Optimizing sustainable feeder bus operation considering realistic networks and heterogeneous demand

A mathematical model is developed to optimize social and fiscal sustainable operation of a feeder bus system considering realistic network and heterogeneous demand. The objective total profit is a nonlinear, mixed integer function, which is maximized by optimizing the number of stops, headway, and fare. The stops are located which maximize the ridership. The demand elasticity for the bus service is dependent on passengers' access distance, wait time, in‐vehicle time, and fare. An optimization algorithm is developed to search for the optimal solution that maximizes the profit. The modeling approach is applied to planning a bus transit system within Woodbridge, New Jersey. Copyright © 2011 John Wiley & Sons, Ltd.     

A model of stoppings on urban bus routes

The amount of time required to pick up and discharge passengers is an important issue in the planning and modeling of urban bus systems. Several past studies have employed models of this component of bus travel time which are based, in part, on a model of the number of stoppings the bus makes to pick up or discharge passengers. Most past versions of this model have assumed that expected demand does not vary from stop to stop or from trip to trip, but that the number of passengers demanding service at any given stop during any given trip follows a Poisson distribution. An alternative model is derived, based on the assumption that expected demand varies among stops and times of day but is fixed from day to day at any given stop and time of day. Boarding and alighting survey data are used to verify that the “average-demand” Poisson model consistently overestimates the number of stoppings and to calibrate an approximate version of the alternative model. A stop-spacing optimization model previously developed by Kikuchi and Vuchic is reevaluated using the alternative stopping model in place of the average demand model used in the original version. The results are found to be considerably different, thus indicating that transit route optimization models are sensitive to the way in which stopping processes are modeled.     

Optimization of bus stop placement for routes on uneven topography

The improvement and expansion of public transport is an increasingly important solution to the high congestion costs and worsening environmental impacts of the car dominated transport systems seen in many cities today. The intelligent design of stop locations is one way to improve the quality of PT and thereby improve its ridership. Stop placement is a relatively complex task as it involves a trade-off between two competing goals; accessibility and operation; however this trade-off can be made explicit using an appropriate mathematical model. Many such models have been developed in the literature, however none consider the effects of uneven topography. Topography is an important but often neglected factor in the design of public transportation systems, with the potential to have a significant impact on the accessibility, operation and planning of a transit service. In this work a mathematical modelling approach to bus stop placement is developed which includes considerations of uneven topography in three ways; (1) Its effect on walking speed; (2) Its impact on the attractiveness of an access path to a transit service; and (3) Its effect on acceleration rates at stops. Because of the complexity of the model developed, a heuristic evolutionary algorithm’ is employed to approximate an optimal solution to the model. Finally, the model and solution method are applied to a case study in the Auckland CBD area in New Zealand.     

Optimal control of headway variation on transit routes

Headway control strategies have been proposed as methods for correcting transit service irregularities and thereby reducing passenger wait times at stops. This paper addresses a particular strategy which can be implemented on high frequency routes (headways under 10–12 minutes), in which buses are held at a control stop to a threshold headway. An algorithm is developed which yields the optimal control stop location and optimal threshold headway with respect to a system wait function. The specification of the wait function is based on the development of several empirical models, including a headway variation model and an average delay time model at control stops. A conclusion is reached that the headway variation does not increase linearly along a route, a common assumption made in many previous studies. Furthermore, the location of the optimal control stop and threshold value are sensitive to the passenger boarding profile, as expected. The algorithm itself appears to have practical application to conventional transit operations.     

Isolating high-priority metro and feeder bus transfers using smart card data

Fixed-rail metro (or ‘subway’) infrastructure is generally unable to provide access to all parts of the city grid. Consequently, feeder bus lines are an integral component of urban mass transit systems. While passengers prefer a seamless transfer between these two distinct transportation services, each service’s operations are subject to a different set of factors that contribute to metro-bus transfer delay. Previous attempts to understand transfer delay were limited by the availability of tools to measure the time and cost associated with passengers’ transfer experience. This paper uses data from smart card systems, an emerging technology that automatically collects passenger trip data, to understand transfer delay. The primary objective of this study is to use smart card data to derive a reproducible methodology that isolates high priority transfer points between the metro system and its feeder-bus systems. The paper outlines a methodology to identify transfer transactions in the smart card dataset, estimate bus headways without the aid of geographic location information, estimate three components of the total transfer time (walking time, waiting time, and delay time), and isolate high-priority transfer pairs. The paper uses smart card data from Nanjing, China as a case study. The results isolate eight high priority metro-bus transfer pairs in the Nanjing metro system and finally, offers several targeted measures to improve transfer efficiency.     

A new street connectivity indicator to predict performance for feeder transit services

This paper defines a novel street Connectivity Indicator (C.I.) to predict transit performance by identifying the role that street network connectivity plays in influencing the service quality of demand responsive feeder transit services. This new C.I. definition is dependent upon the expected shortest path between any two nodes in the network, includes spatial features and transit demand distribution information and is easy to calculate for any given service area. Simulation analyses over a range of networks have been conducted to validate the new definition. Results show a desirable monotonic relationship between transit performance and the proposed C.I., whose values are directly proportional and therefore good predictors of the transit performance, outperforming other available indicators, typically used by planners.     

Efficiency measurement of bus routes and exogenous operating environment effects on efficiency

This study develops an independent efficiency measurement model framework of bus routes, so as to treat preferably the heterogeneous outputs in a data envelopment analysis (DEA)-based efficiency measurement. It then introduces four new exogenous operating environment factors at the microscopic level of bus routes, and applies the three-stage DEA approach to incorporate operating environment effects and statistical noise into the efficiency measurement framework. The main purpose is to measure impartially the managerial efficiency of bus routes, purged of operating environment effects and statistical noise, and additionally to investigate the operating environment effects on efficiency. An empirical analysis, based on 39 routes operated in Jiangyin City, China, is presented. The principal finding is that the adoption of the independent efficiency measurement model framework is reasonable and has many virtues. Moreover, the proposed approach could substantially provide decision support both for regulators and for producers of bus services. In addition, the operating environment does indeed significantly affect operating efficiency and quality efficiency, especially the latter.     

Optimal transit service atop ring-radial and grid street networks: A continuum approximation design method and comparisons

Two continuum approximation (CA) optimization models are formulated to design city-wide transit systems at minimum cost. Transit routes are assumed to lie atop a city’s street network. Model 1 assumes that the city streets are laid out in ring-radial fashion. Model 2 assumes that the city streets form a grid. Both models can furnish hybrid designs, which exhibit intersecting routes in a city’s central (downtown) district and only radial branching routes in the periphery. Model 1 allows the service frequency and the route spacing at a location to vary arbitrarily with the location’s distance from the center. Model 2 also allows such variation but in the periphery only.The paper shows how to solve these CA optimization problems numerically, and how the numerical results can be used to design actual systems. A wide range of scenarios is analyzed in this way. It is found among other things that in all cases and for both models: (i) the optimal headways and spacings in the periphery increase with the distance from the center; and (ii) at the boundary between the central district and the periphery both, the optimal service frequency and line spacing for radial lines decrease abruptly in the outbound direction. On the other hand Model 1 is distinguished from Model 2 in that the former produces in all cases: (i) a much smaller central district, and (ii) a high frequency circular line on the outer edge of that central district.Parametric tests with all the scenarios further show that Model 1 is consistently more favorable to transit than Model 2. Cost differences between the two designs are typically between 9% and 13%, but can top 21.5%. This is attributed to the manner in which ring-radial networks naturally concentrate passenger’s shortest paths, and to the economies of demand concentration that transit exhibits. Thus, it appears that ring-radial street networks are better for transit than grids.To illustrate the robustness of the CA design procedure to irregularities in real street networks, the results for all the test problems were then used to design and evaluate transit systems on networks of the “wrong” type – grid networks were outfilled with transit systems designed with Model 1 and ring-radial networks designed with Model 2. Cost increased on average by only 2.7%. The magnitude of these deviations suggests that the proposed CA procedures can be used to design transit systems over real street networks when they are not too different from the ideal and that the resulting costs should usually be very close to those predicted.     

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.     

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.     

The planning of urban bus routes and frequencies: A survey

Urban bus services still play an important role in the movement of people in Britain, although since the 1950's bus patronage has been declining and costs of operation have been increasing. Most of the urban bus networks in Britain (and to a very large extent the Western World) have developed or evolved over the years and it is sometimes said that, despite the changing conditions of bus transport, few of these bus networks in Britain have undergone major re-organisation. A survey was carried out to ascertain this view and to establish the approaches used by British urban bus operators.Five approaches to the planning of urban bus routes and frequencies have been identified: (1) manual; (2) Market Analysis Project; (3) systems analysis; (4) systems analysis with interactive graphics; and (5) mathematical. Previous research in, and application of, the different approaches are described and examined.Between 1970 and 1980, 82.4% of those British urban operators who responded to the survey carried out some kind of major bus study. The survey results run counter to the view that there has been little recent change in urban bus networks in Britain, but the alleged conservatism of the bus industry appears when the approaches used for re-planning bus services are examined - 71.4% of the operators used a manual approach and only a meagre 28.6% made use of simple assignment techniques to predict the potential passenger impacts of the alternative networks appraised.     

Investigating the irregularity of bus routes: highlighting how underlying assumptions of bus models impact the regularity results

A bus route is inherently unstable: when the system is uncontrolled, buses fail to maintain their time‐headways and tend to bunch. Several mathematical bus motion models were proposed to reproduce the bus behavior and assess management strategies. However, no work has established how the choice of a model impacts the irregularity of modeled bus systems, that is, the non‐respect of scheduled headways. Because of this gap, a large body of existing works assumes that the ability of these models to reproduce instability comes only from stochasticity, although the link between stochastic inputs and the level of irregularity remains unknown. Moreover, some recognized phenomena such as a change of travel conditions during a day or delays at signalized intersections are ignored. To address these shortcomings, this paper provides an overview of existing dynamic bus‐focused models and proposes a simple way to classify them. Commonly used deterministic and stochastic models are compared, which allows quantifying the relative influence of stochasticity of each model component on outputs. Moreover, we show that a change in the system equilibrium in a full deterministic system can lead to irregularity. Finally, this paper proposes a refinement of travel time models to account for non‐dynamic signals. In presence of traffic signals, we show that a bus system can be self‐regulated. Especially, these insights could help to calibrate bus model inputs to better reproduce real data. Copyright © 2014 John Wiley & Sons, Ltd.     

Designing robust rapid transit networks with alternative routes

The aim of this paper is to propose a model for the design of a robust rapid transit network. In this paper, a network is said to be robust when the effect of disruption on total trip coverage is minimized. The proposed model is constrained by three different kinds of flow conditions. These constraints will yield a network that provides several alternative routes for given origin–destination pairs, therefore increasing robustness. The paper includes computational experiments which show how the introduction of robustness influences network design. Copyright © 2010 John Wiley & Sons, Ltd.     

Optimal bus fleet management strategy for emissions reduction

Transportation is a major cause for environmental degradation via exhaust emissions. For many transit-oriented metropolitan areas, bus trips often constitute a sizeable mode share. Managing the bus fleet, in particular updating buses to comply with the newer emissions standards, therefore, can have a substantial impact on transportation-induced air quality. This paper presents the approach of remaining life additional benefit–cost (RLABC) analysis for maximising the total net benefit by either early-retiring or retrofitting the current bus fleet within their lifespans. By referring to the net benefits for different bus types estimated by RLABC analysis, the most beneficial management scheme for the current bus fleet can be identified. Optimal bus fleet management (BFM) models based on the RLABC analysis for the operator and the government are developed. Then a government subsidy plan is produced to achieve win–win solutions, which will offer efficient and flexible management schemes. To illustrate the approach, the largest bus company in Hong Kong, which carries more than 23% of the total trips in Hong Kong, is taken as a case study example. Instead of adopting a fixed retirement plan, such as replacing buses at the age of 17 as is currently practised, the proposed method develops an optimal BFM scheme that progressively phases out buses or retrofits them. This study produces promising results to demonstrate the large benefit of this approach for optimal bus fleet management.     

Radial bus networks with multi-period and many-to-many demand

Mathematical models are developed for optimizing radial bus networks with time dependent demand and supply characteristics. These models can deal with many-to-many demand distribution in heterogeneous rather than idealized geographic environments. With some approximations, closed-form solutions for the optimal route angle, headways for different time periods, and stop spacings for various locations are obtained for a total cost minimization objective. The relations between the decision variables and system parameters are identified analytically. The optimality of a constant ratio between headways and route angle is found to hold with a time related factor. The optimized wait cost, operator cost, and lateral access cost are found to be equal. A numerical example is given for a case with three service periods. It illustrates the applicability of the analytic model to irregular demand patterns that may be directionally imbalanced during some periods.     

A fuzzy-based system for incident detection in urban street networks

Detecting incidents on urban streets or arterials using loop detector data is quite challenging. The pattern of the incident could be quite similar to non-incident cases as intersections get congested. This paper describes the development of a fuzzy logic for incident detection. An Integrated System for Incident Management (

-sim) was developed. An integral component of such system is a microscopic simulator,

-sim-s, an object-oriented model that allows for virtual detector installations at different locations, modeling different intersection layouts, traffic control types and timing, and link characteristics.

-sim-s was utilized to generate various incident scenarios and extracting associated detectors’ accumulative counts. A data clustering technique was utilized to consolidate the various incident scenarios into a single data set for the development of the Fuzzy Logic for incident detection at intersections (

-sim-fl). The

-sim-fl uses the detector data as well as other link properties in flagging detecting incidents.The

-sim-fl can be used to indicate the possibility of an incident, a stalled vehicle, or a sort of traffic disturbance. The devised logic was validated using separate simulation-based incident scenarios.     

Optimal selection of build-operate-transfer projects on transportation networks

This paper considers the problem of how to select highway projects for the build-operate-transfer (BOT) development with the objective of improving the social benefit while ensuring the marketability of those selected. The problem can be viewed as a tri-level leader-follower game and is formulated as a mixed integer program with equilibrium constraints. Without solving the associated problem, we show that optimal tolls and travel times on selected BOT highways can be determined from their attributes under mild assumptions. This leads to an efficient heuristic algorithm for solving the project selection problem.     

The design of interurban bus networks in city centers

This paper proposes a bilevel formulation for solving the Bus Network Design Problem (BNDP) of interurban services entering a major city. It is focused in interurban services because it is a growing problem in most of major cities, yet new in the literature. The layout of interurban bus routes and the locations of transfer stations in the main city are the key factors to provide a competitive public transportation service to commuters in a metropolitan area. The number of commuters in huge urban concentrations is growing due to the difficulties of living near the city center. The objective function of the first level is defined with the aim of reducing user and agency costs. In the second level the performance of users is addressed. Furthermore, a local search method based on the Tabu Search algorithm was carried out to guide the exploration in the solution domain. The results obtained in a set of test problems have demonstrated that the restart parameters of the algorithm play a significant role in the efficiency of the algorithm. Finally, implementation in the large network of Barcelona (Spain) reduces the total cost by 5% with regard to the present situation.     

Study on some bus transport networks in China with considering spatial characteristics

Many real-world networks are embedded in spaces. Recent studies have found that spatial characteristics are closely related to network features. Bus transport networks (BTNs) are typical spatially embedded networks, but their spatial characteristics are commonly disregarded in previous researches. In this paper, we propose a new spatial representation model for BTNs with information on the geographical location of bus stations and routes, for which we named as the ES model. The new model aids in the study of real-world BTNs. By performing a statistical study with the new representation model on three typical BTNs in China, namely the Beijing, Shanghai and Hangzhou BTNs, we identify some network features that are consistent with those revealed by previous studies, as well as some new features such as high clustering of short-distance station pairs (SSPs) and small average number of bus routes in a path. The result shows that the existence of SSPs can significantly influence the characteristics of BTNs. Besides, with the help of the ES model, we designed a new transfer algorithm for BTNs.     

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.