customized bus services have been planned and deployed for major origin-destination (OD) pairs to/from inner cities with limited physical road infrastructure. In this research, we aim to develop a joint optimization model for addressing a number of practical challenges for providing flexible public transportation services. First, how to maintain minimum loading rate requirements and increase the number of customers per bus for the bus operators to reach long-term profitability. Second, how to optimize detailed bus routing and timetabling plans to satisfy a wide range of specific user constraints, such as passengers’ pickup and delivery locations with preferred time windows, through flexible decision for matching passengers to bus routes. From a space-time network modeling perspective, this paper develops a multi-commodity network flow-based optimization model to formulate a customized bus service network design problem so as to optimize the utilization of the vehicle capacity while satisfying individual demand requests defined through space-time windows. We further develop a solution algorithm based on the Lagrangian decomposition for the primal problem and a space-time prism based method to reduce the solution search space. Case studies using both the illustrative and real-world large-scale transportation networks are conducted to demonstrate the effectiveness of the proposed algorithm and its sensitivity under different practical operating conditions.     

Mitigation of disruptions in public transit by Bee Colony Optimization

Dispatchers in many public transit companies face the daily problem of assigning available buses to bus routes under conditions of bus shortages. In addition to this, weather conditions, crew absenteeism, traffic accidents, traffic congestion and other factors lead to disturbances of the planned schedule. We propose the Bee Colony Optimization (BCO) algorithm for mitigation of bus schedule disturbances. The developed model takes care of interests of the transit operator and passengers. The model reassigns available buses to bus routes and, if it is allowed, the model simultaneously changes the transportation network topology (it shortens some of the planned bus routes) and reassigns available buses to a new set of bus routes. The model is tested on the network of Rivera (Uruguay). Results obtained show that the proposed algorithm can significantly mitigate disruptions.     

Solving a discrete multimodal transportation network design problem

This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.     

Optimal feeder bus routes on irregular street networks

The methodology presented here seeks to optimize bus routes feeding a major intermodal transit transfer station while considering intersection delays and realistic street networks. A model is developed for finding the optimal bus route location and its operating headway in a heterogeneous service area. The criterion for optimality is the minimum total cost, including supplier and user costs. Irregular and discrete demand distributions, which realistically represent geographic variations in demand, are considered in the proposed model. The optimal headway is derived analytically for an irregularly shaped service area without demand elasticity, with non‐uniformly distributed demand density, and with a many‐to‐one travel pattern. Computer programs are designed to analyze numerical examples, which show that the combinatory type routing problem can be globally optimized. The improved computational efficiency of the near‐optimal algorithm is demonstrated through numerical comparisons to an optimal solution obtained by the exhaustive search (ES) algorithm. The CPU time spent by each algorithm is also compared to demonstrate that the near‐optimal algorithm converges to an acceptable solution significantly faster than the ES algorithm.     

Driving cycle prediction model based on bus route features

Bus fuel economy is deeply influenced by the driving cycles, which vary for different route conditions. Buses optimized for a standard driving cycle are not necessarily suitable for actual driving conditions, and, therefore, it is critical to predict the driving cycles based on the route conditions. To conveniently predict representative driving cycles of special bus routes, this paper proposed a prediction model based on bus route features, which supports bus optimization. The relations between 27 inter-station characteristics and bus fuel economy were analyzed. According to the analysis, five inter-station route characteristics were abstracted to represent the bus route features, and four inter-station driving characteristics were abstracted to represent the driving cycle features between bus stations. Inter-station driving characteristic equations were established based on the multiple linear regression, reflecting the linear relationships between the five inter-station route characteristics and the four inter-station driving characteristics. Using kinematic segment classification, a basic driving cycle database was established, including 4704 different transmission matrices. Based on the inter-station driving characteristic equations and the basic driving cycle database, the driving cycle prediction model was developed, generating drive cycles by the iterative Markov chain for the assigned bus lines. The model was finally validated by more than 2 years of acquired data. The experimental results show that the predicted driving cycle is consistent with the historical average velocity profile, and the prediction similarity is 78.69%. The proposed model can be an effective way for the driving cycle prediction of bus routes.     

Effects of queue spillover in networks considering simultaneous departure time and route choices

This paper explores the effects of queue spillover in transportation networks, in the context of dynamic traffic assignment. A model of spatial queue is defined to characterize dynamic traffic flow and queuing formation in network links. Network users simultaneously choose departure time and travel route to minimize the travel cost including journey time and unpunctuality penalty. Using some necessary conditions of the dynamic user equilibrium, dynamic network flows are obtained exactly on some networks with typical structure. Various effects of queue spillover are discussed based on the results of these networks, and some new paradoxes of link capacity expansion have been found as a result of such effects. Analytical and exact results in these typical networks show that ignoring queuing length may generate biased solutions, and the link storage capacity is a very important factor concerning the performance of networks.     

Joint optimization of a rail transit line and its feeder bus system

A model is developed for jointly optimizing the characteristics of a rail transit route and its associated feeder bus routes in an urban corridor. The corridor demand characteristics are specified with irregular discrete distributions which can realistically represent geographic variations. The total cost (supplier plus user cost) of the integrated bus and rail network is minimized with an efficient iterative method that successively substitutes variable values obtained through classical analytic optimization. The optimized variables include rail line length, rail station spacings, bus headways, bus stop spacings, and bus route spacing. Computer programs are designed for optimization and sensitivity analysis. The sensitivity of the transit service characteristics to various travel time and cost parameters is discussed. Numerical examples are presented for integrated transit systems in which the rail and bus schedules may be coordinated.     

Bus network design

This paper describes the bus network design problem, summarizes the different approaches that have been proposed for its solution and proposes a new approach incorporating some of the positive aspects of prior work. The proposed approach is intended to be easier to implement and less demanding in terms of both data requirements and analytical sophistication than previous methods. An algorithm is presented that can be used to design new bus routes taking account of both passenger and operator interests; however, this algorithm focuses on only a single component of the overall bus operations planning process described in this paper.     

Identifying the spatial distribution of public transportation trips by node and community characteristics

ABSTRACT

Identifying the spatial distribution of travel activities can help public transportation managers optimize the allocation of resources. In this paper, transit networks are constructed based on traffic flow data rather than network topologies. The PageRank algorithm and community detection method are combined to identify the spatial distribution of public transportation trips. The structural centrality and PageRank values are compared to identify hub stations; the community detection method is applied to reveal the community structures. A case study in Guangzhou, China is presented. It is found that the bus network has a community structure, significant weekday commuting and small-world characteristics. The metro network is tightly connected, highly loaded, and has no obvious community structure. Hub stations show distinct differences in terms of volume and weekend/weekday usage. The results imply that the proposed method can be used to identify the spatial distribution of urban public transportation and provide a new study perspective.     

A discounted recursive logit model for dynamic gridlock network analysis

Emerging sensing technologies such as probe vehicles equipped with Global Positioning System (GPS) devices on board provide us real-time vehicle trajectories. They are helpful for the understanding of the cases that are significant but difficult to observe because of the infrequency, such as gridlock networks. On the premise of this type of emerging technology, this paper propose a sequential route choice model that describes route choice behavior, both in ordinary networks, where drivers acquire spatial knowledge of networks through their experiences, and in extraordinary networks, which are situations that drivers rarely experience, and applicable to real-time traffic simulations. In extraordinary networks, drivers do not have any experience or appropriate information. In such a context, drivers have little spatial knowledge of networks and choose routes based on dynamic decision making, which is sequential and somewhat forward-looking. In order to model these decision-making dynamics, we propose a discounted recursive logit model, which is a sequential route choice model with the discount factor of expected future utility. Through illustrative examples, we show that the discount factor reflects drivers’ decision-making dynamics, and myopic decisions can confound the network congestion level. We also estimate the parameters of the proposed model using a probe taxis’ trajectory data collected on March 4, 2011 and on March 11, 2011, when the Great East Japan Earthquake occurred in the Tokyo Metropolitan area. The results show that the discount factor has a lower value in gridlock networks than in ordinary networks.     

Strategic evacuation planning with pedestrian guidance and bus routing: a mixed integer programming model and heuristic solution

This paper presents a mathematical model to plan emergencies in a densely populated urban zone where a certain numbers of pedestrians depend on transit for evacuation. The proposed model features an integrated operational framework, which simultaneously guides evacuees through urban streets and crosswalks (referred to as “the pedestrian network”) to designated pickup points (e.g., bus stops), and routes a fleet of buses at different depots to those pick‐up points and transports evacuees to their destinations or safe places. In this level, the buses are routed through the so‐called “vehicular network.” An integrated mixed integer linear program that can effectively take into account the interactions between the aforementioned two networks is formulated to find the maximal evacuation efficiency in two networks. Because the large instances of the proposed model are mathematically difficult to solve to optimality, a two‐stage heuristic is developed to solve larger instances of the model. Results from hundreds of numerical examples analysis indicate that proposed heuristic works well in providing (near) optimal or feasibly good solutions for medium‐scale to large‐scale instances that may arise in real transit‐based evacuation situations in a much shorter amount of computational time compared with cplex (can find optimal/feasible solutions for only five instances within 3 hours of running). Copyright © 2016 John Wiley & Sons, Ltd.     

Plan-based flexible bus bridging operation strategy

Bus bridging has been widely used to connect stations affected by metro disruptions such that stranded passengers could resume their journeys. Previous studies generally assumed that a bus operates exclusively on one bridging route with given frequency, which limits the service flexibility and reduce the operational efficiency. We propose a strategy to instruct buses to operate on predefined bridging routes once they are dispatched from depots. Buses are allowed to flexibly serve different bridging routes. Each bus operates based on a bridging plan that lists the stations to serve in sequence instead of route frequencies. A two-stage model is developed to optimize the bridging plans and their assignments to buses with the objectives that balance the operational priorities between minimizing bus bridging time and reducing passenger delay. A Weight Shortest Processing Time first (WSPT) rule based heuristic algorithm is developed to solve the proposed model. The developed model is further incorporated in a rolling horizon framework to handle dynamic passenger arrivals during the disruption period. The effectiveness of the proposed strategy is demonstrated in comparison with alternative strategies in real-world case studies.     

Bus arrival time prediction at bus stop with multiple routes

Provision of accurate bus arrival information is vital to passengers for reducing their anxieties and waiting times at bus stop. This paper proposes models to predict bus arrival times at the same bus stop but with different routes. In the proposed models, bus running times of multiple routes are used for predicting the bus arrival time of each of these bus routes. Several methods, which include support vector machine (SVM), artificial neural network (ANN), k nearest neighbours algorithm (k-NN) and linear regression (LR), are adopted for the bus arrival time prediction. Observation surveys are conducted to collect bus running and arrival time data for validation of the proposed models. The results show that the proposed models are more accurate than the models based on the bus running times of single route. Moreover, it is found that the SVM model performs the best among the four proposed models for predicting the bus arrival times at bus stop with multiple routes.     

A regression model for bus running times in suburban areas of winnipeg

To plan new bus routes in suburban areas, expected bus running times on these routes are needed. Using most readily available relevant variables, a regression model is developed for estimating bus running times. The model is conceptually reasonable and it was tested using data other than that used for estimation.     

Dynamic user equilibrium in public transport networks with passenger congestion and hyperpaths

This paper presents a dynamic user equilibrium for bus networks where recurrent overcrowding results in queues at stops. The route-choice model embedded in the dynamic assignment explicitly considers common lines and strategies with alternative routes. As such, the shortest hyperpath problem is extended to a dynamic scenario with capacity constraints where the diversion probabilities depend on the time at which the stop is reached and on the expected congestion level at that time. In order to reproduce congestion for all the lines sharing a stop, the Bottleneck Queue Model with time-varying exit capacity, introduced in Meschini et al. (2007), is extended. The above is applied to separate queues for each line in order to satisfy the First-In-First-Out principle within every attractive set, while allowing overtaking among passengers with different attractive sets but queuing single file. The application of the proposed model to a small example network clearly reproduces the formation and dispersion of passenger queues due to capacity constraints and thus motivates the implementation of the methodology on a real-size network case as the next step for future research.     

Bus policy — Conclusions from a case study

The main policy conclusions from a recent bus study in the new town of Telford in the U.K. are summarised and discussed. The choice of bus routes and their combination into networks is examined. Alternative fares systems are compared and the implications for the fare levels necessary to cover costs are discussed. It is argued that bus services can generally be financed from the fare-box but that, unless services are cut as passenger demand falls, unduly high fares will result and these will unnecessarily drive more passengers away from the buses. Several particular aspects of service marketing are then examined and the paper concludes by discussing the actual organisation of the bus services.     

Ridership estimation procedure for a transit corridor with new bus rapid transit service

Ridership estimation is a critical step in the planning of a new transit route or change in service. Very often, when a new transit route is introduced, the existing routes will be modified, vehicle capacities changed, or service headways adjusted. This has made ridership forecasts for the new, existing, and modified routes challenging. This paper proposes and demonstrates a procedure that forecasts the ridership of all transit routes along a corridor when a new bus rapid transit (BRT) service is introduced and existing regular bus services are adjusted. The procedure uses demographic data along the corridor, a recent origin–destination survey data, and new and existing transit service features as inputs. It consists of two stages of transit assignment. In the first stage, a transit assignment is performed with the existing transit demand on the proposed BRT and existing bus routes, so that adjustments to the existing bus services can be identified. This transit assignment is performed iteratively until there is no adjustment in transit services. In the second stage, the transit assignment is carried out with the new BRT and adjusted regular bus services, but incorporates a potential growth in ridership because of the new BRT service. The final outputs of the procedure are ridership for all routes and route segments, boarding and alighting volumes at all stops, and a stop‐by‐stop trip matrix. The proposed ridership estimation procedure is applicable to a new BRT route with and without competing regular bus routes and with BRT vehicles traveling in dedicated lanes or in mixed traffic. The application of the proposed procedure is demonstrated via a case study along the Alameda Corridor in El Paso, Texas. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimization of a feeder-bus route design by using a multiobjective programming approach

This paper presents a feeder-bus route design model, capable of minimizing route length, minimizing maximum route travel time of planned routes, and maximizing service coverage for trip generation. The proposed model considers constraints of route connectivity, subtour prevention, travel time upper bound of a route, relationships between route layout and service coverage, and value ranges of decision variables. Parameter uncertainties are dealt with using fuzzy numbers, and the model is developed as a multiobjective programming problem. A case study of a metro station in Taichung City, Taiwan is then conducted. Next, the programming problem in the case study is solved, based on the technique for order preference by similarity to ideal solution approach to obtain the compromise route design. Results of the case study confirm that the routes of the proposed model perform better than existing routes in terms of network length and service coverage. Additionally, increasing the number of feeder-bus routes decreases maximum route travel time, increases service coverage, and increases network length. To our knowledge, the proposed model is the first bus route design model in the literature to consider simultaneously various stakeholder needs and support for bus route planners in developing alternatives for further evaluation efficiently and systematically.     

A structured flexible transit system for low demand areas

Public transit structure is traditionally designed to contain fixed bus routes and predetermined bus stations. This paper presents an alternative flexible-route transit system, in which each bus is allowed to travel across a predetermined area to serve passengers, while these bus service areas collectively form a hybrid “grand” structure that resembles hub-and-spoke and grid networks. We analyze the agency and user cost components of this proposed system in idealized square cities and seek the optimum network layout, service area of each bus, and bus headway, to minimize the total system cost. We compare the performance of the proposed transit system with those of comparable systems (e.g., fixed-route transit network and taxi service), and show how each system is advantageous under certain passenger demand levels. It is found out that under low-to-moderate demand levels, the proposed flexible-route system tends to have the lowest system cost.     

A three-dimensional macroscopic fundamental diagram for mixed bi-modal urban networks

Recent research has studied the existence and the properties of a macroscopic fundamental diagram (MFD) for large urban networks. The MFD should not be universally expected as high scatter or hysteresis might appear for some type of networks, like heterogeneous networks or freeways. In this paper, we investigate if aggregated relationships can describe the performance of urban bi-modal networks with buses and cars sharing the same road infrastructure and identify how this performance is influenced by the interactions between modes and the effect of bus stops. Based on simulation data, we develop a three-dimensional vehicle MFD (3D-vMFD) relating the accumulation of cars and buses, and the total circulating vehicle flow in the network. This relation experiences low scatter and can be approximated by an exponential-family function. We also propose a parsimonious model to estimate a three-dimensional passenger MFD (3D-pMFD), which provides a different perspective of the flow characteristics in bi-modal networks, by considering that buses carry more passengers. We also show that a constant Bus–Car Unit (BCU) equivalent value cannot describe the influence of buses in the system as congestion develops. We then integrate a partitioning algorithm to cluster the network into a small number of regions with similar mode composition and level of congestion. Our results show that partitioning unveils important traffic properties of flow heterogeneity in the studied network. Interactions between buses and cars are different in the partitioned regions due to higher density of buses. Building on these results, various traffic management strategies in bi-modal multi-region urban networks can then be integrated, such as redistribution of urban space among different modes, perimeter signal control with preferential treatment of buses and bus priority.