A stochastic multimodal reliable network design problem under adverse weather conditions

This paper formulates a network design problem (NDP) for finding the optimal public transport service frequencies and link capacity expansions in a multimodal network with consideration of impacts from adverse weather conditions. The proposed NDP aims to minimize the sum of expected total travel time, operational cost of transit services, and construction cost of link capacity expansions under an acceptable level of variance of total travel time. Auto, transit, bus, and walking modes are considered in the multimodal network model for finding the equilibrium flows and travel times. In the proposed network model, demands are assumed to follow Poisson distribution, and weather‐dependent link travel time functions are adopted. A probit‐based stochastic user equilibrium, which is based on the perceived expected travel disutility, is used to determine the multimodal route of the travelers. This model also considers the strategic behavior of the public transport travelers in choosing their routes, that is, common‐line network. Based on the stochastic multimodal model, the mean and variance of total travel time are analytical estimated for setting up the NDP. A sensitivity‐based solution algorithm is proposed for solving the NDP, and two numerical examples are adopted to demonstrate the characteristics of the proposed model. Copyright © 2014 John Wiley & Sons, Ltd.     

Multimodal traveling and its impact on urban transit network design

Multimodal trip making, that is trips using a combination of several modes between origin and destination, is expected to be beneficial to society and might offer advantages to the traveler as well. This article looks at some of the implications of multi‐modality in trip making for the design of urban transit systems since these play an important role in multi‐modal transportation systems. In this respect, the article looks at the strategic design characteristics of urban transit networks, that is line density, stop density and service frequencies for the case of multimodal access to urban transit networks and for hierarchical network structures in urban transit systems. The analyses show that multimodal access does not require alternative network structures. For hierarchical network structures it is concluded that these are primarily determined by the hierarchy in demand densities and thus by hierarchy in urban structures.     

Network equilibrium for congested multi‐mode networks with elastic demand

This paper proposes an elastic demand network equilibrium model for networks with transit and walking modes. In Hong Kong, the multi‐mode transit system services over 90% of the total journeys and the demand on it is continuously increasing. Transit and walking modes are related to each other as transit passengers have to walk to and from transit stops. In this paper, the multi‐mode elastic‐demand network equilibrium problem is formulated as a variational inequality problem where the combined mode and route choices are modeled in a hierarchical logit structures and the total travel demand for each origin‐destination pair is explicitly given by an elastic demand function. In addition, the capacity constraint for transit vehicles and the effects of bi‐directional flows on walkways are considered in the proposed model. All these congestion effects are taken into account for modeling the travel choices. A solution algorithm is developed to solve the multi‐mode elastic‐demand network equilibrium model. It is based on a Block Gauss‐Seidel decomposition approach coupled with the method of successive averages. A numerical example is used to illustrate the application of the proposed model and solution algorithm.     

Calibrating a transit assignment model using smart card data in a large-scale multi-modal transit network

This paper describes a practical automated procedure to calibrate and validate a transit assignment model. An optimization method based on particle swarm algorithm is adopted to minimize a defined error term. This error term which is based on the percentage of root mean square error and the mean absolute percent error encompasses deviation of model outputs from observations considering both segment level as well as the mode level and can be applied to a large scale network. This study is based on the frequency-based assignment model using the concept of optimal strategy while any transit assignment model can be used in the proposed methodological framework. Lastly, the model is validated using another weekday data. The proposed methodology uses automatic fare collection (AFC) data to estimate the origin–destination matrix. This study combines data from three sources: the general transit feed specification, AFC, and a strategic transport model from a large-scale multimodal public transport network. The South-East Queensland (SEQ) network in Australia is used as a case study. The AFC system in SEQ has voluminous and high quality data on passenger boardings and alightings across bus, rail and ferry modes. The results indicate that the proposed procedure can successfully develop a multi-modal transit assignment model at a large scale. Higher dispersions are seen for the bus mode, in contrast to rail and ferry modes. Furthermore, a comparison is made between the strategies used by passengers and the generated strategies by the model between each origin and destination to get more insights about the detailed behaviour of the model. Overall, the analysis indicates that the AFC data is a valuable and rich source in calibrating and validating a transit assignment model.

     

Estimating multimodal transit ridership with a varying fare structure

This paper studies public transport demand by estimating a system of equations for multimodal transit systems where different modes may act competitively or cooperatively. Using data from Athens, Greece, we explicitly correct for higher-order serial correlation in the error terms and investigate two, largely overlooked, questions in the transit literature; first, whether a varying fare structure in a multimodal transit system affects demand and, second, what the determinants of ticket versus travelcard sales may be. Model estimation results suggest that the effect of fare type on ridership levels in a multimodal system varies by mode and by relative ticket to travelcard prices. Further, regardless of competition or cooperation between modes, fare increases will have limited effects on ridership, but the magnitude of these effects does depend on the relative ticket to travelcard prices. Finally, incorrectly assuming serial independence for the error terms during model estimation could yield upward or downward biased parameters and hence result in incorrect inferences and policy recommendations.     

Estimation of population origin–interchange–destination flows on multimodal transit networks

Previous research has combined automated fare-collection (AFC) and automated vehicle-location (AVL) data to infer the times and locations of passenger origins, interchanges (transfers), and destinations on multimodal transit networks. The resultant origin–interchange–destination flows (and the origin–destination (OD) matrices that comprise those flows), however, represent only a sample of total ridership, as they contain only those journeys made using the AFC payment method that have been successfully recorded or inferred. This paper presents a method for scaling passenger-journey flows (i.e., linked-trip flows) using additional information from passenger counts at each station gate and bus farebox, thereby estimating the flows of non-AFC passengers and of AFC passengers whose journeys were not successfully inferred.The proposed method is applied to a hypothetical test network and to AFC and AVL data from London’s multimodal public transit network. Because London requires AFC transactions upon both entry and exit for rail trips, a rail-only OD matrix is extracted from the estimated multimodal linked-trip flows, and is compared to a rail OD matrix generated using the iterative proportional fitting method.     

Performance indicators for public transit connectivity in multi-modal transportation networks

Connectivity plays a crucial role as agencies at the federal and state level focus on expanding the public transit system to meet the demands of a multimodal transportation system. Transit agencies have a need to explore mechanisms to improve connectivity by improving transit service. This requires a systemic approach to develop measures that can prioritize the allocation of funding to locations that provide greater connectivity, or in some cases direct funding towards underperforming areas. The concept of connectivity is well documented in social network literature and to some extent, transportation engineering literature. However, connectivity measures have limited capability to analyze multi-modal public transportation systems which are much more complex in nature than highway networks.In this paper, we propose measures to determine connectivity from a graph theoretical approach for all levels of transit service coverage integrating routes, schedules, socio-economic, demographic and spatial activity patterns. The objective of using connectivity as an indicator is to quantify and evaluate transit service in terms of prioritizing transit locations for funding; providing service delivery strategies, especially for areas with large multi-jurisdictional, multi-modal transit networks; providing an indicator of multi-level transit capacity for planning purposes; assessing the effectiveness and efficiency for node/stop prioritization; and making a user friendly tool to determine locations with highest connectivity while choosing transit as a mode of travel. An example problem shows how the graph theoretical approach can be used as a tool to incorporate transit specific variables in the indicator formulations and compares the advantage of the proposed approach compared to its previous counterparts. Then the proposed framework is applied to the comprehensive transit network in the Washington–Baltimore region. The proposed analysis offers reliable indicators that can be used as tools for determining the transit connectivity of a multimodal transportation network.     

Sustainable commute in a car-dominant city: Factors affecting alternative mode choices among university students

This paper studies university students’ commute and housing behaviors using samples from Los Angeles, a place notorious for car dependence and dominance. It finds that being embedded in this place does not make university students drive alone more than their peers in other places. Being multimodal and having a discounted transit pass increase the odds of alternative modes while holding a parking permit reduces the odds of these modes. Commute distance is positively related to carpool and telecommuting. Gender, status (undergraduate vs. gradate) and age are significantly correlated to biking, walking or public transit. Students living alone are more likely to commute by driving alone than other students. Having friends and classmates living nearby increases the odds of taking public transit. Due to data constraints, this study cannot prove whether there is any correlation between information contagion and the effects of living alone and having friends and classmates living nearby on alternative mode choice. But it proposes that the issue be worthwhile of further investigations. Base on the above, the paper recommends a comprehensive travel demand management program, utilization of information contagion effects of students and promotion of multimodal commute to better promote alternative mode of commute among university students.     

Validating and improving public transport origin–destination estimation algorithm using smart card fare data

Smart card data are increasingly used for transit network planning, passengers’ behaviour analysis and network demand forecasting. Public transport origin–destination (O–D) estimation is a significant product of processing smart card data. In recent years, various O–D estimation methods using the trip-chaining approach have attracted much attention from both researchers and practitioners. However, the validity of these estimation methods has not been extensively investigated. This is mainly because these datasets usually lack data about passengers’ alighting, as passengers are often required to tap their smart cards only when boarding a public transport service. Thus, this paper has two main objectives. First, the paper reports on the implementation and validation of the existing O–D estimation method using the unique smart card dataset of the South-East Queensland public transport network which includes data on both boarding stops and alighting stops. Second, the paper improves the O–D estimation algorithm and empirically examines these improvements, relying on this unique dataset. The evaluation of the last destination assumption of the trip-chaining method shows a significant negative impact on the matching results of the differences between actual boarding/alighting times and the public transport schedules. The proposed changes to the algorithm improve the average distance between the actual and estimated alighting stops, as this distance is reduced from 806 m using the original algorithm to 530 m after applying the suggested improvements.     

Pick‐up locations and bus allocation for transit‐based evacuation planning with demand uncertainty

This paper develops a decision‐support model for transit‐based evacuation planning under demand uncertainty. Demand uncertainty refers to the uncertainty associated with the number of transit‐dependent evacuees. A robust optimization model is proposed to determine the optimal pick‐up points for evacuees to assemble, and allocate available buses to transport the assembled evacuees between the pick‐up locations and different public shelters. The model is formulated as a mixed‐integer linear program and is solved via a cutting plane scheme. The numerical example based on the Sioux Falls network demonstrates that the robust plan yields lower total evacuation time and is reliable in serving the realized evacuee demand. Copyright © 2012 John Wiley & Sons, Ltd.     

Transit network design with allocation of green vehicles: A genetic algorithm approach

The use of fossil fuels in transportation generates harmful emissions that accounts for nearly half of the total pollutants in urban areas. Dealing with this issue, local authorities are dedicating specific efforts to seize the opportunity offered by new fuels and technological innovations in achieving a cleaner urban mobility. In fact, authorities are improving environmental performances of their public transport fleet by procuring cleaner vehicles, usually called low and zero emission vehicles (LEV and ZEV, respectively). Nevertheless there seems to be a lack of methodologies for supporting stakeholders in decisions related to the introduction of green vehicles, whose allocation should be performed since the network design process in order to optimize their available green capacity.In this paper, the problem of clean vehicle allocation in an existing public fleet is faced by introducing a method for solving the transit network design problem in a multimodal, demand elastic urban context dealing with the impacts deriving from transportation emissions.The solving procedure consists of a set of heuristics which includes a routine for route generation and a genetic algorithm for finding a sub-optimal set of routes with the associated frequencies.     

Impact analysis of cordon-based congestion pricing on mode-split for a bimodal transportation network

This paper investigates the impact of cordon-based congestion pricing scheme on the mode-split of a bimodal transportation network with auto and rail travel modes. For any given toll-charge pattern, its impact on the mode-split can be estimated by solving a combined mode-split and traffic-assignment problem. Using a binary logit model for the mode-split, the combined problem is converted into a traffic-assignment problem with elastic demand. Probit-based stochastic user equilibrium (SUE) principle is adopted for this traffic-assignment problem, and a continuously distributed value of time (VOT) is assumed to convert the toll charges and transit fares into time-units. This combined mode-split and traffic-assignment problem is then formulated as a fixed-point model, which can be solved by a convergent Cost Averaging method. The combined mode-split and traffic-assignment problem is then used to analyze a multimodal toll design problem for cordon-based congestion pricing scheme, with the aim of increasing the mode-share of public transport system to a targeted level. Taking the fixed-point model as a constraint, the multimodal toll design problem is thus formulated as a mathematical programming with equilibrium constraints (MPEC) model. A genetic algorithm (GA) is employed to solve this MPEC model, which is then numerical validated by a network example.     

A structural model of temporal change in multi-modal travel demand

A simultaneous equation model is developed to describe temporal trends and shifts in demand among five modes of passenger transportation in the Netherlands. The modes are car driver, car passenger, train, bicycle, and public transit (bus, tram, and subway). The time period is one year (1984–1985). The data are from the week-long travel diaries at six-month intervals of a national panel of households in the Netherlands. The model explains the weekly trip rates for each mode in terms of three types of relationships: links from demand for the same mode at previous points in time (temporal stability or inertia); links to and from demand for other modes at the same point in time (complementarity and competition on a synchronous basis); and links from demand for other modes at previous points in time (substitution effects). a significant model is found with 15 inertial links, 21 synchronous links, and 16 cross-lag links among the variables. It is proposed in interpretations of the link coefficients and overall effects of one variable on another that relationships among the modes are evolving over time. In particular, the model captures the effect of a public transit fare increase that occurred during the time frame of the panel data.     

A traffic flow simulator for short‐term travel time forecasting

This paper presents an off‐line forecasting system for short‐term travel time forecasting. These forecasts are based on the historical traffic count data provided by detectors installed on Annual Traffic Census (ATC) stations in Hong Kong. A traffic flow simulator (TFS) is developed for short‐term travel time forecasting (in terms of offline forecasting), in which the variation of perceived travel time error and the fluctuations of origin‐destination (O‐D) demand are considered explicitly. On the basis of prior O‐D demand and partial updated detector data, the TFS can estimate the link travel times and flows for the whole network together with their variances and covariances. The short‐term travel time forecasting by O‐D pair can also be assessed and the O‐D matrix can be updated simultaneously. The application of the proposed off‐line forecasting system is illustrated by a numerical example in Hong Kong.     

On the distribution of urban road space for multimodal congested networks

Transport systems in real cities are complex with many modes of transport sharing and competing for limited road space. This work intends to understand how space distributions for modes and interactions among modes affect network traffic performance. While the connection between performance of transport systems and general land allocation is the subject of extensive research, space allocation for interacting modes of transport is an open research question. Quantifying the impact of road space distribution on the performance of a congested multimodal transport system with a dynamic aggregated model remains a challenge. In this paper, a multimodal macroscopic fundamental diagram (MFD) is developed to represent the traffic dynamics of a multimodal transport system. Optimization is performed with the objective of minimizing the total passenger hours traveled (PHT) to serve the total demand by redistributing road space among modes. Pricing strategies are also investigated to provide a higher demand shift to more efficient modes. We find by an application to a bi-modal two-region city that (i) the proposed model captures the operational characteristics of each mode, and (ii) optimal dynamic space distribution strategies can be developed. In practice, the approach can serve as a physical dynamic model to inform space distribution strategies for policy makers with different goals of mobility.     

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.     

On seat capacity in traffic assignment to a transit network

Seating or standing make distinct on‐board states to a transit rider, yielding distinct discomfort costs, with potential influence on the passenger route choice onto the transit network. The paper provides a transit assignment model that captures the seating capacity and its occupancy along any transit route. The main assumptions pertain to: the seat capacity by service route, selfish user behaviour, a seat allocation process with priority rules among the riders, according to their prior state either on‐board or at boarding. To each transit leg from access to egress station is associated a set of ‘service modes’, among which the riders are assigned in a probabilistic way, conditionally on their priority status and the ratio between the available capacity and the flow of them. Thus the leg cost is a random variable, with mean value to be included in the trip disutility. Computationally efficient algorithms are provided for, respectively, loading the leg flows and evaluating the leg costs along a transit line. At the network level, a hyperpath formulation is provided for supply‐demand equilibrium, together with a property of existence and an method of successive averages equilibration algorithm. It is shown that multiple equilibria may arise. Copyright © 2010 John Wiley & Sons, Ltd.     

Statistical inference on transit route‐level origin–destination flows using automatic passenger counter data

We consider inferring transit route‐level origin–destination (OD) flows using large amounts of automatic passenger counter (APC) boarding and alighting data based on a statistical formulation. One critical problem is that we need to enumerate the OD flow matrices that are consistent with the APC data for each bus trip to evaluate the model likelihood function. The OD enumeration problem has not been addressed satisfactorily in the literature. Thus, we propose a novel sampler to avoid the need to enumerate OD flow matrices by generating them recursively from the first alighting stop to the last stop of the bus route of interest. A Markov chain Monte Carlo (MCMC) method that incorporates the proposed sampler is developed to simulate the posterior distributions of the OD flows. Numerical investigations on an operational bus route under a realistic OD structure demonstrate the superiority of the proposed MCMC method over an existing MCMC method and a state‐of‐the‐practice method. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal transit fare in a bimodal network under demand uncertainty and bounded rationality

This paper investigates the optimal transit fare in a simple bimodal transportation system that comprises public transport and private car. We consider two new factors: demand uncertainty and bounded rationality. With demand uncertainty, travelers are assumed to consider both the mean travel cost and travel cost variability in their mode choice decision. Under bounded rationality, travelers do not necessarily choose the travel mode of which perceived travel cost is absolutely lower than the one of the other mode. To determine the optimal transit fare, a bi‐level programming is proposed. The upper‐level objective function is to minimize the mean of total travel cost, whereas the lower‐level programming adopts the logit‐based model to describe users' mode choice behaviors. Then a heuristic algorithm based on a sensitivity analysis approach is designed to solve the bi‐level programming. Numerical examples are presented to illustrate the effect of demand uncertainty and bounded rationality on the modal share, optimal transit fare and system performance. Copyright © 2013 John Wiley & Sons, Ltd.     

Analogy of fixed route shared taxi (taxi khattee) and bus services under various demand density and economical conditions

Taxi khattee is a fixed route unregulated shared taxi. It is a very common mode of transportation in Iran. Fixed route, unscheduled operation, open, unlimited pick‐up and drop‐off locations, and share ride are common features of taxi khattees. Low passenger capacity and working in high demand corridors provides for the possibility of high service frequencies any time of the day. Taxi khattees are similar to jitneys, which are obsolete or illegal in many countries. The aim of this research is to design transit network of an area using taxi khattees in addition to buses. The methodology employed in this paper simultaneously considers the costs to the users and operators on the one hand, and those of the public non‐users on the other hand. Taxi khattees are used in the design of a multimodal network along with buses to characterize the appropriate economic domain for their use. Moreover, their operation indices are compared against those of buses. A sensitivity analysis is carried out on various performance measures. Results show taxi khattees should be used in areas where population density is low, work force is inexpensive, social costs are not considered in fare calculation, and users' value of time is high. The study contradicts the common belief that since taxi khattees provide a high frequency compared to buses, they are economically plausible to use in a transit fleet. Copyright © 2011 John Wiley & Sons, Ltd.