Assessing the financial and social costs of public transport in differing operating environments and with endogenous demand

This paper uses a previously developed spreadsheet cost model which simulates public transport modes operated on a 12-km route to analyse the total costs of different passenger demand levels. The previous cost model was a very powerful tool to estimate the social and operator costs for different public transport technologies. However, as the model is strategic, some basic assumptions were made which are relaxed in this paper. First, the speed-flow equation in the original spreadsheet model assumes that speed decreases according to the ratio of the current frequency and the lane capacity which is based on the safety headway without taking into account passenger boardings. However, this may vary in different operating environments. Therefore, the speed-flow equation is improved by moving from a linear equation to a piecewise equation that considers the features of different operating environments. Second, the model assumes that supply is sufficient to meet demand. However, when the level of demand is high for the lower-capacity public transport technologies, passengers may find the incoming vehicle full and therefore, they have to wait more than one service interval. This paper applies queuing theory to investigate the probability of having to wait longer than the expected service headways which will affect the average passenger waiting time. The extra waiting time for each passenger is calculated and applied in the spreadsheet cost model. Third, the original model assumed that demand was externally fixed (exogenous). To evaluate the differences after applying these equations, endogenous demand rather than exogenous demand will be investigated by using the elasticities for passenger waiting time and journey time.     

An analytic investigation of optimal bus size

The use of smaller buses offers passengers a better service frequency for a given service capacity, but costs more to operate per seat provided. Within this trade-off there is an optimal bus size which maximises social benefit. A mathematical model is described which can be solved analytically to provide an explicit relationship between optimal bus size and factors such as operating cost, level of demand, and demand elasticities. The model includes: passenger demand varying with the generalised cost of travel according to a constant elasticity; the effect of changes in bus occupancy on average waiting times and on operating speed; the financial constraint that farebox revenue must equal operating cost less subsidy; an allowance for external benefits associated with generated demand, and for the effect of the flow of buses on traffic congestion; and an operating cost increasing linearly with bus size. The optimal size varies with the square root of demand, and with the unit cost to the power of 0.1 to 0.2. It also increases slowly with the proportion of cost covered by subsidy. For typical urban operating conditions in the United Kingdom the optimal size for a monopoly service lies between 55 and 65 seats assuming the observed relationship between cost and size; it is possible that changes in working practices could make smaller buses relatively cheaper to operate, so reducing the optimal size, but it seems unlikely to fall below 40 seats.     

System optimum and pricing for the day-long commute with distributed demand,autos and transit

The day-long system optimum (SO) commute for an urban area served by auto and transit is modeled as an auto bottleneck with a capacitated transit bypass. A public agency manages the system’s capacities optimally. Commuters are identical except for the times at which they wish to complete their morning trips and start their evening trips, which are given by an arbitrary joint distribution. They value unpunctuality – their lateness or earliness relative to their wish times – with a common penalty function. They must use the same mode for both trips. Commuters are assigned personalized mode and travel start times that collectively minimize society’s generalized cost for the whole day. This includes unpunctuality penalties, queuing delays, travel times and out-of-pocket costs for users, as well as travel supply costs and externalities for society.It is shown that in a SO solution there can be no queuing and that the set of SO solutions forms a convex set. Furthermore, if the schedule penalty that users suffer due to unpunctuality is separable into morning and evening components, then the set of commuters traveling by the same mode arrive at work and depart from work in the order of their wishes. These orders are in general different in the morning and the evening. It is also shown that there always is a SO solution in which users are at all times, and on both modes, either punctual or flowing at capacity. These problem properties are used to identify search methods, both, for SO solutions and for time-dependent tolls and transit fares that preserve the solutions as Nash equilibriums. In every case studied, these prices exist. They must peak concurrently for the two modes in both periods.In special cases involving only one mode, only one period or concentrated demand the solution to the complete problem decomposes by period conditional on the number of transit users, and this facilitates the solution. In these cases the day-long SO cost is the sum of the SO costs for the two peaks considered separately. However, this is not true in general – the solution obtained by combining the two single-period solutions can be infeasible. When this happens, the optimum day-long cost will exceed the sum of the single-period costs. The discrepancy is about 40% of the total schedule penalty for an example representing a large city. Thus, to develop realistic policies the day-long problem must be addressed head on. An approximate method that yields closed form formulas for the case with uniformly distributed wishes is presented.     

Determining optimal frequency and vehicle capacity for public transit routes: A generalized newsvendor model

The level of service on public transit routes is very much affected by the frequency and vehicle capacity. The combined values of these variables contribute to the costs associated with route operations as well as the costs associated with passenger comfort, such as waiting and overcrowding. The new approach to the problem that we introduce combines both passenger and operator costs within a generalized newsvendor model. From the passenger perspective, waiting and overcrowding costs are used; from the operator’s perspective, the costs are related to vehicle size, empty seats, and lost sales. Maximal passenger average waiting time as well as maximal vehicle capacity are considered as constraints that are imposed by the regulator to assure a minimal public transit service level or in order to comply with other regulatory considerations. The advantages of the newsvendor model are that (a) costs are treated as shortages (overcrowding) and surpluses (empty seats); (b) the model presents simultaneous optimal results for both frequency and vehicle size; (c) an efficient and fast algorithm is developed; and (d) the model assumes stochastic demand, and is not restricted to a specific distribution. We demonstrate the usefulness of the model through a case study and sensitivity analysis.     

Automation of paratransit reservation,routing, and scheduling

Santa Clara County, California experienced a sharp growth in demand‐responsive paratransit ridership for individuals with disabilities, as a result of the passage of the 1990 Americans With Disabilities Act (ADA). This paper describes an automated paratransit system for the ADA‐type paratransit operation implemented in Santa Clara County. It automated paratransit reservation, scheduling, and routing functions. The key components of this system were a digital geographic database (DGD) and an automated trip scheduling system (ATSS). Empirical evidence after one year of operation indicates numerous benefits of this automation. There were significant reductions in the paratransit operating costs and an increase in the percent shared rides. The savings in operating costs far exceeded the annualized capital cost of automation. A user survey indicates that these improvements were achieved without degradation to service quality such as vehicle on‐time performance, invehicle travel times, vehicle response to open return, and ride comfort.     

Application of genetic algorithm for scheduling and schedule coordination problems

The problems on scheduling and schedule co‐ordination usually have conflicting objectives related to user's cost and operator's cost. Users want to spend less time to wait, transfer and travel by public buses. Operators are interested in profit making by lesser vehicle operating cost and having a minimum number of buses. As far as level of service is concerned users are interested in lesser crowing while operators are concerned with maximizing profit and thus to have higher load factors. In schedule co‐ordination problems transfer time plays an important role. Users are interested in coordinating services with in acceptable waiting time whereas operators prefer to have lesser services and want to meet higher demands, which invariably increases waiting time. These problems have multiple conflicting objectives and constraints. It is difficult to determine optimum solution for such problems with the help of conventional approaches. It is found that Genetic Algorithm performs well for such multi objective problems.     

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.     

Optimization of headways with stop‐skipping control: a case study of bus rapid transit system

Bus rapid transit system is designed to provide high‐quality and cost‐efficient passenger transportation services. In order to achieve this design objective, effective scheduling strategies are required. This research aims at improving the operation efficiency and service quality of a BRT system through integrated optimization of its service headways and stop‐skipping strategy. Based on cost analysis for both passengers and operation agencies, an optimization model is established. A genetic algorithms based algorithm and an application‐oriented solution method are developed. Beijing BRT Line 2 has been chosen as a case study, and the effectiveness of the optimal headways with stop‐skipping services under different demand levels has been analyzed. The results has shown that, at a certain demand level, the proposed operating strategy can be most advantageous for passengers with an accepted increase of operating costs, under which the optimum headway is between 3.5 and 5.5 min for stop‐skipping services during the morning peak hour depending on the demand with the provision of stop‐skipping services. The effectiveness of the optimal headways with stop‐skipping services is compared with those of existing headways and optimal headways without stop‐skipping services. The results show that operating strategies under the optimal headways with stop‐skipping services outperforms the other two operating strategies with respect to total costs and in‐vehicle time for passengers. Copyright © 2014 John Wiley & Sons, Ltd.     

Optimal design and benefits of a short turning strategy for a bus corridor

We develop a short turning model using demand information from station to station within a single bus line-single period setting, aimed at increasing the service frequency on the more loaded sections to deal with spatial concentration of demand considering both operators’ and users’ costs. We find analytical expressions for optimal values of the design variables, namely frequencies (inside and outside the short cycle), capacity of vehicles and the position of the short turn limit stations. These expressions are used to analyze the influence of different parameters in the final solution. The design variables and the corresponding cost components for operators and users (waiting and in-vehicle times) are compared against an optimized normal operation scheme (single frequency). Applications on actual transit corridors exhibiting different demand profiles are conducted, calculating the optimal values for the design variables and the resulting benefits for each case. Results show the typical demand configurations that are better served using a short turn strategy.     

Optimizing fare and headway to facilitate timed transfer considering demand elasticity

Fare and service frequency significantly affect transit users’ willingness to ride, as well as the supplier's revenue and operating costs. To stimulate demand and increase productivity, it is desirable to reduce the transfer time from one route to another via efficient service coordination, such as timed transfer. Since demand varies both temporally and spatially, it may not be cost-effective to synchronize vehicle arrivals on all connecting routes at a terminal. In this paper, we develop a schedule coordination model to optimize fare and headway considering demand elasticity. The headway of each route is treated as an integer-multiple of a base common headway. A discounted (reduced) fare is applied as an incentive to encourage ridership and, thus, stimulate public transit usage. The objective of the proposed coordination model is used to maximize the total profit subject to the service constraint. A numerical example is given to demonstrate the applicability of the proposed model. The results show that the optimized fare and headway may be carefully applied to yield the maximum profit. The relationship between the decision variables and model parameters is explored in the sensitivity analysis.     

The role of the passenger train in the United States: A cost comparison of the common carriers

The objective of this article is to establish whether the train has a role to play in the market for intercity passenger travel in the United States. To accomplish this objective, we compare the common carriers on the basis of thier cost effectiveness in moving a given flow of passengers between two points a specified distance apart. The comparisons are based on cost models which highlight the technological differences between the modes and eliminate distortions caused by public policy choices. By varying the size of the passenger flow and trip distance, we develop a notion of each common carrier's ideal operating environment. We find that the cost of the right-of-way is the major factor limiting the range of travel situations in which the train is cost competitive with the other common carriers. More specifically, our results indicate that Amtrak's service in the Northeast Corridor should be continued in the short run. In the long run, the possibility of upgrading Amtrak's service in the Northeast Corridor to high-speed service should be investigated. Outside the Northeast Corridor, we find that high-speed train service should be able to cover its operating costs but not its capital costs.     

Congestion-aware system optimal route choice for shared autonomous vehicles

We study the shared autonomous vehicle (SAV) routing problem while considering congestion. SAVs essentially provide a dial-a-ride service to travelers, but the large number of vehicles involved (tens of thousands of SAVs to replace personal vehicles) results in SAV routing causing significant congestion. We combine the dial-a-ride service constraints with the linear program for system optimal dynamic traffic assignment, resulting in a congestion-aware formulation of the SAV routing problem. Traffic flow is modeled through the link transmission model, an approximate solution to the kinematic wave theory of traffic flow. SAVs interact with travelers at origins and destinations. Due to the large number of vehicles involved, we use a continuous approximation of flow to formulate a linear program. Optimal solutions demonstrate that peak hour demand is likely to have greater waiting and in-vehicle travel times than off-peak demand due to congestion. SAV travel times were only slightly greater than system optimal personal vehicle route choice. In addition, solutions can determine the optimal fleet size to minimize congestion or maximize service.     

Electric vehicle charging station locations: Elastic demand,station congestion,and network equilibrium

Battery-only electric vehicles (BEVs) generally offer better air quality through lowered emissions, along with energy savings and security. The issue of long-duration battery charging makes charging-station placement and design key for BEV adoption rates. This work uses genetic algorithms to identify profit-maximizing station placement and design details, with applications that reflect the costs of installing, operating, and maintaining service equipment, including land acquisition. Fast electric vehicle charging stations (EVCSs) are placed across a congested city's network subject to stochastic demand for charging under a user-equilibrium traffic assignment. BEV users’ station choices consider endogenously determined travel times and on-site charging queues. The model allows for congested-travel and congested-station feedback into travelers’ route choices under elastic demand and BEV owners’ station choices, as well as charging price elasticity for BEV charging users.Boston-network results suggest that EVCSs should locate mostly along major highways, which may be a common finding for other metro settings. If 10% of current EV owners seek to charge en route, a user fee of $6 for a 30-min charging session is not enough for station profitability under a 5-year time horizon in this region. However, $10 per BEV charging delivers a 5-year profit of $0.82 million, and 11 cords across 3 stations are enough to accommodate a near-term charging demand in this Boston-area application. Shorter charging sessions, higher fees, and/or allowing for more cords per site also increase profits generally, everything else constant. Power-grid and station upgrades should keep pace with demand, to maximize profits over time, and avoid on-site congestion.     

Economies in U.S. demand responsive transit

This paper develops a neoclassical cost function for demand responsive transit (DRT) system and uses it to test the economies of scale hypothesis. The results show economies of scale and further show that the economies can be explained by speed, local and state subsidies, utilization of seating capacity, fleet utilization and an increase in the number of professionals. Comparison of DRT and bus transit results identifies patterns in policy variables whose effects on cost are the same across modes.     

Impact assessment of the Internet of Things on feeder transit performance

ABSTRACT

Efficient planning for demand responsive transit (DRT) can contribute to fulfilling the first/last mile transport needs for users of a major transit line. With the advancement in communication technologies, the internet is expected to assist this growing need of providing first/last mile connectivity. This is proposed to be achieved through a network created by Internet of Things (IoT). This paper evaluates the effect of implementation of IoT on service quality (or disutility) of DRT for two scenarios – with enabled-IoT (e-IoT) and with disabled-IoT (d-IoT). Data from five different DRT-like systems known as Call-n-Ride (CnR) routes operating in Denver, Colorado, are used for evaluation purposes. These CnR routes are Meridian, Interlocken, South Inverness, Broomfield and Louisville. Results show that, in general, all CnR routes would experience more than a 58 percent decrease in disutility if their operations were based on ‘with e-IoT’ operations. Interlocken would record the largest percentage decrease (74 percent) in disutility if its route service switched from the ‘with d-IoT’ to the ‘with e-IoT’ scenario.     

Multilevel modelling of Demand Responsive Transport (DRT) trips in Greater Manchester based on area-wide socio-economic data

Providing public transport in areas of low demand has long proved to be a challenge to policy makers and practitioners. With the developing economic, social and environmental trends, there is pressure for alternative solutions to the policy of subsidising conventional bus services. One potential solution is to adopt more flexible routes and/or timetables to better match the required demand. Therefore such ‘on demand’ or ‘Demand Responsive Transport’ (DRT) services (known as paratransit in the US) have been adopted in a number of locations. This paper seeks to explore the effects of area-wide factors on the demand of DRT by reporting the results of a statistical analysis of DRT service provision in the metropolitan region of Greater Manchester, the public transport authority of which offers one of the largest and most diverse range of DRT schemes in the UK. Specifically, this paper employs a multilevel modelling approach to investigate the impact of both DRT supply-oriented factors at the service area level and socio-economic factors at the lower super output area (LSOA) level on the average number of trips made by DRT per year. This hierarchical or ‘nested’ structure was adopted because typically the LSOAs within the same Service Area may share similar characteristics. It is found that the demand for DRT services was higher in areas with low car ownership, low population density, high proportion of white people, and high levels of social deprivation, measured in terms of income, employment, education, housing and services, health and disability, and living environment.     

Design and implementation of efficient transit networks: Procedure, case study and validity test

This paper presents and tests a method to design high-performance transit networks. The method produces conceptual plans for geometric idealizations of a particular city that are later adapted to the real conditions. These conceptual plans are generalizations of the hybrid network concept proposed in Daganzo (2010). The best plan for a specific application is chosen via optimization. The objective function is composed of analytic formulae for a concept’s agency cost and user level of service. These formulae include as parameters key demand-side attributes of the city, assumed to be rectangular, and supply-side attributes of the transit technology. They also include as decision variables the system’s line and stop spacings, the degree to which it focuses passenger trips on the city center, and the service headway. These decision variables are sufficient to define an idealized geometric layout of the system and an operating plan. This layout-operating plan is then used as a design target when developing the real, detailed master plan. Ultimately, the latter is simulated to obtain more accurate cost and level of service estimates.This process has been applied to design a high performance bus (HPB) network for Barcelona (Spain). The idealized solution for Barcelona includes 182 km of one-way infrastructure, uses 250 vehicles and costs 42,489 €/h to build and run. These figures only amount to about one third of the agency resources and cost currently used to provide bus service. A detailed design that resembles this target and conforms to the peculiarities of the city is also presented and simulated. The agency cost and user level of service metrics of the simulated system differ from those of the idealized model by less than 10%. Although the designed and simulated HPB systems provide sub-optimal spatial coverage because Barcelona lacks suitable streets, the level of service is good. Simulations suggest that if the proposed system was implemented side-by-side with the current one, it would capture most of the demand.     

Cost benefit analysis of urban minibus operations

Earlier work by the Transport Studies Group of the Polytechnic of Central London on minibus development in Britain for the Transport and Road Research Laboratory provided a financial analysis of intensive urban minibus operation. This is taken as the basis for the application of cost-benefit analysis. Unit operating cost savings and passenger benefits are taken into account, using typical demand elasticities derived from earlier work. Particular attention is paid to the problem of evaluating passenger benefits for which waiting time at the roadside is not necessarily an adequate proxy. A direct survey of passenger waiting times indicates that these do not necessarily decrease when a higher-frequency minibus service replaces a conventional bus service but the improved convenience produces an increase in ridership which may be assessed in terms of a demand curve shift to estimate benefits obtained.     

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.     

Statistical and machine learning approach for planning dial-a-ride systems

Door-to-door transportation service for elderly and persons with disabilities is often called dial-a-ride (DAR), and is usually provided by transit agencies through private contractors. Growth in DAR ridership is reported across the United States and this tendency will likely continue due to aging population. Such trends encourage development of models that can provide decision support in planning new DAR systems or expanding existing ones. Several statistical models were previously developed to predict the required DAR system capacity, given various characteristics of the service region, level-of-service requirements and operator constraints. Our work contributes to this line of research by proposing statistical and machine learning approaches that provide more accurate predictions over a wider range of scenarios. This is accomplished through transformation of variables and application of generalized linear model and support vector regression. Proposed models are built into an online tool that can help transit planners and policy makers: (a) estimate the capacity and operating cost of a DAR system needed to provide the desired level of service, (b) explore tradeoffs between system costs and levels of service, and (c) compare the cost of providing DAR service with other transportation alternatives (e.g., taxi, conventional transit).