Leonid Engelson - Academia.edu (original) (raw)
Papers by Leonid Engelson
This paper proposes an analytical method for stability analysis of traffic flows in a traffic net... more This paper proposes an analytical method for stability analysis of traffic flows in a traffic network with an advanced traveller information system. The presented model describes within-day development of queues when drivers affected by real-time traffic information choose their paths en route. The model reduces to a system of differential equations with delays and discontinuous right hand sides. Equilibrium points
Transportation Research Record: Journal of the Transportation Research Board, 2011
Abstract: The paper presents a theoretical analysis of travelers' scheduling preferences... more Abstract: The paper presents a theoretical analysis of travelers' scheduling preferences and the resulting form of the expected utility that includes travel time reliability measures. A series of research papers and reports used the mean-standard deviation approach to ...
Transportation Research Part C: Emerging Technologies, 2003
Introducing real time traffic information into transportation network makes it necessary to consi... more Introducing real time traffic information into transportation network makes it necessary to consider development of queues and traffic flows as a dynamic process. This paper initiates a theoretical study of conditions under which this process is stable. A model is presented that describes within-one-day development of queues when drivers affected by real-time traffic information choose their paths en route. The model is reduced to a system of differential equations with delay. Equilibrium points of the system correspond to constant queue lengths. Stability of the system is investigated using characteristic values of the linearised minimal face flow. A traffic network example illustrating the method is provided.
Congestion is a major problem in many large cities today. It increases air pollution, travel time... more Congestion is a major problem in many large cities today. It increases air pollution, travel times and travel time uncertainty. City governments introduce policy measures in order to reduce congestion. In Stockholm, a trial with congestion charges has recently been carried out (January 3rd to July 31st, 2006) ). The aim of the trial was to evaluate if road tolls can reduce over-all traffic in the city-centre and also if it can achieve a more efficient usage of the transportation system. To achieve a peak-spreading effect, the congestion charges were time-of-day dependent and higher in the peak hours.
Convexification of the Traffic Equilibrium Problem with Social Marginal Cost Tolls Per Olov Lindb... more Convexification of the Traffic Equilibrium Problem with Social Marginal Cost Tolls Per Olov Lindberg1 and Leonid Engelson2 1 Linkoping University, Dept. of Mathematics, SE-581 83 Linkoping 2 Royal Institute of Technology, Dept. of Infrastructure, SE-100 44 Stockholm e-mails: ...
This paper reviews the transportation models used for predicting impacts of congestion charging i... more This paper reviews the transportation models used for predicting impacts of congestion charging in European cities and carries out in-depth comparison of two such models, METROPOLIS and SILVESTER. Both are mesoscopic dynamic models involving modal split and departure time choice calibrated for the Stockholm baseline situation without charges and applied for modeling effects of congestion charging. The results obtained from the two models are mutually compared and validated against actual outcome of the Stockholm congestion charging scheme. Both models provide significant improvement in realism over static models. However results of cost benefit analysis differ substantially.
Regional traffic models used for transportation planning in Sweden, such as the national modellin... more Regional traffic models used for transportation planning in Sweden, such as the national modelling system Sampers, use different multinomial logit models to forecast travel demand and modal split for different trip purposes. However they do no account for the fact that the value of time varies within a population of travellers making a trip with the same purpose or the
Transportation Research Part B: Methodological, 2015
Different assumptions about travelers' scheduling preferences yield different measures of the cos... more Different assumptions about travelers' scheduling preferences yield different measures of the cost of travel time variability. Only few forms of scheduling preferences provide non-trivial measures which are additive over links in transport networks where link travel times are arbitrarily distributed independent random variables: Assuming smooth preferences, this holds only for specifications with a constant marginal utility of time at the origin and an exponential or affine marginal utility of time at the destination. We apply a generalized version of this model to stated preference data of car drivers' route and mode choice under uncertain travel times. Our analysis exposes some important methodological issues related to complex non-linear scheduling models: One issue is identifying the point in time where the marginal utility of being at the destination becomes larger than the marginal utility of being at the origin. Another issue is that models with the exponential marginal utility formulation suffer from empirical identification problems. Though our results are not decisive, they partly support the constant-affine specification, in which the value of travel time variability is proportional to the variance of travel time.
EURO Journal on Transportation and Logistics, 2015
ABSTRACT We review properties of tolled equilibria in road networks, with users differing in thei... more ABSTRACT We review properties of tolled equilibria in road networks, with users differing in their time values, and study corresponding sensitivities of equilibrium link flows w.r.t. tolls. Possible applications include modeling of individual travellers that have different trip purposes (e.g. work, business, leisure, etc.) and therefore perceive the relation between travel time and monetary cost in dissimilar ways. The typical objective is to reduce the total value of travel time (TVT) over all users. For first best congestion pricing, where all links in the network can be tolled, the solution can be internalized through marginal social cost (MSC) pricing. The MSC equilibrium typically has to be implemented through fixed tolls. The MSC as well as the fixed-toll equilibrium problems can be stated as optimization problems, which in general are convex in the fixed-toll case and non-convex in the MSC case. Thus, there may be several MSC equilibria. Second-best congestion pricing, where one only tolls a subset of the links, is much more complex, and equilibrium flows, times and TVT are not in general differentiable w.r.t. tolls in sub-routes used by several classes. For generic tolls, where the sets of shortest paths are stable, we show how to compute Jacobians (w.r.t positive tolls) of link flows and times as well as of the TVT. This can be used in descent schemes to find tolls that minimize the TVT at least locally. We further show that a condition of independent equilibrium cycles, together with a natural extension of the single class regularity condition of strict complementarity, leads to genericity, and hence existence of said Jacobians.
Operations Research Proceedings 2002, 2003
Multi-Class User Equilibria under Social Marginal Cost Pricing Leonid Engelson1, Per Olov Lindber... more Multi-Class User Equilibria under Social Marginal Cost Pricing Leonid Engelson1, Per Olov Lindberg2, and Maria Daneva2 1 Inregia, Box 12519, SE-10229, Stockholm, 2 Linkoping University, Dept. of Mathematics, SE-581 83 Linkoping, e-mails: Iee3inregia. se, ...
Transportation Research Part B: Methodological, 2011
This paper considers the value of travel time variability under scheduling preferences that are d... more This paper considers the value of travel time variability under scheduling preferences that are defined in terms of linearly time varying utility rates associated with being at the origin and at the destination. The main result is a simple expression for the value of travel time ...
Applied Optimization, 2006
We study congestion pricing of road networks with users differing only in their time values. In p... more We study congestion pricing of road networks with users differing only in their time values. In particular, we analyze the marginal social cost (MSC) pricing, a tolling scheme that charges each user a penalty corresponding to the value of the delays inflicted on other users, as well as its implementation through fixed tolls. We show that the variational inequalities characterizing the corresponding equilibria can be stated in symmetric or nonsymmetric forms. The symmetric forms correspond to optimization problems, convex in the fixed-toll case and nonconvex in the MSC case, which hence may have multiple equilibria. The objective of the latter problem is the total value of travel time, which thus is minimized at the global optima of that problem. Implementing close-to-optimal MSC tolls as fixed tolls leads to equilibria with possibly non-unique class specific flows, but with identical close-to-optimal values of the total value of travel time. Finally we give an adaptation, to the MSC setting, of the Frank-Wolfe algorithm, which is further applied to some test cases, including Stockholm.
Transportation Research Part B: Methodological, 2011
This paper derives a measure of travel time variability for travellers equipped with scheduling p... more This paper derives a measure of travel time variability for travellers equipped with scheduling preferences defined in terms of time-varying utility rates, and who choose departure time optimally. The corresponding value of travel time variability is a constant that depends only on preference parameters. The measure is unique in being additive with respect to independent parts of a trip. It has the variance of travel time as a special case. Extension is provided to the case of travellers who use a scheduled service with fixed headway.
Transportation Research Part A: Policy and Practice, 2013
ABSTRACT This paper compares forecast effects of the Stockholm congestion charges with actual out... more ABSTRACT This paper compares forecast effects of the Stockholm congestion charges with actual outcomes. The most important concerns during the design of the congestion charging scheme were the traffic reduction in bottlenecks, the increase in public transport ridership, the decrease of vehicle kilometres in the city centre, and potential traffic effects on circumferential roads. Comparisons of forecasts and actual outcomes show that the transport model predicted all of these factors well enough to allow planners to draw correct conclusions regarding the design and preparations for the scheme. The one major shortcoming was that the static assignment network model was unable to predict the substantial reductions of queuing times. We conclude that the transport model worked well enough to be useful as decision support, performing considerably better than unaided “experts’ judgments”, but that results must be interpreted taking the model’s limitations into account. The positive experiences from the Stockholm congestion charges hence seem to be transferable to other cities in the sense that if a charging system is forecast to have beneficial effects on congestion, then this is most likely true.
Transportation Planning and Technology, 2014
ABSTRACT As congestion pricing has moved from theoretical ideas in the literature to real-world i... more ABSTRACT As congestion pricing has moved from theoretical ideas in the literature to real-world implementation, the need for decision support when designing pricing schemes has become evident. This paper deals with the problem of finding optimal toll levels and locations in a road traffic network and presents a case study of Stockholm. The optimisation problem of finding optimal toll levels, given a predetermined cordon, and the problem of finding both optimal toll locations and levels are presented, and previously developed heuristics are used for solving these problems. For the Stockholm case study, the possible welfare gains of optimising toll levels in the current cordon and optimising both toll locations and their corresponding toll levels are evaluated. It is shown that by tuning the toll levels in the current congestion pricing cordon used in Stockholm, the welfare gain can be increased significantly, and furthermore improved by allowing a toll on a major bypass highway. It is also shown that, by optimising both toll locations and levels, a congestion pricing scheme with welfare gain close to what can be achieved by marginal social cost pricing can be designed with tolls being located on only a quarter of the tollable links.
Networks and Spatial Economics, 2009
Abstract Road traffic congestion is an increasing problem in urban areas. Building new roads ofte... more Abstract Road traffic congestion is an increasing problem in urban areas. Building new roads often attracts latent demand and turns parts of the city into building sites for several years. Policy measures that stimulate more effective use of the existing network, such as variable road ...
This paper proposes an analytical method for stability analysis of traffic flows in a traffic net... more This paper proposes an analytical method for stability analysis of traffic flows in a traffic network with an advanced traveller information system. The presented model describes within-day development of queues when drivers affected by real-time traffic information choose their paths en route. The model reduces to a system of differential equations with delays and discontinuous right hand sides. Equilibrium points
Transportation Research Record: Journal of the Transportation Research Board, 2011
Abstract: The paper presents a theoretical analysis of travelers' scheduling preferences... more Abstract: The paper presents a theoretical analysis of travelers' scheduling preferences and the resulting form of the expected utility that includes travel time reliability measures. A series of research papers and reports used the mean-standard deviation approach to ...
Transportation Research Part C: Emerging Technologies, 2003
Introducing real time traffic information into transportation network makes it necessary to consi... more Introducing real time traffic information into transportation network makes it necessary to consider development of queues and traffic flows as a dynamic process. This paper initiates a theoretical study of conditions under which this process is stable. A model is presented that describes within-one-day development of queues when drivers affected by real-time traffic information choose their paths en route. The model is reduced to a system of differential equations with delay. Equilibrium points of the system correspond to constant queue lengths. Stability of the system is investigated using characteristic values of the linearised minimal face flow. A traffic network example illustrating the method is provided.
Congestion is a major problem in many large cities today. It increases air pollution, travel time... more Congestion is a major problem in many large cities today. It increases air pollution, travel times and travel time uncertainty. City governments introduce policy measures in order to reduce congestion. In Stockholm, a trial with congestion charges has recently been carried out (January 3rd to July 31st, 2006) ). The aim of the trial was to evaluate if road tolls can reduce over-all traffic in the city-centre and also if it can achieve a more efficient usage of the transportation system. To achieve a peak-spreading effect, the congestion charges were time-of-day dependent and higher in the peak hours.
Convexification of the Traffic Equilibrium Problem with Social Marginal Cost Tolls Per Olov Lindb... more Convexification of the Traffic Equilibrium Problem with Social Marginal Cost Tolls Per Olov Lindberg1 and Leonid Engelson2 1 Linkoping University, Dept. of Mathematics, SE-581 83 Linkoping 2 Royal Institute of Technology, Dept. of Infrastructure, SE-100 44 Stockholm e-mails: ...
This paper reviews the transportation models used for predicting impacts of congestion charging i... more This paper reviews the transportation models used for predicting impacts of congestion charging in European cities and carries out in-depth comparison of two such models, METROPOLIS and SILVESTER. Both are mesoscopic dynamic models involving modal split and departure time choice calibrated for the Stockholm baseline situation without charges and applied for modeling effects of congestion charging. The results obtained from the two models are mutually compared and validated against actual outcome of the Stockholm congestion charging scheme. Both models provide significant improvement in realism over static models. However results of cost benefit analysis differ substantially.
Regional traffic models used for transportation planning in Sweden, such as the national modellin... more Regional traffic models used for transportation planning in Sweden, such as the national modelling system Sampers, use different multinomial logit models to forecast travel demand and modal split for different trip purposes. However they do no account for the fact that the value of time varies within a population of travellers making a trip with the same purpose or the
Transportation Research Part B: Methodological, 2015
Different assumptions about travelers' scheduling preferences yield different measures of the cos... more Different assumptions about travelers' scheduling preferences yield different measures of the cost of travel time variability. Only few forms of scheduling preferences provide non-trivial measures which are additive over links in transport networks where link travel times are arbitrarily distributed independent random variables: Assuming smooth preferences, this holds only for specifications with a constant marginal utility of time at the origin and an exponential or affine marginal utility of time at the destination. We apply a generalized version of this model to stated preference data of car drivers' route and mode choice under uncertain travel times. Our analysis exposes some important methodological issues related to complex non-linear scheduling models: One issue is identifying the point in time where the marginal utility of being at the destination becomes larger than the marginal utility of being at the origin. Another issue is that models with the exponential marginal utility formulation suffer from empirical identification problems. Though our results are not decisive, they partly support the constant-affine specification, in which the value of travel time variability is proportional to the variance of travel time.
EURO Journal on Transportation and Logistics, 2015
ABSTRACT We review properties of tolled equilibria in road networks, with users differing in thei... more ABSTRACT We review properties of tolled equilibria in road networks, with users differing in their time values, and study corresponding sensitivities of equilibrium link flows w.r.t. tolls. Possible applications include modeling of individual travellers that have different trip purposes (e.g. work, business, leisure, etc.) and therefore perceive the relation between travel time and monetary cost in dissimilar ways. The typical objective is to reduce the total value of travel time (TVT) over all users. For first best congestion pricing, where all links in the network can be tolled, the solution can be internalized through marginal social cost (MSC) pricing. The MSC equilibrium typically has to be implemented through fixed tolls. The MSC as well as the fixed-toll equilibrium problems can be stated as optimization problems, which in general are convex in the fixed-toll case and non-convex in the MSC case. Thus, there may be several MSC equilibria. Second-best congestion pricing, where one only tolls a subset of the links, is much more complex, and equilibrium flows, times and TVT are not in general differentiable w.r.t. tolls in sub-routes used by several classes. For generic tolls, where the sets of shortest paths are stable, we show how to compute Jacobians (w.r.t positive tolls) of link flows and times as well as of the TVT. This can be used in descent schemes to find tolls that minimize the TVT at least locally. We further show that a condition of independent equilibrium cycles, together with a natural extension of the single class regularity condition of strict complementarity, leads to genericity, and hence existence of said Jacobians.
Operations Research Proceedings 2002, 2003
Multi-Class User Equilibria under Social Marginal Cost Pricing Leonid Engelson1, Per Olov Lindber... more Multi-Class User Equilibria under Social Marginal Cost Pricing Leonid Engelson1, Per Olov Lindberg2, and Maria Daneva2 1 Inregia, Box 12519, SE-10229, Stockholm, 2 Linkoping University, Dept. of Mathematics, SE-581 83 Linkoping, e-mails: Iee3inregia. se, ...
Transportation Research Part B: Methodological, 2011
This paper considers the value of travel time variability under scheduling preferences that are d... more This paper considers the value of travel time variability under scheduling preferences that are defined in terms of linearly time varying utility rates associated with being at the origin and at the destination. The main result is a simple expression for the value of travel time ...
Applied Optimization, 2006
We study congestion pricing of road networks with users differing only in their time values. In p... more We study congestion pricing of road networks with users differing only in their time values. In particular, we analyze the marginal social cost (MSC) pricing, a tolling scheme that charges each user a penalty corresponding to the value of the delays inflicted on other users, as well as its implementation through fixed tolls. We show that the variational inequalities characterizing the corresponding equilibria can be stated in symmetric or nonsymmetric forms. The symmetric forms correspond to optimization problems, convex in the fixed-toll case and nonconvex in the MSC case, which hence may have multiple equilibria. The objective of the latter problem is the total value of travel time, which thus is minimized at the global optima of that problem. Implementing close-to-optimal MSC tolls as fixed tolls leads to equilibria with possibly non-unique class specific flows, but with identical close-to-optimal values of the total value of travel time. Finally we give an adaptation, to the MSC setting, of the Frank-Wolfe algorithm, which is further applied to some test cases, including Stockholm.
Transportation Research Part B: Methodological, 2011
This paper derives a measure of travel time variability for travellers equipped with scheduling p... more This paper derives a measure of travel time variability for travellers equipped with scheduling preferences defined in terms of time-varying utility rates, and who choose departure time optimally. The corresponding value of travel time variability is a constant that depends only on preference parameters. The measure is unique in being additive with respect to independent parts of a trip. It has the variance of travel time as a special case. Extension is provided to the case of travellers who use a scheduled service with fixed headway.
Transportation Research Part A: Policy and Practice, 2013
ABSTRACT This paper compares forecast effects of the Stockholm congestion charges with actual out... more ABSTRACT This paper compares forecast effects of the Stockholm congestion charges with actual outcomes. The most important concerns during the design of the congestion charging scheme were the traffic reduction in bottlenecks, the increase in public transport ridership, the decrease of vehicle kilometres in the city centre, and potential traffic effects on circumferential roads. Comparisons of forecasts and actual outcomes show that the transport model predicted all of these factors well enough to allow planners to draw correct conclusions regarding the design and preparations for the scheme. The one major shortcoming was that the static assignment network model was unable to predict the substantial reductions of queuing times. We conclude that the transport model worked well enough to be useful as decision support, performing considerably better than unaided “experts’ judgments”, but that results must be interpreted taking the model’s limitations into account. The positive experiences from the Stockholm congestion charges hence seem to be transferable to other cities in the sense that if a charging system is forecast to have beneficial effects on congestion, then this is most likely true.
Transportation Planning and Technology, 2014
ABSTRACT As congestion pricing has moved from theoretical ideas in the literature to real-world i... more ABSTRACT As congestion pricing has moved from theoretical ideas in the literature to real-world implementation, the need for decision support when designing pricing schemes has become evident. This paper deals with the problem of finding optimal toll levels and locations in a road traffic network and presents a case study of Stockholm. The optimisation problem of finding optimal toll levels, given a predetermined cordon, and the problem of finding both optimal toll locations and levels are presented, and previously developed heuristics are used for solving these problems. For the Stockholm case study, the possible welfare gains of optimising toll levels in the current cordon and optimising both toll locations and their corresponding toll levels are evaluated. It is shown that by tuning the toll levels in the current congestion pricing cordon used in Stockholm, the welfare gain can be increased significantly, and furthermore improved by allowing a toll on a major bypass highway. It is also shown that, by optimising both toll locations and levels, a congestion pricing scheme with welfare gain close to what can be achieved by marginal social cost pricing can be designed with tolls being located on only a quarter of the tollable links.
Networks and Spatial Economics, 2009
Abstract Road traffic congestion is an increasing problem in urban areas. Building new roads ofte... more Abstract Road traffic congestion is an increasing problem in urban areas. Building new roads often attracts latent demand and turns parts of the city into building sites for several years. Policy measures that stimulate more effective use of the existing network, such as variable road ...