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.     

An algorithm for finding reasonable paths in transit networks

In this paper, reasonable paths in transit networks are defined as possible paths that satisfy the acceptable time criterion and transfer‐walk criterion. A recursive algorithm for finding all of the reasonable paths in a transit network that does not involve a rapid increase in program run‐time with network size is presented. Realistic transit networks in Hong Kong and Guangzhou were selected as case studies of the different phases of the development of a trip planning system. Transport planning practitioners and potential users were invited to test the system to evaluate its performance. The results of the prototype evaluation were satisfactory, and the viability of the system as a useful tool for supporting decision‐making has been confirmed by the positive feedback that was obtained from survey questionnaires.     

Long-term planning for ring-radial urban rail transit networks

Extensive work exists on regular rail network planning. However, few studies exist on the planning and design of ring-radial rail transit systems. With more ring transit lines being planned and built in Asia, Europe and the America's, a detailed study on ring transit lines is timely. An analytical model to find the optimal number of radial lines in a city for any demand distribution is first introduced. Secondly, passenger route choice for different rail networks is analyzed, for a many-to-many Origin-Destination (OD) demand distribution, based on a total travel time cost per passenger basis. The routes considered are: (1) radial lines only; (2) ring line only or radial lines and ring line combined; or (3) direct access to a destination without using the rail system. Mathematica and Matlab are used to code the route choice model. A cost-benefit optimization model to identify the feasibility and optimality of a ring line is proposed. Unlike simulations and agent-based models, this model is shown to be easily transferable to many ring-radial transit networks. The City of Calgary is used as an example to illustrate the applicability of each model. The existing urban rail network and trip distribution are major influencing factors in judging the feasibility and optimal location of the ring line. This study shows the potential net benefit of introducing a ring line by assessing changes in passengers’ costs. The changes in passenger cost parameters, such as ride cost and access cost, are shown to greatly influence the feasibility of a ring line.     

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.     

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.     

Estimation of origin‐destination matrices for a multimodal public transit network

This paper presents a procedure for the estimation of origin‐destination (O‐D) matrices for a multimodal public transit network. The system consists of a number of favored public transit modes that are obtained from a modal split process in a traditional four‐step transportation model. The demand of each favored mode is assigned to the multimodal network, which is comprised of a set of connected links of different public transit modes. An entropy maximization procedure is proposed to simultaneously estimate the O‐D demand matrices of all favored modes, which are consistent with target data sets such as the boarding counts and line segment flows that are observed directly in the network. A case study of the Hong Kong multimodal transit network is used to demonstrate the effectiveness of the proposed methodology.     

A reliability‐based traffic assignment model for multi‐modal transport network under demand uncertainty

In densely populated and congested urban areas, the travel times in congested multi‐modal transport networks are generally varied and stochastic in practice. These stochastic travel times may be raised from day‐to‐day demand fluctuations and would affect travelers' route and mode choice behaviors according to their different expectations of on‐time arrival. In view of these, this paper presents a reliability‐based user equilibrium traffic assignment model for congested multi‐modal transport networks under demand uncertainty. The stochastic bus frequency due to the unstable travel time of bus route is explicitly considered. By the proposed model, travelers' route and mode choice behaviors are intensively explored. In addition, a stochastic state‐augmented multi‐modal transport network is adopted in this paper to effectively model probable transfers and non‐linear fare structures. A numerical example is given to illustrate the merits of the proposed model. Copyright © 2012 John Wiley & Sons, Ltd.     

Evaluating the feasibility of a passive travel survey collection in a complex urban environment: Lessons learned from the New York City case study

The combination of increasing challenges in administering household travel surveys and advances in global positioning systems (GPS)/geographic information systems (GIS) technologies motivated this project. It tests the feasibility of using a passive travel data collection methodology in a complex urban environment, by developing GIS algorithms to automatically detect travel modes and trip purposes. The study was conducted in New York City where the multi-dimensional challenges include urban canyon effects, an extreme dense and diverse set of land use patterns, and a complex transit network. Our study uses a multi-modal transportation network, a set of rules to achieve both complexity and flexibility for travel mode detection, and develops procedures and models for trip end clustering and trip purpose prediction. The study results are promising, reporting success rates ranging from 60% to 95%, suggesting that in the future, conventional self-reported travel surveys may be supplemented, or even replaced, by passive data collection methods.     

Planning hierarchical urban transit systems for reductions in greenhouse gas emissions

Public transit systems with high occupancy can reduce greenhouse gas (GHG) emissions relative to low-occupancy transportation modes, but current transit systems have not been designed to reduce environmental impacts. This motivates the study of the benefits of design and operational approaches for reducing the environmental impacts of transit systems. For example, transit agencies may replace level-of-service (LOS) by vehicle miles traveled (VMT) as a criterion in evaluating design and operational changes. In previous work, we explored the unintended consequences of lowering transit LOS on emissions in a single-technology transit system. Herein, we extend the analysis to account for a more realistic case: a transit system with a hierarchical structure (trunk and feeder lines) providing service to a city where demand is elastic. By considering the interactions between the trunk and the feeder systems, we provide a quantitative basis for designing and operating integrated urban transit systems that can reduce GHG emissions and societal costs. We find that highly elastic transit demand may cancel emission reduction potentials resulting from lowering LOS, due to demand shifts to lower occupancy vehicles. However, for mass transit modes, these potentials are still significant. Transit networks with buses, bus rapid transit or light rail as trunk modes should be designed and operated near the cost-optimal point when the demand is highly elastic, while this is not required for metro. We find that the potential for unintended consequences increases with the size of the city. Our results are robust to uncertainties in the costs and emissions parameters.     

Analytic hierarchy process application in selecting the mode of transport for a logistics company

As a multi‐criteria decision‐making (MCDM) method, the analytic hierarchy process (AHP) has been used considerably to solve hierarchical or network‐based decision problems in socio‐economic fields. Following an in‐depth explanation of the transport function in logistics and an overview of the MCDM methods, the AHP model is employed in the paper for a logistics company in selecting the most suitable way of transportation between two given locations in Turkey. The criteria used in the selection of transportation modes are identified as the cost, speed, safety, accessibility, reliability, environmental friendliness, and flexibility. Several cost parameters (transportation, storage, handling, bosphorus crossover) are incorporated into the decision‐making process. The application is carried out in instructional character. The results of the study indicate that the railway transportation, which is not widely used in Turkey, is also an alternative and suitable means of transportation. Copyright © 2013 John Wiley & Sons, Ltd.     

On the allocation of city space to multiple transport modes

Abstract

This paper analyzes urban multimodal transportation systems in an aggregated way. To describe the aggregate behavior of traffic in cities, use is made of an idea that is now receiving some attention: the macroscopic fundamental diagram (MFD). We demonstrate through simulation how the MFD can be used to monitor and control a real network, in this case a portion of San Francisco, using readily available input data. We then show how different modes interact on the same network and discuss how these interactions might be incorporated into an MFD for multimodal networks. The work unveils two main results: first, it confirms recent results showing that restricting access to a city's congested areas can improve mobility for all travelers, including those who endure the restrictions; and second, that dedicating street space to collective transport modes can improve accessibility for all modes, even those from which space is taken away.     

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.     

A schedule-based time-dependent trip assignment model for transit networks

A schedule-based time-dependent trip assignment model for transit networks is presented. First the transit network model is formulated using the schedule-based approach, in which the vehicles are assumed to arrive punctually in accordance with a scheduled time-table. Based on a previously developed time-dependent shortest path algorithm, an all-or-nothing network loading procedure is employed to assign the passenger trips onto the network. Both the passenger demand and scheduled time-table are time-varying. This provides a versatile tool for the evaluation of the performance of transit networks subject to peak period loading. A case study using the Mass Transit Railway System in Hong Kong is given to illustrate the potential applications of the model.     

Optimization of grid bus transit systems with elastic demand

Current analytic models for optimizing urban bus transit systems tend to sacrifice geographic realism and detail in order to obtain their solutions. The models presented here shows how an optimization approach can be successful without oversimplifying spatial characteristics and demand patterns of urban areas and how a grid bus transit system in a heterogeneous urban environment with elastic demand is optimized. The demand distribution over the service region is discrete, which can realistically represent geographic variation. Optimal network characteristics (route and station spacings), operating headways and fare are found, which maximize the total operator profit and social welfare. Irregular service regions, many‐to‐many demand patterns, and vehicle capacity constraints are considered in a sequential optimization process. The numerical results show that at the optima the operator profit and social welfare functions are rather flat with respect to route spacing and headway, thus facilitating the tailoring of design variables to the actual street network and particular operating schedule without a substantial decrease in profit. The sensitivities of the design variables to some important exogenous factors are also presented.     

Impact of ITS measures on public transport: A Case study

Intelligent Transport Systems (ITS) have a wide range of applications. They range from the more traditional signal coordination system to concepts such as smart cars and smart roads. This paper describes transit‐based ITS measures in Singapore. The island‐state has plans to double the current 90 km rail network over the next ten years and has also implemented or committed to implement many ITS initiatives that impact upon the public transport systems. The aim of these investments is to achieve a high transit modal share using a comprehensive transit network. ITS measures that can promote this aim include: automatic vehicle location systems for buses and taxis, integrated transit fare systems using contactless smart cards, rail information systems, multi‐modal travel guides on Internet and electronic road pricing. The potential impacts of these measures are delay reduction, more comfort, productivity gain and better network accessibility. ITS measures do not necessarily add physical capacity to a public transport system but are excellent supporting measures to encourage the modal shift to transit, particularly if a quality transit system is already in place.     

Activity-based market equilibrium for capacitated multimodal transport systems

Empirical studies have shown that demand for multimodal transport systems is highly correlated with activity schedules of individuals. Nonetheless, existing analytical equilibrium models of multimodal systems have only considered trip-based demand. We propose a new market equilibrium model that is sensitive to traveler activity schedules and system capacities. The model is based on a constrained mixed logit model of activity schedule choice, where each schedule in the choice set is generated with a multimodal extension of the household activity pattern problem. The extension explicitly accounts for both passenger choices of activity participation and multimodal choices like public transit, walking, and vehicle parking. The market equilibrium is achieved with Lagrangian relaxation to determine the optimal dual price of the capacity constraint, and a method of successive averages with column generation finds an efficient choice set of activity schedules to assign flows over the dynamic network load capacities. An example illustrates the model and algorithm, effects similar to Vickrey’s morning commute model can be observed as a special case. A case study of the Oakville Go Transit station access “last mile” problem in the Greater Toronto Area is conducted with 166 survey samples reflecting 3680 individuals. Results suggest that a $10 fixed parking fee at Oakville station would lead to a reduction of access auto share from 54.8% to 49.5%, an increase in access transit share from 20.7% to 25.9%, and a disutility increase of 11% for the of single-activity residents of Oakville.     

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.     

Transit system network design

This article formulates a transit network design model for determining frequencies of each transit line in a network. This transit network design model requires a mode-split assignment model with distinct transit lines, each with its own specified frequency, to capture the mode split effects of increases or decreases in individual transit line frequencies. It is shown how to refine conventional mode-split assignment models to include this feature. The resulting model includes more precise measures of transit access and transfer delays, so that it more accurately predicts mode choices and link flows. This variation of the mode-split assignment model uses Dial's transit loader to solve Frank-Wolfe subproblems, using frequencies of individual transit lines to find fastest transit paths, considering access time, ride time, and any transfer delays. Computational shortcuts using the standard Hooke-Jeeves algorithm are demonstrated.     

Transit-network design methodology for actual-size road networks

The main purpose of this study is to design a transit network of routes for handling actual-size road networks. This transit-network design problem is known to be complex and cumbersome. Thus, a heuristic methodology is proposed, taking into account the major concerns of transit authorities such as budget constraints, level-of-service standards and the attractiveness of the transit routes. In addition, this approach considers other important aspects of the problem including categorization of stops, multiclass of transit vehicles, hierarchy planning, system capacity (which has been largely ignored in past studies) and the integration between route-design and frequency-setting analyses. The process developed starts with the construction of a set of potential stops using a clustering concept. Then, by the use of Newton gravity theory and a special shortest-path procedure, a set of candidate routes is formed, categorized by hierarchy (mass, feeder, local routes). In the last step of the process a metaheuristic search engine is launched over the candidate routes, incorporating budgetary constraints, until a good solution is found. The algorithm was tested on the actual-size transit network of the city of Winnipeg; the results show that under the same conditions (budget and constraints) the proposed set of routes resulted in a reduction of 14% of total travel time compared to the existing transit network. In addition the methodology developed is compared favorably with other studies using the transit network of Mandl benchmark. The generality of the methodology was tested on the recent real dataset (pertaining to the year 2010) of the larger city of Chicago, in which a more efficient and optimized scheme was proposed for the existing rail system.