Disruption management in public transit: the bee colony optimization approach

Disruptions in carrying out planned bus schedules occur daily in many public transit companies. Disturbances are often so large that it is necessary to perform re-planning of planned bus and crew activities. Dispatchers in charge of traffic operations must frequently find an answer to the following question in a very short period of time: How should available buses be distributed among bus routes in order to minimize total passengers' waiting time on the network? We propose a model for assigning buses to scheduled routes when there is a shortage of buses. The proposed model is based on the bee colony optimization (BCO) technique. It is a biologically inspired method that explores collective intelligence applied by honey bees during the nectar collecting process. It has been shown that this developed BCO approach can generate high-quality solutions within negligible processing times.     

The allocation of buses in heavily utilized networks with overlapping routes

Many transit systems outside North America are characterized by networks with extensively overlapping routes and buses frequently operating at, or close to, capacity. This paper addresses the problem of allocating a fleet of buses between routes in this type of system; a problem that must be solved recurrently by transit planners. A formulation of the problem is developed which recognizes passenger route choice behavior, and seeks to minimize a function of passenger wait time and bus crowding subject to constraints on the number of buses available and the provision of enough capacity on each route to carry all passengers who would select it. An algorithm is developed based on the decomposition of the problem into base allocation and surplus allocation components. The base allocation identifies a feasible solution using an (approx.) minimum number of buses. The surplus allocation is illustrated for the simple objective of minimizing the maximum crowding level on any route. The bus allocation procedure developed in this paper has been applied to part of the Cairo bus system in a completely manual procedure, and is proposed to be the central element of a short-range bus service planning process for that city.     

Heuristic approach to the airline schedule disturbances problem

Abstract

When disturbances make it impossible to realise the planned flight schedule, the dispatcher at the airline operational centre defines a new flight schedule based on airline policy, in order to reduce the negative effects of these perturbations. Depending on airline policy, when designing the new flight schedule, the dispatcher delays or cancels some flights and reassigns some flights to available aircraft. In this paper, a decision support system (DSS) for solving the airline schedule disturbances problem is developed aiming to assist decision makers in handling disturbances in real-time. The system is based on a heuristic algorithm, which generates a list of different feasible schedules ordered according to the value of an objective function. The dispatcher can thus select and implement one of them. In this paper, the possibilities of DSS are illustrated by real numerical examples that concern JAT Airways' flight schedule disturbances.     

Bus maintenance systems and maintenance scheduling: model formulations and solutions

This paper deals with the problem of scheduling bus maintenance activities. The scheduling of maintenance activities is an important component in bus transit operations planning process. The other components include network route design, setting timetables, scheduling vehicles, and assignment of drivers. This paper presents a mathematical programming approach to the problem. This approach takes as input a given daily operating schedule for all buses assigned to a depot along with available maintenance resources. It, then, attempts to design daily inspection and maintenance schedules for the buses that are due for inspection so as to minimize the interruptions in the daily bus operating schedule, and maximize the utilization of the maintenance facilities. Three integer programming formulations are presented and different properties of the problem are discussed. Several heuristic methods are presented and tested. Some of these procedures produce very close to optimal solutions very efficiently. In some cases, the computational times required to obtain these solutions are less than 1% of the computational time required for the conventional branch and bound algorithm. Several small examples are offered and the computational results of solving the problem for an actual, 181-bus transit property are reported.     

Merging bus routes in Hong Kong’s central business district: Analysis and models

A significant portion of the 200,000 people working in Hong Kong’s central business district (CBD) relies on buses as their primary means of transport. During peak hours, nearly a thousand double-decker buses pour into a tiny area of 150 ha. This causes traffic congestion and air pollution. Moreover, given that the flow is uni-directional (into the CBD in the morning and out of the CBD in the afternoon), the occupancy of buses in the CBD is actually low.In this paper, we propose to reduce traffic congestion and to increase bus occupancy by merging bus routes. We describe the peculiar situation of the CBD in Hong Kong and explain the necessary conditions for the possible success of merging routes. Our analysis shows that merging will lead to an overall benefit for all parties, including government, bus operators, and passengers. The actual merging decisions, which routes to merge and at what frequencies buses should run, are determined by a mathematical model. The model also shows quantitatively the benefits of merging routes and the impacts of other factors. The procedure that we follow and the model that we adopt can be applied to other CBD.     

Real-time control of buses for schedule coordination at a terminal

Recently, bus transit operators have begun to adopt technologies that enable bus locations to be tracked from a central location in real-time. Combined with other technologies, such as automated passenger counting and wireless communication, it is now feasible for these operators to execute a variety of real-time strategies for coordinating the movement of buses along their routes. This paper compares control strategies that depend on technologies for communication, tracking and passenger counting, to those that depend solely on local information (e.g., time that a bus arrived at a stop, and whether other connecting buses have also arrived). We also develop methods to forecast bus arrival times, which are most accurate for lines with long headways, as is usually the case in timed transfer systems. These methods are tested in simulations, which demonstrate that technology is most advantageous when the schedule slack is close to zero, when the headway is large, and when there are many connecting buses.     

Time of day intervals partition for bus schedule using GPS data

Time of day partition of bus operating hours is a prerequisite of bus schedule design. Reasonable partition plan is essential to improve the punctuality and level of service. In most mega cities, bus vehicles have been equipped with global positioning system (GPS) devices, which is convenient for transit agency to monitor bus operations. In this paper, a new algorithm is developed based on GPS data to partition bus operating hours into time of day intervals. Firstly, the impacts of passenger demand and network traffic state on bus operational performance are analyzed. Then bus dwell time at stops and inter-stop travel time, which can be attained based on GPS data, are selected as partition indexes. For buses clustered in the same time-of-day interval, threshold values of differences in dwell time at stops and inter-stop travel time are determined. The buses in the same time-of-day interval should have adjacent dispatching numbers, which is set as a constraint. Consequently, a partition algorithm with three steps is developed. Finally, a bus route in Suzhou China is taken as an example to validate the algorithm. Three partition schemes are given by setting different threshold values for the two partition indexes. The present scheme in practice is compared with the three proposed schemes. To balance the number of ToD intervals and partition precision, a Benefit Evaluation Index is proposed, for a better time-of-day interval plan.     

Design and development of interactive trip planning for web-based transit information systems

This article presents a Web-based transit information system design that uses Internet Geographic Information Systems (GIS) technologies to integrate Web serving, GIS processing, network analysis and database management. A path finding algorithm for transit network is proposed to handle the special characteristics of transit networks, e.g., time-dependent services, common bus lines on the same street, and non-symmetric routing with respect to an origin/destination pair. The algorithm takes into account the overall level of services and service schedule on a route to determine the shortest path and transfer points. A framework is created to categorize the development of transit information systems on the basis of content and functionality, from simple static schedule display to more sophisticated real time transit information systems. A unique feature of the reported Web-based transit information system is the Internet-GIS based system with an interactive map interface. This enables the user to interact with information on transit routes, schedules, and trip itinerary planning. Some map rendering, querying, and network analysis functions are also provided.     

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.     

Real-time bus route state forecasting using particle filter and mesoscopic modeling

In the absence of system control strategies, it is common to observe bus bunching in transit operations. A transit operator would benefit from an accurate forecast of bus operations in order to control the system before it becomes too disrupted to be restored to a stable condition. To accomplish this, we present a general bus prediction framework. This framework relies on a stochastic and event-based bus operation model that provides sets of possible bus trajectories based on the observation of current bus positions, available via global positioning system (GPS) data. The median of the set of possible trajectories, called a particle, is used as the prediction. In particular, this enables the anticipation of irregularities between buses. Several bus models are proposed depending on the dwell and inter-stop running time representations. These models are calibrated and applied to a real case study thanks to the high quality data provided by TriMet (the Portland, Oregon, USA transit district). Predictions are finally evaluated by an a posteriori comparison with the real trajectories. The results highlight that only bus models accounting for the bus load can provide valid forecasts of a bus route over a large prediction horizon, especially for headway variations. Accounting for traffic signal timings and actual traffic flows does not significantly improves the prediction. Such a framework paves the way for further development of refined dynamic control strategies for bus operations.     

Integrated optimization of bus priority operations in connected vehicle environment

Most previous works associated with transit signal priority merely focus on the optimization of signal timings, ignoring both bus speed and dwell time at bus stops. This paper presents a novel approach to optimize the holding time at bus stops, signal timings, and bus speed to provide priority to buses at isolated intersections. The objective of the proposed model is to minimize the weighted average vehicle delays of the intersection, which includes both bus delay and impact on nearby intersection traffic, ensuring that buses clear these intersections without being stopped by a red light. A set of formulations are developed to explicitly capture the interaction between bus speed, bus holding time, and transit priority signal timings. Experimental analysis is used to show that the proposed model has minimal negative impacts on general traffic and outperforms the no priority, signal priority only, and signal priority with holding control strategies (no bus speed adjustment) in terms of reducing average bus delays and stops. A sensitivity analysis further demonstrates the potential of the proposed approach to be applied to bus priority control systems in real‐time under different traffic demands, bus stop locations, and maximum speed limits. Copyright © 2016 John Wiley & Sons, Ltd.     

Modeling schedule recovery processes in transit operations for bus arrival time prediction

Many existing algorithms for bus arrival time prediction assume that buses travel at free‐flow speed in the absence of congestion. As a result, delay incurred at one stop would propagate to downstream stops at the same magnitude. In reality, skilled bus operators often constantly adjust their speeds to keep their bus on schedule. This paper formulates a Markov chain model for bus arrival time prediction that explicitly captures the behavior of bus operators in actively pursuing schedule recovery. The model exhibits some desirable properties in capturing the schedule recovery process. It guarantees provision of the schedule information if the probability of recovering from the current schedule deviation is sufficiently high. The proposed model can be embedded into a transit arrival time estimation model for transit information systems that use both real‐time and schedule information. It also has the potential to be used as a decision support tool to determine when dynamic or static information should be used.     

Optimally combined headway and timetable reliable public transport system

This paper presents a model-based multiobjective control strategy to reduce bus bunching and hence improve public transport reliability. Our goal is twofold. First, we define a proper model, consisting of multiple static and dynamic components. Bus-following model captures the longitudinal dynamics taking into account the interaction with the surrounding traffic. Furthermore, bus stop operations are modeled to estimate dwell time. Second, a shrinking horizon model predictive controller (MPC) is proposed for solving bus bunching problems. The model is able to predict short time-space behavior of public transport buses enabling constrained, finite horizon, optimal control solution to ensure homogeneity of service both in time and space. In this line, the goal with the selected rolling horizon control scheme is to choose a proper velocity profile for the public transport bus such that it keeps both timetable schedule and a desired headway from the bus in front of it (leading bus). The control strategy predicts the arrival time at a bus stop using a passenger arrival and dwell time model. In this vein, the receding horizon model predictive controller calculates an optimal velocity profile based on its current position and desired arrival time. Four different weighting strategies are proposed to test (i) timetable only, (ii) headway only, (iii) balanced timetable - headway tracking and (iv) adaptive control with varying weights. The controller is tested in a high fidelity traffic simulator with realistic scenarios. The behavior of the system is analyzed by considering extreme disturbances. Finally, the existence of a Pareto front between these two objectives is also demonstrated.     

Energy consumption and cost-benefit analysis of hybrid and electric city buses

This paper presents a cost-benefit analysis (CBA) of hybrid and electric city buses in fleet operation. The analysis is founded on an energy consumption analysis, which is carried out on the basis of extensive simulations in different bus routes. A conventional diesel city bus is used as a reference for the CBA. Five different full size hybrid and electric city bus configurations were considered in this study; two parallel and two series hybrid buses, and one electric city bus. Overall, the simulation results indicate that plug-in hybrid and electric city buses have the best potential to reduce energy consumption and emissions. The capital and energy storage system costs of city buses are the most critical factors for improving the cost-efficiency of these alternative city bus configurations. Furthermore, the operation schedule and route planning are important to take into account when selecting hybrid and electric city buses for fleet operation.     

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.     

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.     

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.     

Analyzing urban bus service reliability at the stop, route, and network levels

Improving the reliability of bus service has the potential to increase the attractiveness of public transit to current and prospective riders. An understanding of service reliability is necessary to develop strategies that help transit agencies provide better services. However, few studies have been conducted analyzing bus reliability in the metropolis of China. This paper presents an in-depth analysis of service reliability based on bus operational characteristics in Beijing. Three performance parameters, punctuality index based on routes (PIR), deviation index based on stops (DIS), and evenness index based on stops (EIS), are proposed for the evaluation of bus service reliability. Reliability involves routes, stops, punctuality, deviation, and evenness. The relationship among the three parameters is discussed using a numerical example. Subsequently, through a sampling survey of bus lines in Beijing, service reliability at the stop, route, and network levels are estimated. The effects of route length, headway, the distance from the stop to the origin terminal, and the use of exclusive bus lanes are also analyzed. The results indicate low service reliability for buses in Beijing and a high correlation between service reliability and route length, headway, distance from the stop to the origin terminal, and the provision of exclusive bus lanes.     

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.