The University of Southampton
University of Southampton Institutional Repository

Transit economics

Transit economics
Transit economics
Transit service is a for-hire, shared urban passenger transportation service that is fixed-route and scheduled. The study of the economics of transit systems (especially U.S. public transit systems and U.K. public transport) has been responsible for many developments in transport economics, including advances in demand forecasting, cost modeling, pricing policy, regulatory studies and appraisal techniques. It has attracted the attention of Nobel laureates such as Robert Fogel, Daniel McFadden and William Vickrey. The developments have only periodically been brought together, typically in textbooks such as those of Nash (1982) and Berechman (1993) or in best practice guides such as those produced by TRL in the U.K. and TRB in the U.S. ([Balcombe et al., 2004] and [TRB, 2005]). This peer-reviewed issue advances the transit economics literature by its papers written by some of the world's leading academic researchers in transit economics.
The issue begins with Ken Gwilliam's review of the evolution of transit economics. As well as illustrating the depth and breadth of the extant literature, this paper shows that some issues – such as the analysis of cost and demand parameters – are perennial, with development mostly in the mathematical sophistication of the analytical techniques employed, while others – such as issues of ownership and competitive form – reflect wider trends in economic thinking. In addition, some issues – such as the relationship between transit and development – are universal, while others – such as the role of small vehicles and the informal sector- impact mostly on developing countries. Many of these topics are explored in subsequent papers in this issue, albeit largely from a developed country perspective. The overall conclusion – that transit is critical to the achievement of a wide range of social, economic and environmental objectives and therefore needs appropriate institutions to ensure its integration with the strategic management of the rest of urban development policy – is also supported by a number of papers in this issue.
With respect to developments in demand analysis, David Hensher presents an error component, mixed logit model that can account for – between-alternative error structures, scale differences between revealed preference and stated preference data sets, unobserved preference heterogeneity and state or reference dependency. This model is compared with the nested logit models for which revealed and stated preference data sets are choice-based weighted for pooling. The error component, mixed logit and the nested logit models are used to investigate individual preference choices for bus, train and car commuting trips. The empirical results suggest that nested logit models are incapable of accounting for the potential correlation induced through repeated observations in pooled preference data sets. Further, the nested logit model does not recognize the impact of heterogeneity on choice outcomes. Unlike the nested logit model, the error component, mixed logit model can account for scale differences among multiple data sets. This suggests that the error component, mixed logit model should replace the nested logit model as the state-of-the-art tool in the analysis of transit choices.
Kjell Jansson, Harald Lang and Dan Mattsson investigate optimal economic interventions in scheduled public transport. Passengers for a given origin–destination pair are assumed to be homogenous (as much as possible) with respect to travel time valuation. Given passenger demand for various time periods, the public transport firm is assumed to reach decisions regarding inputs and prices well ahead of their use and implementation. Further, the generalized cost for a passenger trip consists of a component that is common to all passengers and a passenger-specific component. In utilizing these assumptions Jansson et al. investigate the relationships between optimal price, frequency of service and public transport firm size under welfare and profit maximization. They conclude, unsurprisingly, that a monopoly profit maximizing public transport firm has too few passengers and too low a service frequency from a welfare maximization point of view. However, a price subsidy formula can result in the transport operator choosing a welfare optimal price, frequency of service and public transport firm size. Alternatively, for profit maximizing transport firms under competition, a tax per departure can lead to outcomes closer to welfare optimum, by preventing excess supply. This suggests that financial interventions by governments in public transport markets need to be re-thought.
Odd Larsen and Øyvind Sunde also undertake a largely theoretical study to re-assess the role of waiting time and information in transit service. They find that for real-life networks determination of optimal waiting times, onboard times, transfers and even walking time becomes rather complicated. The reason is that several route and path options may be available for a given transit trip – the so called ‘common lines’ problem.
In the authors' view the assumptions used in most current transit assignment models are unrealistic with respect to system characteristics and traveler behavior – not least of which when it comes to the issue of information available to transit users and how this information is used. Most transit systems, at least in developed countries, are reasonably reliable and timetable information is frequently available at transit stops. Experienced transit users may even have information that surpasses the information provided by timetables or displays at transit stops. However, at the same time transit users are not a homogeneous group with respect to preferences and information. Therefore, a new transit assignment principle is proposed that is based on a weighted logit model specification that embeds an accurate description of the routes with respect to headways and riding times, assuming that timetable information is available. The specification allows for a trade-off between riding time and waiting time. Simple formulas for route probabilities and expected waiting times are derived. The specification also provides a solution for three important issues: The relevant choice set, the formulation and scaling of “utilities” and the estimation of average waiting time. Tests suggest that the specification is robust and produces results that are realistic and could provide an improved algorithm for transit assignment.
Moving on to the topics of productivity and cost efficiency, Borger, Kerstens and Staat study problems commonly encountered in efficiency studies that use non-parametric Data Envelopment Analysis (DEA). These problems include – the inability to draw conclusions about the statistical properties of the efficiency estimators, the inability of small samples to adequately represent technology thus resulting in biased estimates of efficiency, and the difficulty of testing relevant economic hypotheses. To overcome these problems they employ recent developments in the application of bootstrap techniques in non-parametric frontier analysis and apply them to Norwegian transit data. More specifically, they use a selection of the most recently developed techniques for estimating non-parametric convex (DEA) cost frontiers for transit systems to show their usefulness in testing characteristics of transit cost structures, and to derive cost efficiency scores.
The authors adopt a four-stage approach. The first derives bootstrap cost efficiency measures, the second uses bootstrap techniques to test for constant returns to scale, the third relates cost efficiency to firm characteristics in a two-stage bootstrap procedure similar to that found in Simar and Wilson (2007), and the fourth applies a Monte Carlo simulation technique as found in Zhang and Bartels (1998) to compare the results in two samples of different sizes, and to alleviate the sample size problem. The paper thus brings together some of the most recent developments in bootstrap DEA techniques. The findings include a substantial bias (as much as 25%) in the parametric efficiency measures, a rejection of constant returns to scale and an identification of only one covariate of cost efficiency. The Monte Carlo simulation results show that the efficiency scores of Norwegian and French transit systems were similar under variable returns to scale but diverged considerably under constant returns to scale.
Johan Holmgren, Jan Owen Jansson and Anders Ljungberg bring together demand and cost issues by addressing the following questions: Is local public transport under the threat of extermination in medium-sized cities and smaller towns? If so, what can be done to elevate this threat? They investigate these questions via a case study of the Swedish town of Linkoping that has a population of 140,000 citizens and where bus transport is the only mode of local public transport. Using bus trips per capita from 1946 to 2006 as the dependent variable in an empirical model, Holmgren et al. found negative effects of fare and car ownership on ridership, but positive effects from bus vehicle-kilometers, female labor force participation and the proportion of people living in the outer suburbs. The steady increase in female car ownership, with the increase in the number of two-car households, has been the main cause of the decline in total bus trips in Linkoping over the years. The authors conclude that the declining ridership trend in Linkoping can be reversed by not charging fares for off-peak service, regarding local bus services as merit goods and providing a level of service above the basic minimum to the extent that the incremental benefits of the service exceed its incremental costs.
John Preston also brings together transit demand and cost by developing simulation models to analyze competition in the rail and bus transit sectors in the U.K. and Sweden. For U.K. rail, he considers a route with approximately 2 million passengers per year linking two major cities. The route has substantial commuting at both ends. The incumbent and the new entrant railroads utilize by assumption the same rolling stock. The simulation results indicate that if the new entrant were to add two additional services, it would attract a market share of between 6% and 12%; this market share would increase between 45% and 57% when it provided the same service and frequency of service as the incumbent firm. Similar percentages were found for Sweden, where fare competition from the new entrant railroad had a large impact on the market share for high frequency routes, while fringe competition had less impact on market share.
For bus markets, Preston applied simulation models to two commercial corridors in a major provincial city in England for the purpose of identifying the welfare and financial impacts of changes in fares and service quality as well as service quantity combinations. Opposite effects from fare reduction and service frequency enhancement were found. On a busy route with two operators, frequency reductions had more impact on welfare than fare reduction, and fare reduction reduced profitability while frequency reductions increased it. On a second route with low service frequency/quality and one operator, fare reductions improved welfare and reduced profitability but frequency reductions led to welfare losses and increased profitability. Preston cautions that though this finding is an incentive for the operator to reduce frequency on this latter route it does not because doing so could attract new entrants to the route. In further analysis of the second route, a combination of fare adjustments and quality enhancements in terms of bus priority improvements paid by the Local Authority is examined, with frequency remaining unchanged. The results show that this combination enhances both welfare and profit, and that while fare increases result in a small gain in profitability, fare reductions harm it. This work illustrates the increased complexity of public transport market outcomes if competition is permitted.
Kofi Obeng and R. Sakano examine the effects of operating and capital subsidies on the total factor productivity (TFP) of public transit systems when subsidies have both lump-sum and input substitution effects. They show in two proofs that operating and capital subsidies increase the costs of resources and reduce TFP in the presence of system diseconomies of scale and the absence of technical change in public transit systems. They also use an unbalanced panel data set of U.S. public transit systems for the years 1985–2004 to investigate the effects of subsidies on TFP. Their empirical results indicate that the substitution effects of transit subsidies increase TFP by 0.03% per year when the effects relate only to input use. For public transit systems that exhibit slight diseconomies of scale and when both the lump-sum and substitution effects of the subsidies on TFP are considered, TFP decreases by 0.02% per year.
James Peoples, Wayne Talley and Bin Wang investigate public transit earnings, employment and privatization in the U.S. They note that transit subsidies may create unintended rent that may be shared with transit workers, and that high union transit wages may reflect the compensation needed to attract and keep well-qualified workers. They build upon previous work by Talley (1998) that showed the lack of union premium on labor earnings after privatization and local municipalities' propensities to employ contract workers as an effect of privatization. The effect of privatization on public transit labor earnings and employment is investigated from estimations of public transit labor earnings and employment equations. The hypothesized explanatory variables include worker characteristics, residency location, educational attainment and occupation. Their estimation results suggest that transit workers with a high school diploma, who are male, that reside in the city and the western part of the U.S, who are older, that work long hours, and who are employed as technicians, professionals and managers receive higher earnings. The estimation results also indicate a 58.93% wage premium for union transit workers residing in a non-privatized metropolitan area as opposed to a lower premium of 21.54% for those residing in a privatized metropolitan area.
The estimated employment equation suggests strong positive relationships between union membership, age and the operative occupation and the probability of public transit employment. Weaker positive relationships were found between professional and technician occupations and the probability of public transit employment. Peoples et al. estimate that “union public transit workers in completely privatized localities are 62.24% more likely to be employed in the public sector than union transit workers employed in non-privatized localities.” The labor cost savings from privatization can be derived from “the enhanced employment of relatively low wage non-union workers in the public sector of public transit services.”
In the final paper Roger Vickerman addresses the important issue of the relationships between transport interventions and wider economic development. Early work implied that “transport is critical”, later work stressed the need to “be aware of double counting” and more recently the belief is that “wider economic benefits are the key” has become prevalent, particularly in the U.K. However, the author cautions against simple rules in transport appraisal. The evidence on both the property impacts of transit development and the scope for agglomeration benefits implies on average modest effects of a 10–20 percent uplift – some impacts appear larger, some smaller (including some of the wrong sign), but they depend critically on local circumstances. There is a need to bring together disparate approaches from urban economics and transportation economics in order to obtain a fuller understanding of the impacts of agglomeration economies and reductions in imperfect competition and to present a more rigorous model of the wider economic benefits of transit investment.
It is likely that the current high gas and petrol prices worldwide will lead to a re-assessment of the economics of transit in many countries. The tools found in the papers in this issue may be used to determine appropriate transit prices and the quantity and quality of output, as well as the levels and forms of subsidies. The papers also provide insight into the importance of institutional factors, e.g., those relating to transit competition and ownership. Transit policy in the recent past has often been characterized by inappropriate investments and interventions from the ignorance of economic realties by the political process. These mistakes should not be repeated if transit is to enjoy a sustained revival
0739-8859
1-3
Obeng, Kofi
3f9b2364-e847-4449-a1e5-f25180215f42
Preston, John M.
ef81c42e-c896-4768-92d1-052662037f0b
Talley, Wayne K.
1fa864d5-bb94-46d5-acd4-3a7c704b1d04
Obeng, Kofi
3f9b2364-e847-4449-a1e5-f25180215f42
Preston, John M.
ef81c42e-c896-4768-92d1-052662037f0b
Talley, Wayne K.
1fa864d5-bb94-46d5-acd4-3a7c704b1d04

Obeng, Kofi, Preston, John M. and Talley, Wayne K. (2008) Transit economics. Research in Transportation Economics, 23 (1), 1-3. (doi:10.1016/j.retrec.2008.10.001).

Record type: Article

Abstract

Transit service is a for-hire, shared urban passenger transportation service that is fixed-route and scheduled. The study of the economics of transit systems (especially U.S. public transit systems and U.K. public transport) has been responsible for many developments in transport economics, including advances in demand forecasting, cost modeling, pricing policy, regulatory studies and appraisal techniques. It has attracted the attention of Nobel laureates such as Robert Fogel, Daniel McFadden and William Vickrey. The developments have only periodically been brought together, typically in textbooks such as those of Nash (1982) and Berechman (1993) or in best practice guides such as those produced by TRL in the U.K. and TRB in the U.S. ([Balcombe et al., 2004] and [TRB, 2005]). This peer-reviewed issue advances the transit economics literature by its papers written by some of the world's leading academic researchers in transit economics.
The issue begins with Ken Gwilliam's review of the evolution of transit economics. As well as illustrating the depth and breadth of the extant literature, this paper shows that some issues – such as the analysis of cost and demand parameters – are perennial, with development mostly in the mathematical sophistication of the analytical techniques employed, while others – such as issues of ownership and competitive form – reflect wider trends in economic thinking. In addition, some issues – such as the relationship between transit and development – are universal, while others – such as the role of small vehicles and the informal sector- impact mostly on developing countries. Many of these topics are explored in subsequent papers in this issue, albeit largely from a developed country perspective. The overall conclusion – that transit is critical to the achievement of a wide range of social, economic and environmental objectives and therefore needs appropriate institutions to ensure its integration with the strategic management of the rest of urban development policy – is also supported by a number of papers in this issue.
With respect to developments in demand analysis, David Hensher presents an error component, mixed logit model that can account for – between-alternative error structures, scale differences between revealed preference and stated preference data sets, unobserved preference heterogeneity and state or reference dependency. This model is compared with the nested logit models for which revealed and stated preference data sets are choice-based weighted for pooling. The error component, mixed logit and the nested logit models are used to investigate individual preference choices for bus, train and car commuting trips. The empirical results suggest that nested logit models are incapable of accounting for the potential correlation induced through repeated observations in pooled preference data sets. Further, the nested logit model does not recognize the impact of heterogeneity on choice outcomes. Unlike the nested logit model, the error component, mixed logit model can account for scale differences among multiple data sets. This suggests that the error component, mixed logit model should replace the nested logit model as the state-of-the-art tool in the analysis of transit choices.
Kjell Jansson, Harald Lang and Dan Mattsson investigate optimal economic interventions in scheduled public transport. Passengers for a given origin–destination pair are assumed to be homogenous (as much as possible) with respect to travel time valuation. Given passenger demand for various time periods, the public transport firm is assumed to reach decisions regarding inputs and prices well ahead of their use and implementation. Further, the generalized cost for a passenger trip consists of a component that is common to all passengers and a passenger-specific component. In utilizing these assumptions Jansson et al. investigate the relationships between optimal price, frequency of service and public transport firm size under welfare and profit maximization. They conclude, unsurprisingly, that a monopoly profit maximizing public transport firm has too few passengers and too low a service frequency from a welfare maximization point of view. However, a price subsidy formula can result in the transport operator choosing a welfare optimal price, frequency of service and public transport firm size. Alternatively, for profit maximizing transport firms under competition, a tax per departure can lead to outcomes closer to welfare optimum, by preventing excess supply. This suggests that financial interventions by governments in public transport markets need to be re-thought.
Odd Larsen and Øyvind Sunde also undertake a largely theoretical study to re-assess the role of waiting time and information in transit service. They find that for real-life networks determination of optimal waiting times, onboard times, transfers and even walking time becomes rather complicated. The reason is that several route and path options may be available for a given transit trip – the so called ‘common lines’ problem.
In the authors' view the assumptions used in most current transit assignment models are unrealistic with respect to system characteristics and traveler behavior – not least of which when it comes to the issue of information available to transit users and how this information is used. Most transit systems, at least in developed countries, are reasonably reliable and timetable information is frequently available at transit stops. Experienced transit users may even have information that surpasses the information provided by timetables or displays at transit stops. However, at the same time transit users are not a homogeneous group with respect to preferences and information. Therefore, a new transit assignment principle is proposed that is based on a weighted logit model specification that embeds an accurate description of the routes with respect to headways and riding times, assuming that timetable information is available. The specification allows for a trade-off between riding time and waiting time. Simple formulas for route probabilities and expected waiting times are derived. The specification also provides a solution for three important issues: The relevant choice set, the formulation and scaling of “utilities” and the estimation of average waiting time. Tests suggest that the specification is robust and produces results that are realistic and could provide an improved algorithm for transit assignment.
Moving on to the topics of productivity and cost efficiency, Borger, Kerstens and Staat study problems commonly encountered in efficiency studies that use non-parametric Data Envelopment Analysis (DEA). These problems include – the inability to draw conclusions about the statistical properties of the efficiency estimators, the inability of small samples to adequately represent technology thus resulting in biased estimates of efficiency, and the difficulty of testing relevant economic hypotheses. To overcome these problems they employ recent developments in the application of bootstrap techniques in non-parametric frontier analysis and apply them to Norwegian transit data. More specifically, they use a selection of the most recently developed techniques for estimating non-parametric convex (DEA) cost frontiers for transit systems to show their usefulness in testing characteristics of transit cost structures, and to derive cost efficiency scores.
The authors adopt a four-stage approach. The first derives bootstrap cost efficiency measures, the second uses bootstrap techniques to test for constant returns to scale, the third relates cost efficiency to firm characteristics in a two-stage bootstrap procedure similar to that found in Simar and Wilson (2007), and the fourth applies a Monte Carlo simulation technique as found in Zhang and Bartels (1998) to compare the results in two samples of different sizes, and to alleviate the sample size problem. The paper thus brings together some of the most recent developments in bootstrap DEA techniques. The findings include a substantial bias (as much as 25%) in the parametric efficiency measures, a rejection of constant returns to scale and an identification of only one covariate of cost efficiency. The Monte Carlo simulation results show that the efficiency scores of Norwegian and French transit systems were similar under variable returns to scale but diverged considerably under constant returns to scale.
Johan Holmgren, Jan Owen Jansson and Anders Ljungberg bring together demand and cost issues by addressing the following questions: Is local public transport under the threat of extermination in medium-sized cities and smaller towns? If so, what can be done to elevate this threat? They investigate these questions via a case study of the Swedish town of Linkoping that has a population of 140,000 citizens and where bus transport is the only mode of local public transport. Using bus trips per capita from 1946 to 2006 as the dependent variable in an empirical model, Holmgren et al. found negative effects of fare and car ownership on ridership, but positive effects from bus vehicle-kilometers, female labor force participation and the proportion of people living in the outer suburbs. The steady increase in female car ownership, with the increase in the number of two-car households, has been the main cause of the decline in total bus trips in Linkoping over the years. The authors conclude that the declining ridership trend in Linkoping can be reversed by not charging fares for off-peak service, regarding local bus services as merit goods and providing a level of service above the basic minimum to the extent that the incremental benefits of the service exceed its incremental costs.
John Preston also brings together transit demand and cost by developing simulation models to analyze competition in the rail and bus transit sectors in the U.K. and Sweden. For U.K. rail, he considers a route with approximately 2 million passengers per year linking two major cities. The route has substantial commuting at both ends. The incumbent and the new entrant railroads utilize by assumption the same rolling stock. The simulation results indicate that if the new entrant were to add two additional services, it would attract a market share of between 6% and 12%; this market share would increase between 45% and 57% when it provided the same service and frequency of service as the incumbent firm. Similar percentages were found for Sweden, where fare competition from the new entrant railroad had a large impact on the market share for high frequency routes, while fringe competition had less impact on market share.
For bus markets, Preston applied simulation models to two commercial corridors in a major provincial city in England for the purpose of identifying the welfare and financial impacts of changes in fares and service quality as well as service quantity combinations. Opposite effects from fare reduction and service frequency enhancement were found. On a busy route with two operators, frequency reductions had more impact on welfare than fare reduction, and fare reduction reduced profitability while frequency reductions increased it. On a second route with low service frequency/quality and one operator, fare reductions improved welfare and reduced profitability but frequency reductions led to welfare losses and increased profitability. Preston cautions that though this finding is an incentive for the operator to reduce frequency on this latter route it does not because doing so could attract new entrants to the route. In further analysis of the second route, a combination of fare adjustments and quality enhancements in terms of bus priority improvements paid by the Local Authority is examined, with frequency remaining unchanged. The results show that this combination enhances both welfare and profit, and that while fare increases result in a small gain in profitability, fare reductions harm it. This work illustrates the increased complexity of public transport market outcomes if competition is permitted.
Kofi Obeng and R. Sakano examine the effects of operating and capital subsidies on the total factor productivity (TFP) of public transit systems when subsidies have both lump-sum and input substitution effects. They show in two proofs that operating and capital subsidies increase the costs of resources and reduce TFP in the presence of system diseconomies of scale and the absence of technical change in public transit systems. They also use an unbalanced panel data set of U.S. public transit systems for the years 1985–2004 to investigate the effects of subsidies on TFP. Their empirical results indicate that the substitution effects of transit subsidies increase TFP by 0.03% per year when the effects relate only to input use. For public transit systems that exhibit slight diseconomies of scale and when both the lump-sum and substitution effects of the subsidies on TFP are considered, TFP decreases by 0.02% per year.
James Peoples, Wayne Talley and Bin Wang investigate public transit earnings, employment and privatization in the U.S. They note that transit subsidies may create unintended rent that may be shared with transit workers, and that high union transit wages may reflect the compensation needed to attract and keep well-qualified workers. They build upon previous work by Talley (1998) that showed the lack of union premium on labor earnings after privatization and local municipalities' propensities to employ contract workers as an effect of privatization. The effect of privatization on public transit labor earnings and employment is investigated from estimations of public transit labor earnings and employment equations. The hypothesized explanatory variables include worker characteristics, residency location, educational attainment and occupation. Their estimation results suggest that transit workers with a high school diploma, who are male, that reside in the city and the western part of the U.S, who are older, that work long hours, and who are employed as technicians, professionals and managers receive higher earnings. The estimation results also indicate a 58.93% wage premium for union transit workers residing in a non-privatized metropolitan area as opposed to a lower premium of 21.54% for those residing in a privatized metropolitan area.
The estimated employment equation suggests strong positive relationships between union membership, age and the operative occupation and the probability of public transit employment. Weaker positive relationships were found between professional and technician occupations and the probability of public transit employment. Peoples et al. estimate that “union public transit workers in completely privatized localities are 62.24% more likely to be employed in the public sector than union transit workers employed in non-privatized localities.” The labor cost savings from privatization can be derived from “the enhanced employment of relatively low wage non-union workers in the public sector of public transit services.”
In the final paper Roger Vickerman addresses the important issue of the relationships between transport interventions and wider economic development. Early work implied that “transport is critical”, later work stressed the need to “be aware of double counting” and more recently the belief is that “wider economic benefits are the key” has become prevalent, particularly in the U.K. However, the author cautions against simple rules in transport appraisal. The evidence on both the property impacts of transit development and the scope for agglomeration benefits implies on average modest effects of a 10–20 percent uplift – some impacts appear larger, some smaller (including some of the wrong sign), but they depend critically on local circumstances. There is a need to bring together disparate approaches from urban economics and transportation economics in order to obtain a fuller understanding of the impacts of agglomeration economies and reductions in imperfect competition and to present a more rigorous model of the wider economic benefits of transit investment.
It is likely that the current high gas and petrol prices worldwide will lead to a re-assessment of the economics of transit in many countries. The tools found in the papers in this issue may be used to determine appropriate transit prices and the quantity and quality of output, as well as the levels and forms of subsidies. The papers also provide insight into the importance of institutional factors, e.g., those relating to transit competition and ownership. Transit policy in the recent past has often been characterized by inappropriate investments and interventions from the ignorance of economic realties by the political process. These mistakes should not be repeated if transit is to enjoy a sustained revival

This record has no associated files available for download.

More information

Published date: 2008

Identifiers

Local EPrints ID: 74267
URI: http://eprints.soton.ac.uk/id/eprint/74267
ISSN: 0739-8859
PURE UUID: 46848e69-b467-43f6-8e86-a5c47edd7ead
ORCID for John M. Preston: ORCID iD orcid.org/0000-0002-6866-049X

Catalogue record

Date deposited: 12 Mar 2010
Last modified: 14 Mar 2024 02:51

Export record

Altmetrics

Contributors

Author: Kofi Obeng
Author: John M. Preston ORCID iD
Author: Wayne K. Talley

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×