Intermodal Transit System Coordination

In urban areas where transit demand is widely spread, passengers may be served by an intermodal transit system, consisting of a rail transit line (or a bus rapid transit route) and a number of feeder routes connecting at different transfer stations. In such a system, passengers may need one or more transfers to complete their journey. Therefore, scheduling vehicles operating in the system with special attention to reduce transfer time can contribute significantly to service quality improvements. Schedule synchronization may significantly reduce transfer delays at transfer stations where various routes interconnect. Since vehicle arrivals are stochastic, slack time allowances in vehicle schedules may be desirable to reduce the probability of missed connections. An objective total cost function, including supplier and user costs, is formulated for optimizing the coordination of a general intermodal transit network. A four-stage procedure is developed for determining the optimal coordination status among routes at every transfer station. Considering stochastic feeder vehicle arrivals at transfer stations, the slack times of coordinated routes are optimized, by balancing the savings from transfer delays and additional cost from slack delays and operating costs. The model thus developed is used to optimize the coordination of an intermodal transit network, while the impact of a range of factors on coordination (e.g., demand, standard deviation of vehicle arrival times, etc) is examined.     

Multiple period optimization of bus transit systems

Analytic models are developed for optimizing bus services with time dependence and elasticity in their demand characteristics. Some supply parameters, i.e. vehicle operating costs and speeds are also allowed to vary over time. The multiple period models presented here allow some of the optimized system characteristics (e.g. route structure) to be fized at values representing the best compromise over different time periods, while other characteristics (e.g. service headways) may be optimized within each period. In a numerical example the demand is assumed to fluctuate over a daily cycle (e.g. peak, offpeak and night), although the same models can also be used for other cyclical or noncyclical demand variations over any number of periods. Models are formulated and compared for four types of conditions, which include steady fixed demand, cyclical fixed demand, steady equilibrium demand and cyclical equilibrium demand. When fixed demand is assumed, the optimization objective is minimum total system cost, including operator cost and user cost, while operator profit and social welfare are the objective functions maximized for equilibrium demand. The major results consist of closed form solutions for the route spacings, headways, fares and costs for optimized feeder bus services under various demand conditions. A comparison of the optimization results for the four cases is also presented. When demand and bus operating characteristics are allowed to vary over time, the optimal functions are quite similar to those for steady demand and supply conditions. The optimality of a constant ratio between the headway and route spacing, which is found at all demand densities if demand is steady, is also maintained with a multi-period adjustment factor in cyclical demand cases, either exactly or with a relatively negligible approximation. These models may be used to analyze and optimize fairly complex feeder or radial bus systems whose demand and supply characteristics may vary arbitrarily over time.     

Optimal slack time for timed transfers at a transit terminal

At transit terminals where two routes interchange passengers, total system costs may be reduced by allowing some “slack” time in the vehicle schedules to decrease the probability of missed connections. Transfer cost functions are formulated and used to determine optimal slack time for simple systems with transfers between one bus route and one rail line. Some analytic results are derived for empirical discrete and Gumbel distributions of bus arrival times. Relations between the optimal slack times and headways, transfer volumes, passenger time values, bus operating costs, and standard deviations of bus and train arrivals are also developed numerically using normally distributed arrivals. However, the proposed numerical approach can optimize slack times for any observed arrival distributions. The results provide some guidelines on desirable slack times and show that schedule coordination between the two routes is not worth attempting when standard deviations of arrivals exceed certain levels. Possible extensions of this work are suggested in the last section.     

Agent based model for dynamic ridesharing

Dynamic ridesharing involves a service provider that matches potential drivers and passengers with similar itineraries allowing them to travel together and share the costs. Centralized (binary integer programming) and decentralized (dynamic auction-based multi-agent) optimization algorithms are formulated to match passengers and drivers. Numerical experiments on the decentralized approach provides near optimal solutions for single-driver, single-passenger cases with lower computational burden. The decentralized approach is then extended to accommodate both multi-passenger and multi-driver matches. The results indicate higher user cost savings and vehicle kilometers traveled (VKT) savings when allowing multi-passenger rides. Sensitivity analysis is conducted to test the impact of the service provider commission rate on revenue and system reliability. While short term revenue can be maximized at a commission rate of roughly 50% of each trip’s cost, the resulting drop in system reliability would be expected to reduce patronage and revenues in the longer term.     

Unreliable trains and induced rescheduling: implications for cost-benefit analysis

This paper is concerned with the assessment of generalized user cost reductions in the cost-benefit analysis (CBA) of transport policies that aim at reducing unreliability. In particular, we investigate the implications of railway passengers’ anticipating departure behavior when train services were unreliable. A simple model is established to describe and predict such anticipating behavior. Our numerical example shows how travelers’ anticipating departures and scheduling costs depend on the level of unreliability. The possible bias incurred by ignoring the reliability and schedule delay costs reductions in the traditional CBA can be quite substantial. Given our assumptions and parameterization, the underestimation of ignoring these costs could range from 33 to 75% of total generalized user cost reductions.     

Transport system management in San Francisco: an assessment

The paper reports the results of a transportation corridor study. The emphasis in the study is in transportation system management (TSM) policies although some capital intensive alternatives are also considered.

The results suggest that currently popular TSM policies in U.S.A., even when augmented with capital intensive changes, have only marginal impacts on modal choices. These currently popular policies, high occupancy vehicle priority lanes, improved bus and express bus service, increased feeder bus service and so forth, appear to confer benefits to well to do suburbanites but do not improve the transportation of urban dwellers.

Another interesting result is that if user costs were increased to cover the full costs of transportation the transit fares for low income people would increase ten percent and the increase for urban dwellers would be about 20 percent. Interestingly, there would be no change in bus fares for either group. However, for high income travellers and suburbanites the increase in transit fares would be in excess of 100 percent. Thus, the current fare structure is inequitable making the low income people and the urban dwellers to pay a much larger share of their transportation cost than the often well to do suburbanites.     

Integrated modeling of high performance passenger and freight train planning on shared-use corridors in the US

This paper studies strategic level train planning for high performance passenger and freight train operations on shared-use corridors in the US. We develop a hypergraph-based, two-level approach to sequentially minimize passenger and freight costs while scheduling train services. Passenger schedule delay and freight lost demand are explicitly modeled. We explore different solution strategies and conclude that a problem-tailored linearized reformulation yields superior computational performance. Using realistic parameter values, our numerical experiments show that passenger cost due to schedule delay is comparable to in-vehicle travel time cost and rail fare. In most cases, marginal freight cost increase from scheduling more passenger trains is higher than marginal reduction in passenger schedule delay cost. The heterogeneity of train speed reduces the number of freight trains that can run on a corridor. Greater tolerance for delays could reduce lost demand and overall cost on the freight side. The approach developed in the paper could be applied to other scenarios with different parameter values.     

A multi-period dial-a-ride problem with driver consistency

Dial-a-ride services provide disabled and elderly people with a personalized mode of transportation to preserve their mobility. Typically, several users with different pickup and dropoff locations are transported on a vehicle simultaneously. The focus in dial-a-ride problems (DARPs) is mainly on minimizing routing cost. Service quality has been taken into account in the models by imposing time windows and limiting the maximum ride time of each user. We extend the classical DARP by an additional feature of service quality referred to as driver consistency. Customers of dial-a-ride services are often sensitive to changes in their daily routine. This aspect includes the person who is providing the transportation service, i.e., the driver of the vehicle. Our problem, called the driver consistent dial-a-ride problem (DC-DARP), considers driver consistency by bounding the maximum number of different drivers that transport a user over a multi-period planning horizon.We propose different formulations of the problem and examine their efficiency when applied in a Branch-and-Cut fashion. Additionally, we develop a large neighborhood search algorithm that generates near-optimal solutions in a short amount of time.Over 1000 instances are generated with close reference to real world scenarios. Extensive computational experiments are conducted in order to assess the quality of the solution approaches and to provide insights into the new problem. Results reveal that the cost of offering driver consistency varies greatly in magnitude. Depending on the instance, the cost of assigning one driver to each user can be up to 27.98% higher compared to a low-cost solution. However, routing cost increases by not more than 5.80% if users are transported by at least two drivers.     

Traveler delay costs and value of time with trip chains, flexible activity scheduling and information

The delay costs of traffic disruptions and congestion and the value of travel time reliability are typically evaluated using single trip scheduling models, which treat the trip in isolation of previous and subsequent trips and activities. In practice, however, when activity scheduling to some extent is flexible, the impact of delay on one trip will depend on the actual and predicted travel time on itself as well as other trips, which is important to consider for long-lasting disturbances and when assessing the value of travel information. In this paper we extend the single trip approach into a two trips chain and activity scheduling model. Preferences are represented as marginal activity utility functions that take scheduling flexibility into account. We analytically derive trip timing optimality conditions, the value of travel time and schedule adjustments in response to travel time increases. We show how the single trip models are special cases of the present model and can be generalized to a setting with trip chains and flexible scheduling. We investigate numerically how the delay cost depends on the delay duration and its distribution on different trips during the day, the accuracy of delay prediction and travel information, and the scheduling flexibility of work hours. The extension of the model framework to more complex schedules is discussed.     

A dispatching decision support system for countering delay propagation in intermodal logistics networks

This paper specifies a dispatching decision support system devoted to managing intermodal logistics operations while countering delay and delay propagation. When service disruptions occur within a logistics network where schedule coordination is employed, a dispatching control model determines through an optimization process whether each ready outbound vehicle should be dispatched immediately or held to wait for some late incoming vehicles. Decisions should consider potential missed-connection costs that may occur not only at the next transfer terminals but also at hubs located further downstream. Numerical examples and a sensitivity analysis with different slack time settings for attenuating delay propagation are presented.     

On the cost of misperceived travel time variability

Because individuals may misperceive travel time distributions, using the implied reduced form of the scheduling model might fall short of capturing all costs of travel time variability. We reformulate a general scheduling model employing rank-dependent utility theory and derive two special cases as econometric specifications to study these uncaptured costs. It is found that reduced-form expected cost functions still have a mean–variance form when misperception is considered, but the value of travel time variability is higher. We estimate these two models with stated-preference data and calculate the empirical cost of misperception. We find that: (i) travelers are mostly pessimistic and thus tend to choose departure times too early to achieve a minimum cost, (ii) scheduling preferences elicited using a stated-choice method can be relatively biased if probability weighting is not considered, and (iii) the extra cost of misperceiving the travel time distribution might be nontrivial when time is valued differently over the time of day and is substantial for some people.     

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.     

The evening commute with cars and transit: Duality results and user equilibrium for the combined morning and evening peaks

This paper extends Vickrey’s (1969) commute problem for commuters wishing to pass a bottleneck for both cars and transit that share finite road capacity. In addition to this more general framework considering two modes, the paper focuses on the evening rush, when commuters travel from work to home. Commuters choose which mode to use and when to travel in order to minimize the generalized cost of their own trips, including queueing delay and penalties for deviation from a preferred schedule of arrival and departure to and from work. The user equilibrium for the isolated morning and evening commutes are shown to be asymmetric because the schedule penalty in the morning is the difference between the departure and wished curves, and the schedule penalty in the evening is the difference between the arrival and wished curves. It is shown that the system optimum in the morning and evening peaks are symmetric because queueing delay is eliminated and the optimal arrival curves are the same as the departure curves.The paper then considers both the morning and evening peaks together for a single mode bottleneck (all cars) with identical travelers that share the same wished times. For a schedule penalty function of the morning departure and evening arrival times that is positive definite and has certain properties, a user equilibrium is shown to exist in which commuters travel in the same order in both peaks. The result is used to illustrate the user equilibrium for two cases: (i) commuters have decoupled schedule preferences in the morning and evening and (ii) commuters must work a fixed shift length but have flexibility when to start. Finally, a special case is considered with cars and transit: commuters have the same wished order in the morning and evening peaks. Commuters must use the same mode in both directions, and the complete user equilibrium solution reveals the number of commuters using cars and transit and the period in the middle of each rush when transit is used.     

Marginal costs of freeway traffic congestion with on-road pollution exposure externality

The health cost of on-road air pollution exposure is a component of traffic marginal costs that has not previously been assessed. The main objective of this paper is to introduce on-road pollution exposure as an externality of traffic, particularly important during traffic congestion when on-road pollution exposure is highest. Marginal private and external cost equations are developed that include on-road pollution exposure in addition to time, fuel, and pollution emissions components. The marginal external cost of on-road exposure includes terms for the marginal vehicle’s emissions, the increased emissions from all vehicles caused by additional congestion from the marginal vehicle, and the additional exposure duration for all travelers caused by additional congestion from the marginal vehicle. A sensitivity analysis shows that on-road pollution exposure can be a large portion (18%) of marginal social costs of traffic flow near freeway capacity, ranging from 4% to 38% with different exposure parameters. In an optimal pricing scenario, excluding the on-road exposure externality can lead to 6% residual welfare loss because of sub-optimal tolls. While regional pollution generates greater costs in uncongested conditions, on-road exposure comes to dominate health costs on congested freeways because of increased duration and intensity of exposure. The estimated marginal cost and benefit curves indicate a theoretical preference for price controls to address the externality problem. The inclusion of on-road exposure costs reduces the magnitudes of projects required to cover implementation costs for intelligent transportation system (ITS) improvements; the net benefits of road-pricing ITS systems are increased more than the net benefits of ITS traffic flow improvements. When considering distinct vehicle classes, inclusion of on-road exposure costs greatly increases heavy-duty vehicle marginal costs because of their higher emissions rates and greater roadway capacity utilization. Lastly, there are large uncertainties associated with the parameters utilized in the estimation of health outcomes that are a function of travel pollution intensity and duration. More research is needed to develop on-road exposure modeling tools that link repeated short-duration exposure and health outcomes.     

Life cycle emissions and cost model for urban light duty vehicles

The growth of vehicle sales and use internationally requires the consumption of significant quantities of energy and materials, and contributes to the deterioration of air-quality and climate conditions. Advanced propulsion systems and electric drive vehicles have substantially different characteristics and impacts. They require life cycle assessments and detailed comparisons with gasoline powered vehicles which, in turn, should lead to critical updates of traditional models and assumptions. For a comprehensive comparison of advanced and traditional light duty vehicles, a model is developed that integrates external costs, including emissions and time losses, with societal and consumer life cycle costs. Life cycle emissions and time losses are converted into costs for seven urban light duty vehicles. The results, which are based on vehicle technology characteristics and transportation impacts on environment, facilitate vehicle comparisons and support policy making in transportation. Substantially, more sustainable urban transportation can be achieved in the short-term by promoting policies that increase vehicle occupancy; in the intermediate-term by increasing the share of hybrid vehicles in the car market and in the long-term by the widespread use of electric vehicles. A sensitivity-analysis of life cost results revealed that vehicle costs change significantly for different geographical areas depending on vehicle taxation, pricing of gasoline, electric power and pollution. Current practices in carbon and air quality pricing favor oil and coal based technologies. However, increasing the cost of electricity from coal and other fossil fuels would increase the variable cost for electric vehicles, and tend to favor the variable cost of hybrid vehicles.     

Investigating the impact of stochastic vehicle arrivals to optimal stop spacing and headway for a feeder bus route

Stop spacing and service frequency (i.e., the inverse of headway) are key elements in transit service planning. The trade‐offs between increasing accessibility and reducing travel time, which affect transit system performance, need to be carefully evaluated. The objective of this study is to optimize stop spacing and headway for a feeder bus route, considering the relationship between the variance of inter‐arrival time (VIAT), which yields the minimum total cost (including user and operator costs). A solution algorithm, called successive substitution, is adapted to efficiently search for the optimal solutions. In a numerical example, the developed model is applied to planning a feeder bus route in Newark, New Jersey. The results indicate that the optimal stop spacing should be longer that those suggested by previous studies where the impact of VIAT was ignored. Reducing VIAT via certain operational control strategies (i.e., holding/stop‐skipping, transit signal priority) may shorten stop spacing and improve accessibility. Copyright © 2014 John Wiley & Sons, Ltd.     

Distance and time in intermodal goods transport networks in Europe: A generic approach

This paper is about distance and time as factors of competitiveness of intermodal transport. It reviews the relevance of the factors, evaluates time models in practice, compares network distances and times in alternative bundling networks with geometrically varied layouts, and points out how these networks perform in terms of vehicle scale, frequency and door-to-door time. The analysis focuses on intermodal transport in Europe, especially intermodal rail transport, but is in search for generic conclusions. The paper does not incorporate the distance and time results in cost models, and draws conclusions for transport innovation, wherever this is possible without cost modelling. For instance, the feature vehicle scale, an important factor of transport costs, is analysed and discussed.Distance and time are important factors of competitiveness of intermodal transport. They generate (direct) vehicle costs and – via transport quality – indirect costs to the customers. Clearly direct costs/prices are the most important performance of the intermodal transport system. The relevance of quality performances is less clarified. Customers emphasise the importance of a good match between the transport and the logistic system. In this framework (time) reliability is valued high. Often transport time, arrival and departure times, and frequency have a lower priority. But such conclusions can hardy be generalised. The range of valuations reflects the heterogeneity of situations. Some lack of clarity is obviously due to overlapping definitions of different performance types.The following parts of the paper are about two central fields of network design, which have a large impact on transport costs and quality, namely the design of vehicle roundtrips (and acceleration of transport speed) and the choice of bundling type: do vehicles provide direct services or run in what we call complex bundling networks? An example is the hub-and-spoke network. The objective of complex bundling is to increase vehicle scale and/or transport frequency even if network volumes are restricted. Complex bundling requires intermediate nodes for the exchange of load units. Examples of complex bundling networks are the hub-and-spoke network or the line network.Roundtrip and bundling design are interrelated policy fields: an acceleration of the roundtrip speed, often desirable from the cost point of view, can often only be carried out customer friendly, if the transport frequency is increased. But often the flow size is not sufficient for a higher frequency. Then a change of bundling model can be an outcome.Complex bundling networks are known to have longer average distances and times, the latter also due to the presence of additional intermediate exchange nodes. However, this disadvantage is – inside the limits of maximal vehicle sizes – overruled by the advantage of a restricted number of network links. Therefore generally, complex bundling networks have shorter total vehicle distances and times. This expression of economies of scale implies lower vehicle costs per load unit.The last part of the paper presents door-to-door times of load units of complex bundling networks and compares them with unimodal road transport. The times of complex bundling networks are larger than that of networks with direct connections, but nevertheless competitive with unimodal road transport, except for short distances.     

A new shared vehicle system for urban areas

The paper concerns the conceptual design of a transport system for pedestrian areas. The proposed transport system is based on a fleet of eco-sustainable Personal Intelligent City Accessible Vehicles (PICAVs). The vehicles are shared through the day by different users and the following specific services will be provided: instant access, open ended reservation and one way trips. Referring to the proposed transport system, a new methodology to optimise the fleet dimension and its distribution among the stations is proposed in this paper. The problem faced is an optimisation problem where the cost function to be minimised takes into account both the transport system cost and the user costs that depend on the waiting times. A random search algorithm has been adopted. Given a fleet dimension and its distribution among the stations, the waiting times of the users are assessed by a microscopic simulation. The simulation model tracks the second-by-second activity of each PICAV user, as well as the second-by-second activity of each vehicle. The overall methodology has been implemented in an object-oriented simulator. The proposed transport system has been planned and simulated for the historical city centre of Genoa, Italy.     

Demand responsive transit systems with time-dependent demand: User equilibrium,system optimum,and management strategy

The operating cost of a demand responsive transit (DRT) system strictly depends on the quality of service that it offers to its users. An operating agency seeks to minimize operating costs while maintaining the quality of service while users experience costs associated with scheduling, waiting, and traveling within the system. In this paper, an analytical model is employed to approximate the agency's operating cost for running a DRT system with dynamic demand and the total generalized cost that users experience as a result of the operating decisions. The approach makes use of Vickrey's (1969) congestion theory to model the dynamics of the DRT system in the equilibrium condition and approximate the generalized cost for users when the operating capacity is inadequate to serve the time-dependent demand over the peak period without excess delay. The efficiency of the DRT system can be improved by optimizing one of three parameters that define the agency's operating decision: (1) the operating capacity of the system, (2) the number of passengers that have requested a pick-up and are awaiting service, and (3) the distribution of requested times for service from the DRT system. A schedule management strategy and dynamic pricing strategies are presented that can be implemented to manage demand and reduce the total cost of the DRT system by keeping the number of waiting requests optimized over the peak period. In the end, proposed optimization strategies are compared using a numerical example.     

A discrete dynamical system of formulating traffic assignment: Revisiting Smith’s model

Through relaxing the behavior assumption adopted in Smith’s model (Smith, 1984), we propose a discrete dynamical system to formulate the day-to-day evolution process of traffic flows from a non-equilibrium state to an equilibrium state. Depending on certain preconditions, the equilibrium state can be equivalent to a Wardrop user equilibrium (UE), Logit-based stochastic user equilibrium (SUE), or boundedly rational user equilibrium (BRUE). These equivalence properties indicate that, to make day-to-day flows evolve to equilibrium flows, it is not necessary for travelers to choose their routes based on actual travel costs of the previous day. Day-to-day flows can still evolve to equilibrium flows provided that travelers choose their routes based on estimated travel costs which satisfy these preconditions. We also show that, under a more general assumption than the monotonicity of route cost function, the trajectory of the dynamical system converges to a set of equilibrium flows by reasonably setting these parameters in the dynamical system. Finally, numerical examples are presented to demonstrate the application and properties of the dynamical system. The study is helpful for understanding various processes of forming traffic jam and designing an algorithm for calculating equilibrium flows.