This document discusses convergence in strategic transport models. It defines convergence as reaching equilibrium between demand and supply models. Demand models predict demand given travel costs, while supply models predict costs given demand. Iterative methods are needed to find the equilibrium point where these intersect. The document compares different iterative methods, such as the method of repeated approximations and method of successive averages, which improve convergence by enforcing contraction. Non-contraction maps may not converge, so averaging schemes are proposed to enforce contraction. The best method depends on the level and speed of convergence achieved without overly complex implementation.
This document summarizes research into improving models for predicting traffic-actuated phase times in traffic signal timing design. Existing models make simplifying assumptions that result in inaccurate phase time predictions. The research aims to develop an improved methodology by accounting for operational effects like progression and queue blockage. Experimental results indicate the new methodology more accurately calculates actuated phase times, which could lead to better traffic signal timing plans and reduced congestion.
Multi depot Time-dependent Vehicle Routing Problem with Heterogeneous FleetArian Razmi Farooji
The document summarizes a study comparing NSGA II and MOSA algorithms for solving a multi-depot vehicle routing problem with time-dependent travel times and a heterogeneous fleet. The problem involves routing vehicles from multiple depots to serve customers within time windows while minimizing costs and number of routes. NSGA II and MOSA were tested on randomly generated small, medium, and large problems. Results showed that on average, MOSA performed better than the model on small problems, while NSGA II performed comparably to the model.
Multi-objective and Multi-constrained UAV Path Plan Optimum Selection Based o...Angelo State University
This document discusses optimizing flight path planning for unmanned aerial vehicles (UAVs) using grey relational analysis. It establishes an optimal decision-making system and mathematical model for UAV flight paths that considers multiple objectives like minimizing costs and avoiding threats. Grey relational analysis is used to deal with relationships between various cost indicators and constraints to solve the optimization model. The model is applied to a problem involving 17 radar threats, 5 missile threats, 10 artillery threats, and 2 climate threats to obtain an optimal flight path.
8 capacity-analysis ( Transportation and Traffic Engineering Dr. Sheriff El-B...Hossam Shafiq I
This document discusses concepts related to transportation capacity analysis including:
- Definitions of level of service (LOS) categories A through F and their characteristics.
- How capacity is defined as the maximum hourly rate of vehicles that can pass a point under prevailing conditions.
- Procedures from the Highway Capacity Manual (HCM) for calculating capacity for basic freeway sections and the impacts of factors like lane width, lateral clearance, and free flow speed.
- The relationships between capacity, LOS, and transportation design and how capacity analysis can inform design.
In this presentation, a new routing model was introduced in the form of integer linear programming by combining the concepts of time windows and multiple demands and by considering the two contradictory goals of minimizing travel: cost and maximizing demand coverage.
The document discusses various formulations of the Vehicle Routing Problem with Backhauls (VRPB). It begins by providing background on the VRPB and its history. It then describes several common variants of the VRPB that have been studied in literature, including the Vehicle Routing Problem with Backhauls (VRPB), Mixed Vehicle Routing Problem with Backhauls (MVRPB), Multiple Depot Mixed Vehicle Routing Problem with Backhauls (MDMVRPB), Vehicle Routing Problem with Backhauls and Time Windows (VRPBTW), and others. For each variant, the document outlines key characteristics and constraints and references relevant literature and studies.
Queuing theory and traffic flow analysisReymond Dy
This document discusses queuing theory and traffic flow analysis models. It describes common assumptions in queuing models, such as arrival and departure patterns, number of service channels, and queuing discipline. Four specific queuing models are explained for traffic analysis: D/D/1 for simple systems, M/D/1 and M/M/1 where traffic intensity is less than 1, and M/M/N where intensity may be greater than 1. Key metrics defined include average queue length, waiting time, and time in the system. Formulas are provided for calculating these metrics in M/D/1, M/M/1, and M/M/N queuing models.
IRJET- A Comparative Forecasting Analysis of ARIMA Model Vs Random Forest Alg...IRJET Journal
This document presents a comparative analysis of forecasting energy demand using two different methods: an ARIMA time series model and a Random Forest machine learning algorithm. Both methods are applied to monthly and yearly timespan data from a small-scale industrial load dataset. The accuracy of forecasts from each method is compared. The document provides background on the importance of energy forecasting for power grid management. It also describes the ARIMA and Random Forest models in more detail for short-term and long-term load forecasting.
This document summarizes research into improving models for predicting traffic-actuated phase times in traffic signal timing design. Existing models make simplifying assumptions that result in inaccurate phase time predictions. The research aims to develop an improved methodology by accounting for operational effects like progression and queue blockage. Experimental results indicate the new methodology more accurately calculates actuated phase times, which could lead to better traffic signal timing plans and reduced congestion.
Multi depot Time-dependent Vehicle Routing Problem with Heterogeneous FleetArian Razmi Farooji
The document summarizes a study comparing NSGA II and MOSA algorithms for solving a multi-depot vehicle routing problem with time-dependent travel times and a heterogeneous fleet. The problem involves routing vehicles from multiple depots to serve customers within time windows while minimizing costs and number of routes. NSGA II and MOSA were tested on randomly generated small, medium, and large problems. Results showed that on average, MOSA performed better than the model on small problems, while NSGA II performed comparably to the model.
Multi-objective and Multi-constrained UAV Path Plan Optimum Selection Based o...Angelo State University
This document discusses optimizing flight path planning for unmanned aerial vehicles (UAVs) using grey relational analysis. It establishes an optimal decision-making system and mathematical model for UAV flight paths that considers multiple objectives like minimizing costs and avoiding threats. Grey relational analysis is used to deal with relationships between various cost indicators and constraints to solve the optimization model. The model is applied to a problem involving 17 radar threats, 5 missile threats, 10 artillery threats, and 2 climate threats to obtain an optimal flight path.
8 capacity-analysis ( Transportation and Traffic Engineering Dr. Sheriff El-B...Hossam Shafiq I
This document discusses concepts related to transportation capacity analysis including:
- Definitions of level of service (LOS) categories A through F and their characteristics.
- How capacity is defined as the maximum hourly rate of vehicles that can pass a point under prevailing conditions.
- Procedures from the Highway Capacity Manual (HCM) for calculating capacity for basic freeway sections and the impacts of factors like lane width, lateral clearance, and free flow speed.
- The relationships between capacity, LOS, and transportation design and how capacity analysis can inform design.
In this presentation, a new routing model was introduced in the form of integer linear programming by combining the concepts of time windows and multiple demands and by considering the two contradictory goals of minimizing travel: cost and maximizing demand coverage.
The document discusses various formulations of the Vehicle Routing Problem with Backhauls (VRPB). It begins by providing background on the VRPB and its history. It then describes several common variants of the VRPB that have been studied in literature, including the Vehicle Routing Problem with Backhauls (VRPB), Mixed Vehicle Routing Problem with Backhauls (MVRPB), Multiple Depot Mixed Vehicle Routing Problem with Backhauls (MDMVRPB), Vehicle Routing Problem with Backhauls and Time Windows (VRPBTW), and others. For each variant, the document outlines key characteristics and constraints and references relevant literature and studies.
Queuing theory and traffic flow analysisReymond Dy
This document discusses queuing theory and traffic flow analysis models. It describes common assumptions in queuing models, such as arrival and departure patterns, number of service channels, and queuing discipline. Four specific queuing models are explained for traffic analysis: D/D/1 for simple systems, M/D/1 and M/M/1 where traffic intensity is less than 1, and M/M/N where intensity may be greater than 1. Key metrics defined include average queue length, waiting time, and time in the system. Formulas are provided for calculating these metrics in M/D/1, M/M/1, and M/M/N queuing models.
IRJET- A Comparative Forecasting Analysis of ARIMA Model Vs Random Forest Alg...IRJET Journal
This document presents a comparative analysis of forecasting energy demand using two different methods: an ARIMA time series model and a Random Forest machine learning algorithm. Both methods are applied to monthly and yearly timespan data from a small-scale industrial load dataset. The accuracy of forecasts from each method is compared. The document provides background on the importance of energy forecasting for power grid management. It also describes the ARIMA and Random Forest models in more detail for short-term and long-term load forecasting.
This document discusses vehicle routing and scheduling models and algorithms. It introduces basic models like the Traveling Salesman Problem (TSP), Vehicle Routing Problem (VRP), and Pickup and Delivery Problem with Time Windows (PDPTW). Construction heuristics like savings, insertion, and set covering algorithms are presented to find initial feasible solutions that can then be improved using local search methods. The document outlines practical considerations and recent variants like dynamic and stochastic routing problems.
This document contains an assignment submission for a course on computer based optimization methods. It includes the student's name, registration number, learning center details, course and subject information, date of submission, and spaces for marks awarded and evaluator signatures.
The document also contains the student's answers to 4 questions. The questions are about applications of operations research, Erlang distributions, solving a linear programming problem graphically, and using finite queuing tables. The student provides detailed responses to each question discussing the relevant concepts.
This document discusses multi-modal journey planning and describes a proposed solution approach. It summarizes the multi-modal journey planning problem, characteristics, previous work, and proposes a hybrid approach using a mathematical programming model combined with heuristic methods like Dijkstra's algorithm. The approach involves using the programming model to solve the multi-modal journey planning problem after applying Dijkstra's algorithm and graph techniques to pre-process the data.
Route optimization algorithm are the mathematical formula that solve routing problems..
Some types of routing:
1) Vehicle Routing Problem (VRP)
2) Traveling Salesman Problem (TSP)
3) Ant Colony Optimization (ACO)
Quasi dynamic traffic assignment on the large scale congested network of Noor...Luuk Brederode
Presentation at the European transport conference 2016 (Barcelona) (full paper available from https://aetransport.org/past-etc-papers/conference-papers-2016?abstractId=4872&state=b)
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
IRJET- Performance Analysis of a Synchronized Receiver over Noiseless and Fad...IRJET Journal
This document summarizes the performance analysis of a synchronized receiver over noiseless and fading channels. It presents a baseband communications system that implements data phase transmission using a single-tone waveform. The behavior of the received signal when transmitted over a noiseless channel and a fading frequency selective channel with additive white Gaussian noise is analyzed. Key plots analyzed include the channel output power spectrum, cross-spectral phase between the equalizer input and output, control signal for the equalizer, and scatter plots of the equalizer input, output, and descrambler output. The analysis shows distortion of the signal due to noise in the fading channel.
This paper proposes a Cycle-count Accurate Transaction level (CCA-TLM) full bus modeling technique called Composite Master-Slave-pair and Arbiter Transaction (CMSAT) model. The CMSAT model uses a two-phase arbiter model and master-slave models to efficiently and accurately simulate bus contention in complex Multi-Processor System-on-Chip designs. Experimental results show the CMSAT model performs 23 times faster than a Cycle-Accurate bus model while maintaining 100% accurate timing information.
This document discusses route choice models and recent developments in the field. It introduces the basic components of a route choice model, including a transportation network, origin-destination pairs, link and path attributes. It then describes several classic models: the shortest path model, Dial's approach using a multinomial logit model on efficient paths, and the path size logit which addresses issues with overlapping paths in the multinomial logit. The document also discusses challenges with path enumeration and different approaches to address this such as stochastic path generation and sampling of alternatives from the universal set of paths.
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
Urban transportation system - methods of route assignmentStudent
The document discusses various methods of route assignment in transportation systems, including:
- All-or-nothing assignment method, which assigns all trips to the minimum path but does not account for capacity.
- Direction curve method, which predicts route usage based on travel time or distance saved on a new facility.
- Capacity restraint assignment techniques, which iteratively assign trips accounting for changing travel times due to congestion.
- Multi-route assignment technique, which recognizes that not all travelers choose the absolute minimum path and distributes trips across multiple routes factoring attributes like travel time and cost.
This document summarizes different techniques for assigning routes in transportation network modeling. It describes the all-or-nothing assignment method, direction curve method, capacity restraint assignment techniques, and multi-route assignment technique. For each method, it provides details on the approach, limitations, and examples of models that use the technique. The document is presented by five students as part of their course on urban transportation systems.
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
Adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. This is of particular interest in regions of high traffic density, which may be caused by high volume peak time traffic, accidents or closure of one or more lanes of the road.
This document summarizes a presentation on a new Hybrid Optimization of Train Schedules (HOTS) model for improving rail capacity through timetable management. HOTS uses simulation data and optimization to automatically reschedule trains, resolving conflicts while maintaining operational constraints. It was tested on single-track and multi-track corridors, successfully improving initial timetables by reducing conflicts and compressing schedules. HOTS demonstrates the tradeoff between capacity utilization and levels of service under different initial timetable scenarios. Future work includes enhancing the model's capabilities and applying it to other rail networks like public transit.
The talk I gave at WBS 2020 Quant Finance Conference, Spring Edition, on "re-imagining" XVA so as to integrate it naturally into the front office workflow.
The key idea is to represent all FMTMs in spectral form via inline regression (even those FMTMs that are originally generated analytically within forward MC), and to treat this step as completion of "extended model" calibration. The regression coefficients can then be treated as derived market data, somewhat similar to non-parametric local volatility.
Viewed this way, extended model (MC) is generating not only true background factors, but also FMTMs, which can be trivially reconstructed when and where needed, together with the rest of the background factors. Collateral dynamics specification can then be interpreted as XVA "payoff", possibly scripted.
1) The document discusses a method for calculating capital valuation adjustment (KVA), which accounts for the cost of regulatory capital.
2) It proposes the stochastic grid bundling method (SGBM) as an efficient technique for pricing KVA that can handle the "P-in-Q" problem more accurately than approximation methods.
3) Numerical examples applying SGBM to interest rate derivatives show it provides close results to nested Monte Carlo with much lower computational cost, and allows for hedging the volatility of KVA costs.
The document summarizes the SPLT Transformer method for addressing optimism bias in sequence modeling for reinforcement learning. It introduces limitations in previous offline RL methods, describes the SPLT Transformer approach which uses a sampling-based planning algorithm and separate transformer models for policy and world prediction. Experiments show SPLT Transformer outperforms previous offline RL baselines on D4RL benchmarks and a simulated self-driving task, generalizing better to unseen data by addressing overly optimistic behavior through trajectory sampling and selection.
This document discusses traffic simulation and modelling. It covers different types of traffic models including microscopic, mesoscopic, and macroscopic models. Microscopic models track individual vehicles, macroscopic models aggregate traffic flow data, and mesoscopic models have aspects of both. Simulation models are presented as an alternative to analytical models which require extensive field data collection. The advantages of simulation include being cheaper than field studies and allowing testing of alternative strategies. Current traffic simulation software can model traffic flow at different scales.
This document discusses vehicle routing and scheduling models and algorithms. It introduces basic models like the Traveling Salesman Problem (TSP), Vehicle Routing Problem (VRP), and Pickup and Delivery Problem with Time Windows (PDPTW). Construction heuristics like savings, insertion, and set covering algorithms are presented to find initial feasible solutions that can then be improved using local search methods. The document outlines practical considerations and recent variants like dynamic and stochastic routing problems.
This document contains an assignment submission for a course on computer based optimization methods. It includes the student's name, registration number, learning center details, course and subject information, date of submission, and spaces for marks awarded and evaluator signatures.
The document also contains the student's answers to 4 questions. The questions are about applications of operations research, Erlang distributions, solving a linear programming problem graphically, and using finite queuing tables. The student provides detailed responses to each question discussing the relevant concepts.
This document discusses multi-modal journey planning and describes a proposed solution approach. It summarizes the multi-modal journey planning problem, characteristics, previous work, and proposes a hybrid approach using a mathematical programming model combined with heuristic methods like Dijkstra's algorithm. The approach involves using the programming model to solve the multi-modal journey planning problem after applying Dijkstra's algorithm and graph techniques to pre-process the data.
Route optimization algorithm are the mathematical formula that solve routing problems..
Some types of routing:
1) Vehicle Routing Problem (VRP)
2) Traveling Salesman Problem (TSP)
3) Ant Colony Optimization (ACO)
Quasi dynamic traffic assignment on the large scale congested network of Noor...Luuk Brederode
Presentation at the European transport conference 2016 (Barcelona) (full paper available from https://aetransport.org/past-etc-papers/conference-papers-2016?abstractId=4872&state=b)
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
IRJET- Performance Analysis of a Synchronized Receiver over Noiseless and Fad...IRJET Journal
This document summarizes the performance analysis of a synchronized receiver over noiseless and fading channels. It presents a baseband communications system that implements data phase transmission using a single-tone waveform. The behavior of the received signal when transmitted over a noiseless channel and a fading frequency selective channel with additive white Gaussian noise is analyzed. Key plots analyzed include the channel output power spectrum, cross-spectral phase between the equalizer input and output, control signal for the equalizer, and scatter plots of the equalizer input, output, and descrambler output. The analysis shows distortion of the signal due to noise in the fading channel.
This paper proposes a Cycle-count Accurate Transaction level (CCA-TLM) full bus modeling technique called Composite Master-Slave-pair and Arbiter Transaction (CMSAT) model. The CMSAT model uses a two-phase arbiter model and master-slave models to efficiently and accurately simulate bus contention in complex Multi-Processor System-on-Chip designs. Experimental results show the CMSAT model performs 23 times faster than a Cycle-Accurate bus model while maintaining 100% accurate timing information.
This document discusses route choice models and recent developments in the field. It introduces the basic components of a route choice model, including a transportation network, origin-destination pairs, link and path attributes. It then describes several classic models: the shortest path model, Dial's approach using a multinomial logit model on efficient paths, and the path size logit which addresses issues with overlapping paths in the multinomial logit. The document also discusses challenges with path enumeration and different approaches to address this such as stochastic path generation and sampling of alternatives from the universal set of paths.
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
Urban transportation system - methods of route assignmentStudent
The document discusses various methods of route assignment in transportation systems, including:
- All-or-nothing assignment method, which assigns all trips to the minimum path but does not account for capacity.
- Direction curve method, which predicts route usage based on travel time or distance saved on a new facility.
- Capacity restraint assignment techniques, which iteratively assign trips accounting for changing travel times due to congestion.
- Multi-route assignment technique, which recognizes that not all travelers choose the absolute minimum path and distributes trips across multiple routes factoring attributes like travel time and cost.
This document summarizes different techniques for assigning routes in transportation network modeling. It describes the all-or-nothing assignment method, direction curve method, capacity restraint assignment techniques, and multi-route assignment technique. For each method, it provides details on the approach, limitations, and examples of models that use the technique. The document is presented by five students as part of their course on urban transportation systems.
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.
Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.
The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.
Adjusting the flow in crucial areas can maximize the overall throughput of traffic along a stretch of road. This is of particular interest in regions of high traffic density, which may be caused by high volume peak time traffic, accidents or closure of one or more lanes of the road.
This document summarizes a presentation on a new Hybrid Optimization of Train Schedules (HOTS) model for improving rail capacity through timetable management. HOTS uses simulation data and optimization to automatically reschedule trains, resolving conflicts while maintaining operational constraints. It was tested on single-track and multi-track corridors, successfully improving initial timetables by reducing conflicts and compressing schedules. HOTS demonstrates the tradeoff between capacity utilization and levels of service under different initial timetable scenarios. Future work includes enhancing the model's capabilities and applying it to other rail networks like public transit.
The talk I gave at WBS 2020 Quant Finance Conference, Spring Edition, on "re-imagining" XVA so as to integrate it naturally into the front office workflow.
The key idea is to represent all FMTMs in spectral form via inline regression (even those FMTMs that are originally generated analytically within forward MC), and to treat this step as completion of "extended model" calibration. The regression coefficients can then be treated as derived market data, somewhat similar to non-parametric local volatility.
Viewed this way, extended model (MC) is generating not only true background factors, but also FMTMs, which can be trivially reconstructed when and where needed, together with the rest of the background factors. Collateral dynamics specification can then be interpreted as XVA "payoff", possibly scripted.
1) The document discusses a method for calculating capital valuation adjustment (KVA), which accounts for the cost of regulatory capital.
2) It proposes the stochastic grid bundling method (SGBM) as an efficient technique for pricing KVA that can handle the "P-in-Q" problem more accurately than approximation methods.
3) Numerical examples applying SGBM to interest rate derivatives show it provides close results to nested Monte Carlo with much lower computational cost, and allows for hedging the volatility of KVA costs.
The document summarizes the SPLT Transformer method for addressing optimism bias in sequence modeling for reinforcement learning. It introduces limitations in previous offline RL methods, describes the SPLT Transformer approach which uses a sampling-based planning algorithm and separate transformer models for policy and world prediction. Experiments show SPLT Transformer outperforms previous offline RL baselines on D4RL benchmarks and a simulated self-driving task, generalizing better to unseen data by addressing overly optimistic behavior through trajectory sampling and selection.
This document discusses traffic simulation and modelling. It covers different types of traffic models including microscopic, mesoscopic, and macroscopic models. Microscopic models track individual vehicles, macroscopic models aggregate traffic flow data, and mesoscopic models have aspects of both. Simulation models are presented as an alternative to analytical models which require extensive field data collection. The advantages of simulation include being cheaper than field studies and allowing testing of alternative strategies. Current traffic simulation software can model traffic flow at different scales.
2019-2020 research findings in Public Transit from the Centre for Transport Studies, University of TWENTE. The presented findings at the Transportation Research board include overcrowding, operational control, electric buses, and train assignment.
This document discusses traffic flow models and characteristics observed from field data. It describes single and multiregime models. Single regime models like Greenshields model traffic flow with one set of equations across the entire density range while multiregime models divide traffic flow into separate regimes with different governing equations for free flow, congested flow, and transitional flow conditions. The document also covers calibrating these models using field data to determine parameters like free flow speed and jam density.
Context-aware recommender systems (CARS) help improve the effectiveness of recommendations by adapting to users' preferences in different contextual situations. One approach to CARS that has been shown to be particularly effective is Context-Aware Matrix Factorization (CAMF). CAMF incorporates contextual dependencies into the standard matrix factorization (MF) process, where users and items are represented as collections of weights over various latent factors. In this paper, we introduce another CARS approach based on an extension of matrix factorization, namely, the Sparse Linear Method (SLIM). We develop a family of deviation-based contextual SLIM (CSLIM) recommendation algorithms by learning rating deviations in different contextual conditions. Our CSLIM approach is better at explaining the underlying reasons behind contextual recommendations, and our experimental evaluations over five context-aware data sets demonstrate that these CSLIM algorithms outperform the state-of-the-art CARS algorithms in the top-$N$ recommendation task. We also discuss the criteria for selecting the appropriate CSLIM algorithm in advance based on the underlying characteristics of the data.
Guest lecture at TU Delft: Travel demand models: from trip- to activity-basedLuuk Brederode
The document describes travel demand models, specifically comparing trip-based and activity-based models. It discusses that activity-based models add real-world constraints like household constraints and space/time constraints that make them better able to model today's transport questions involving mobility trends. The methodology of the BRUTUS activity-based model is then outlined, including how it uses a population synthesizer to generate synthetic populations, samples trip chains while respecting constraints, and runs destination and mode choice models to simulate trips.
1) Edward Robson developed a model to integrate economic evaluation of transport network changes with transport demand modeling to allow for rapid assessments of consumer benefits.
2) The model calculates consumer surplus for each origin-destination pair based on changes in generalized costs between the existing and proposed networks using a logsum formula.
3) The model was tested on a proposal to add a metro network to Sydney, finding an estimated increase in consumer surplus of $63,997 per morning commute period according to the logsum calculation.
Traffic assignment of motorized private transport in OmniTRANS transport plan...Luuk Brederode
Traffic assignment methods available in OmniTRANS transport planning software, categorized using the framework described in https://www.tandfonline.com/doi/abs/10.1080/01441647.2016.1207211
.
Presentation given during the 2016 conference Analysis and Control on Networks: trends and perspectives in Padua, Italy. Presentation provides an engineerings perspective on the various issues with see with the modelling and management of crowds, and some of the new modelling approaches.
Improving travel time estimates for car in the Dutch NRM-west strategic trans...Luuk Brederode
Presentation at the European transport conference 2017 (Barcelona) (full paper available from https://aetransport.org/past-etc-papers/conference-papers-2017?abstractId=5685&state=b)
- The document discusses methods for estimating traffic matrices, which describe the flow of traffic between origin-destination pairs in a network.
- Early methods relied on direct measurements, which are computationally intensive. Recent approaches use inference based on link measurements and routing information.
- Current research looks at techniques like principal component analysis, Kalman filtering, and incorporating additional data like access link measurements to improve estimates while reducing measurement needs. Hybrid methods combining analysis and some direct measurements are also promising.
Effective Travel Time Estimation: When Historical Trajectories over Road Netw...ivaderivader
DeepOD is a model that estimates travel times between origin-destination pairs based on historical trajectory data over road networks. It generates representations of the OD input and its affiliated trajectories using spatial and temporal embedding methods. This allows it to fully utilize trajectory information. DeepOD outperforms other OD-based models by reducing the gap between representations of the OD input and its trajectories through domain adaptation. However, it cannot fully capture differences between individual trajectories when making predictions.
Spot speed studies involve measuring the instantaneous speeds of vehicles at a point on the road. There are two main methods - measuring the time taken to travel a short distance or using a radar speed meter. Spot speeds are useful for traffic planning, road design, setting speed limits, and accident analysis. The radar method is efficient as it can instantly and automatically measure and record speeds accurately. Time-mean speed is the average of all instantaneous speeds measured, while space-mean speed represents the average speed of all vehicles traveling along a road section. Spot speed studies provide important input for various traffic engineering problems.
Presented by Dr Andrew Smith at the 2nd Economic Conference of the French Railway Regulatory Body (ARAF).
May 26th 2014 - Paris.
www.its.leeds.ac.uk/people/a.smith
www.regulation-ferroviaire.fr
The document discusses model predictive control (MPC) schemes for freeway traffic management that incorporate capacity drop phenomena. It summarizes the cell transmission model (CTM) and how capacity drop can be included in CTM simulations. It then describes MPC schemes that use CTM models to optimize ramp metering control. Computational analyses are presented that evaluate the solution times of the optimization problems in the MPC formulations. Simulation analyses compare density profiles from different CTM models on various traffic datasets.
The document discusses evaluating the reliability of road networks by accounting for variability in traffic demands and road capacities. It presents a new methodology that uses multiple demand and capacity scenarios to evaluate how traffic signal timing plans perform under different conditions. This provides measures of a plan's robustness. The methodology was tested on a case study road in California. Results showed the new higher-capacity timing plan reduced average delays and stops compared to the original plan under most scenarios.
Revolutionise your Machine Learning Workflow using Scikit-Learn PipelinesPhilip Goddard
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20151216 convergence of quasi dynamic assignment models
1. 1Challenge the future
Convergence of (quasi) dynamic
assignment models
Luuk Brederode
Consultant DAT.mobility /
PhD student Delft University
2. 2Challenge the future
Contents
1. Convergence? What and why?
2. Generic description of equilibria in strategic transport models
3. How do we reach convergence?
-break-
4. Example: convergence of quasi dynamic assignment model STAQ
within BBMA (Brabant Brede Model Aanpak)
5. Example: convergence of mode/destination choice model,
departure time model and STAQ (assignment) within BBMA
6. General conclusions
4. 4Challenge the future
Context: strategic transport
models
• Strategic models are used for long term decisions we are
interested in the long term effects of measures.
• Long term effects of measures can be (totally) different than
short term effects! This was already observed in the 1950’s:
6. 6Challenge the future
• Change in behavior is triggered by change of circumstances (e.g.
travel time on a route decreases; train ticket prices increase,…)
• Each change has its own response time
• One cannot change departure time within the day
• One does not change his mode or destination overnight (mainly due to mode and activity
availability and habit)
• Changing origin mostly involves relocation…
Seconds Minutes Hours Days Weeks Months Years Decades
Response time to changed circumstances
Change of Origin
Change of destination
Change of mode
Change of departure time
Why are long term effects
different? (1/2)
Change of route
7. 7Challenge the future
• Because these choice types are strongly related
• Because choices of different people are interrelated
• In peoples minds route, departure time, mode and destination are often chosen simultaneously
• Location choice is often related to the accessibility of a location
• Attractiveness of mode, destination, departure time and route alternatives depends on their
usage by other people.
Why are long term effects
different? (2/2)
Change of Origin
Change of destination
Change of mode
Change of departure time
Seconds Minutes Hours Days Weeks Months Years Decades
Change of route
Response time to changed circumstances
8. 8Challenge the future
Choices and interactions in
strategic transport models
• In transport models we assume sequential choices
• Not all transport models have a departure time choice model
• Mode and destination choice models are usually combined
• Most modern transport models have feedback loops
• Note that the assignment model itself contains a loop
between route demand and infrastructural supply
Change of Origin
Change of destination
Change of mode
Change of departure time
Change of route
Seconds Minutes Hours Days Weeks Months Years Decades
Response time to changed circumstances
Trip Generation model
Mode choice model
Destination choice model
Departure time choice model
Assignment model
9. 9Challenge the future
Feedback loops and iterations in
strategic transport models
• Usually models are equilibrated ‘from the inside out’:
Route Choice Model
Route demand
Network loading model
Route travel times
Assignment model
OD travel times
(skim matrix)
Departure Time
Choice Model
OD demand
(OD-matrix)
Mode/destination
Choice Model
To reach route choice equilibrium: x times assignment
To reach departure time choice equilibrium: y times departure time choice +
y*x times assignment
To reach total equilibrium: z times mode/destination choice +
z*y times departure time choice +
z*y*x times assignment
10. 10Challenge the future
Convergence – what and why?
Conclusions
• Convergence is the extent to which we have reached
equilibrium
• In strategic transport models we want to reach equilibrium
because we are interested in the long term effects of
measures
• Finding the equilibrium is computationally expensive because
we need to take into account:
• Interaction effects between different choices (mode, destination,
departure time and route)
• Interaction effects between people making these different
choices
12. 12Challenge the future
Demand and supply models
• Demand models determine demand on OD or route level,
given travel times on all ODpairs, routes, modes and
departure times.
• An ‘economist look’ on demand models:
Route Choice modelRoute travel times Route demand
Departure Time
Choice Model
Travel times per
departure time
(skim matrices)
Demand per departure
time (OD matrices)
Mode/destination
Choice Model
Modal travel times
(skim matrices)
Demand per mode
(OD matrices)
D
c Analogy with
distribution functions of
a gravity model ZKM
D=f1(c)
13. 13Challenge the future
Demand and supply models
• Supply models determine travel times on route or OD level,
given demand on all routes/ODpairs, departure times and
modes.
• An ‘economist look’ on supply models:
Network loading modelRoute demand Route travel time
Assignment model
for departure time t
Demand for
departure time t
(ODmatrix)
Travel times per
departure time (skim
matrices)
Assignment model
for mode m and
departure time t
Demand per mode
m, dep time t and
OD (skim matrices)
Demand per mode
(OD matrices)
D
c
Analogy with BPR
functions in a static
assignment model
c=f2(D)
14. 14Challenge the future
Relationship between demand and
supply
• Thus, we are looking for the intersection of supply and
demand curves:
• This can be formulated as a fixed point problem in which we
look for equilibrium Demand D* and cost c*:
• where: f1: demand model as function of cost
f2: supply model as function of demand
c
D=f1(c) c=f2(D)
D*
c*
* *
1
*
1 2
( )
( ( ))
D f c
f f D
15. 15Challenge the future
Relationship between demand and
supply
• However, our demand supply functions (f1 and f2):
• Cannot be expressed as analytical function;
• Are multidimensional (each route and OD pair have their own)
• Are non-separable (demand and cost on a route or OD pair can
be (and mostly are) dependent on cost and demand on other
routes and ODpairs
• So….
17. 17Challenge the future
Methods to reach convergence
• The most basic method is the method of repeated
approximations (MRA) simply puts demand and supply
models in a loop:
• As a formula (one Odpair/route):
• As a formula (matrixNotation):
• It has been proved that MRA only converges when the
combined supply and demand function is a
contraction map (see next slides)
ciDemandModel Di SupplyModel
1 2 1 1 1 2 1 1( ( )) ( ( ))i i i i iD f f D D f f D D
1 2 1 2( ( )) ( ( ))f f f f i i-1 i-1 i-1 i-1D D D I D D
1 2( ( ))f f i-1D
18. 18Challenge the future
Contraction map?? an example
• Assume single dimensional curves:
• This is a contraction map! MRA iterations (green dotted lines)
converges to the equilibrium, because:
D0
c0
D1
c1
D2
c2
D3
c3
D4
c4
c=f2(D)
(supply Model)
D=f1(c)
(Demand Model)
D
2 ( )f D
1( )f c
c
1
1 1
2
( ) 1.1 40 ( ) 1/ 1.1( 40)
( ) 0.75 0
D f c c f D D
c f D D
1
2 2 1
1
( ) ( ) ( )
( )
0.75 0.909
f D f D f Dc
D f c D D
19. 19Challenge the future
Non-contraction maps
1
1 1
2
( ) 1.1 40 ( ) 1/ 1.1( 40)
( ) 1.0 0
D f c c f D D
c f D D
1
1 1
2
( ) 1.0 40 ( ) 1/ 1.0( 40)
( ) 1.0 0
D f c c f D D
c f D D
1
2 2 1
1
( ) ( ) ( )
( )
1 0.909
f D f D f Dc
D f c D D
1
2 2 1
1
( ) ( ) ( )
( )
1 1
f D f D f Dc
D f c D D
Diverges! Cyclic unstable!
20. 20Challenge the future
Improving convergence
• Method of successive averages (MSA)
• Averages demand over all previous iterations
• As a formula (one Odpair/route):
• As a formula (matrixNotation):
• Virtually no extra calculation time needed per iteration
ciDemand model Di Supply ModelMSA iD
1iDi+=1
1 1 2 1 1
1
( ( ))i i i iD D f f D D
i
1 2
1
( ( ))f f
i
i i-1 i-1 i-1D D I D D
21. 21Challenge the future
MSA speeds up if contraction
1 0
1
( )
2
D D
0D1D
2 1
1
( )
3
D D
3 2
1
( )
4
D D
4 3
1
( )
5
D D
5 4
1
( )
6
D D
23. 23Challenge the future
Other averaging schemes based on
the MSA concept
• Apply instead of (when it is called Polyak)
• Reset the iterationnumber at a fixed iteration interval (Rich
and Nielsen (2015) advise resetting every 5 iteraties.
• Reset the iterationnumber using some scheme. Cantarella et
al (2015) advise to start with a reset interval of 2 iterations
and increase this number by 1 after each reset.
• Scaling the weighing factor using a factor <1. Cantarella et
al (2015) advise a scaling factor in the range [0.7,0.8].
• Method of weighed successive averages (MwSA) using
• The self regulating average (SRA): chooses a large or small
step size, based on the level of convergence of the current
iteration
1/i
1/i 2/3
1..
/d d
i
i i
24. 24Challenge the future
Weighing factors over iterations
MSA based methods (1/2)
• MRA vs methods compliant with Blum’s theorem
26. 26Challenge the future
Non-MSA based methods
• Newton and Broyden methods work quite well, but require
explicit calculation of Jacobian (matrix of partial derivatives)
and inversion of large matrices
• These methods are therefore not applicable to strategic
transport model systems
• Intersection method does not perform well in
multidimensional situations
• Fixed weighing factors: heuristic that proves to be very
application specific
29. 29Challenge the future
Choosing a convergence method /
averaging scheme
• Criteria:
• Level of convergence
• Speed of convergence (e.g. compared to MRA or MSA)
• Usage of heuristic parameters (not preferred)
• Complexity of implementation
• The level and speed of convergence can be determined by:
• The duality gap (preferred, since it is directly derived from the
definition of the user equilibrium)
• For departure time choice and mode destination choice models,
often ‘normal’ distance functions not using the cost are being
used (MSE,RMSE,…,SSIM)
30. 30Challenge the future
Convergence measure
route vs network loading model
• The duality gap is directly derived from the definition of the
users equilibrium of Wardrop (1952):
The journey times in all routes actually used are equal and less
than those which would be experienced by a single vehicle on any
unused route
Travel times on all used routes between an od pair must be
equal
• The duality gap is the normalized number of vehicle*hours
spent on the network, compared to the fastest route on each
OD pair.
𝑫𝑮 =
𝒐𝒅 𝒓∈𝑹 𝒐𝒅
𝑫 𝒐𝒅 𝒇 𝒓(𝒕 𝒓 − 𝒕 𝒎𝒊𝒏,𝒐𝒅)
𝒐𝒅 𝑫 𝒐𝒅 𝒕 𝒎𝒊𝒏,𝒐𝒅
31. 31Challenge the future
Convergence measure
route vs network loading model
• The stochastic duality gap is directly derived from the
duality gap and the definition of the stochastic user
equilibrium (Fisk 1980):
The perceived journey times in all routes actually used are equal
and less than those which would be experienced by a single
vehicle on any unused route
Perceived travel times on all used routes between an od pair
must be equal
• Given an Multinomial Logit route choice model, replace 𝒕 𝒓
by 𝒕 𝒓 +
𝟏
𝝁 𝒐𝒅
ln 𝑫 𝒐𝒅 𝒇 𝒓
• Derivation in Bliemer et al (2013)*
*http://atrf.info/papers/2013/2013_bliemer_raadsen_de_romph_smits.pdf
33. 33Challenge the future
Supply and demand models used
in this example
• We only focus on the assignment model
• We used:
• STAQ as network loading model;
• Multinomial logit as route choice model
• MSA and SRA as averaging schemes
Route Choice Model
Route demand
Network loading model
Route travel times
Assignment model
OD travel times
(skim matrix)
Departure Time
Choice Model
OD demand
(OD-matrix)
Mode/destination
Choice Model
34. 34Challenge the future
From static (STA) and dynamic (DTA)
assignment models to STAQ
Static models
• Speed-flow curve
• Stationary travel demand
• Single time period
• No hard capacity constraints
due to lack of node model
First order dynamic models
• Fundamental diagram
• Variable travel demand
• Multiple time periods
• Hard capacity constraints
due to explicit node model
STAQ
(Brederode et al. 2010, Bliemer et al. 2012)
• Fundamental diagram
• Stationary travel demand
• Single time period
• Hard capacity constraints
due to explicit node model
35. 35Challenge the future 35
From static to STAQ (1/2)
Capacity = 4000 veh/h
Capacity = 6000 veh/h
Demand= 4200 veh/h
A B
What is the queue length and travel time from A to B after one hour?
In traditional static network loading model:
- No physical queue, delay within the bottleneck
- Travel time derived from travel time function:
cap
cap
36. 36Challenge the future
From static to STAQ (2/2)
Capacity = 4000 veh/h
Capacity = 6000 veh/h
Demand= 4200 veh/h
A B
In STAQ: Squeezing…
- Queue length: 1150m
- Travel time: 12 min.
Queuing…
4000
0.95
4200
What is the queue length and travel time from A to B after one hour?
State 2 State 1State 3
37. 37Challenge the future
Options for STAQ
• Different options on how to use STAQ:
• With or without spillback (queuing phase can be disabled)
• Junction modelling:
• None
• Only turndelays (only route choice affected)
• Turncapacities and turndelays (route choice and network loading
affected)
• Averaging scheme
• Method of successive averages (MSA)
• Self Regulating Average (SRA)
38. 38Challenge the future
Test runs
• How do these options affect convergence?
• What would be a good tolerance for the duality gap value
Run# Title treshold Averaging scheme Spillback JM Iterations
1 MSA no spillback, no JM 1 MSA false False 100
2 MSA no spillback, turndelays 1 MSA false turndelays 100
3 MSA no spillback, JM 1 MSA false true 100
4 MSA spillback, no JM 1 MSA true false 100
5 MSA spillback, turndelays 1 MSA true turndelays 100
6 MSA spillback, JM 1 MSA true true 100
7 SRA no spillback, no JM 1 SRA false false 100
8 SRA no spillback, turndelays 1 SRA false turndelays 100
9 SRA no spillback, JM 1 SRA false true 100
10 SRA spillback, no JM 1 SRA true false 100
11 SRA spillback, turndelays 1 SRA true turndelays 100
12 SRA spillback, JM 1 SRA true true 100
39. 39Challenge the future
3.321 Centroids
142.336 Links
106.780 Nodes
808.708 Used OD pairs
1.272.330 Routes
Case: BBMA network (Province of
Noord Brabant)
41. 41Challenge the future
Convergence - conclusions
• Runs with spillback do NOT converge:
• interaction effects between users too large, therefore the implicit cost function is no
longer diagonally dominant
• The duality gap never gets below 5.0E-04 and keeps oscillating
• Runs witout spillback do converge sufficiently:
• MSA with full junction modelling: after 80 iterations (2:15 h) duality gap ≈ 1.0E-04
• SRA with full junction modelling: after 32 iterations (0:54 h) duality gap < 1.0E-04
• SRA with full junction modelling: after 40 iterations (1:07 h) duality gap ≈ 5.0E-03
• Run without spillback and junction modelling truly converges:
• SRA after 12 iterations (0:19 h) duality gap < 1.0E-04
• SRA after 19 iterations (0:30 h) duality gap < 1.0E-05
• SRA after 100 iterations (2:37 h) duality gap <5.0E-11 (~1E-14 == machine precision)
42. 42Challenge the future
Determining tolerance on duality
gap
• According to Boyce, Ralevic-Dekic and Bar-Gera (2004)*, a
duality gap of 1E-04 should be enough.
• Run 9 (SRA, no spillback, JM) proved to be the most realistic,
whilst still converging.
• For this run, we compared the link flows of the following
intermediate iterations with the most converged situation
(iteration 100, DG =3.5E-05)
• We thus used iteration 100 as a benchmark
*David Boyce, Biljana Ralevic-Dekic, and Hillel Bar-Gera - Convergence of Traffic Assignments: How Much Is Enough?
Technical Report Number 155, January 2004 - National Institute of Statistical Sciences
49. 49Challenge the future
Determining tolerance on duality
gap - conclusions
• Around Tilburg, a duality gap tolerance of 1E-03 proved to be
low enough
• Network wide, a duality gap tolerance of 5E-04 proved to be
low enough. This is mainly needed in Eindhoven, where there
where some unresolved some issues with network coarsity.
• Similar results on Haaglanden, Amsterdam and Leuven
networks
50. 50Challenge the future
5. Example: convergence of
mode/destination choice model,
departure time choice model and
STAQ
51. 51Challenge the future
Supply and demand models used
in this example
• We only focus on the assignment model
• We used:
• MD-PIT departure time choice model (logit based)
• Doubly constrained multimodal gravity model for
mode/destination choice
Route Choice Model
Route demand
Network loading model
Route travel times
Assignment model
OD travel times
(skim matrix)
Departure Time
Choice Model
OD demand
(OD-matrix)
Mode/destination
Choice Model
52. 52Challenge the future
Departure Time Choice Model
(TOD)
• Convergence of TOD iterations (using STAQ assignments
converged to 5E-04 )
55. 55Challenge the future
Tolerance on the duality gap
(departure time loop)
• After iteration 4, no noticeable changes occur
• Which means –again- a tolerance on the duality gap of 1E-04
• Note: we use an assumption that simplifies the departure
time choice model:
• Travel time in the off peak periods is not affected by the
increase of traffic demand due to departure time shifts
• This means that once demand is in the off peak, it will stay
there over iterations
58. 58Challenge the future
Tolerance on the duality gap
(gravity model loop)
• After iteration 4, no noticeable changes occur (as in TOD)
• Which means –again- a tolerance on the duality gap of 1E-04
• Note:
• Distribution functions where not recalibrated after replacing
static traffic assignment model with STAQ
• As such, the gravity model is too sensitive, and too much
demand was moved to public transport and bike
• Recalibration of the gravity model is likely to lead to a more
subtle equilibrium, and thus more car users, and thus harder to
equilibrate the assignment model (note: duality gaps on sheet 40 won’t
be affected, because these where based on runs without feedback loops to gravity
model and TOD)
59. 59Challenge the future
Conclusions – assignment model
• Adding spillback to the assignment model causes non-
convergence
• Junction modelling also has a clear impact on convergence of
the assignment model, but acceptable levels of convergence
can still be reached
• The self regulating average improves convergence of
assignment model, making it capable to reach machine
precision
60. 60Challenge the future
Conclusions – departure time and
mode/destination models
• Departure time choice model converges really fast (3
iterations), mainly due to assumption of fixed travel times in
off peak period
• Mode/destination choice model parameters need to be
recalibrated due to change in assignment method (definition
of travel time has changed!)
• Mode/destination choice loop also converges relatively fast (3
iterations)
62. 62Challenge the future
Conclusions part 1
• In strategic models, (user) equilibrium is an important
concept. Due to interaction effects between choices and
between people making those choices
• Each demand model within strategic transport models
(destination choice, mode choice, departure time choice,
route choice) should be brought in equilibrium with its
respective supply model.
• When assuming that the equilibrium can mathematically be
described as a fixed point problem, we can use MSA based
techniques to enforce and/or speed up convergence towards
it.
63. 63Challenge the future
Conclusions part 2
• It is worthwhile to spend some time on finding a way to
minimize the number of iterations needed for all equilibria in
the model (z*y*x assignments, z*y TOD’s, z gravity models)
• The duality gap as convergence measure is the most direct
translation of the definition of user equilibrium, and as such
the most suitable indicator
• A duality gap value of 1E-04 seems to be a suited level of
convergence for assignment, TOD and gravity model
• This seems to be a model independent conclusion
64. 64Challenge the future
Thank you for your attention!
• Looking for a interesting topic for your masters thesis
assignment or internship?
• Equillibria and convergence
• Quasi dynamic assignment models
• Demand matrix estimation using (quasi) dynamic assignment
models
• Network aggregation to improve calculation speed
• Automatic transport model network generation using TomTom
or Here data sources
• Improved bicycle modelling in strategic model systems
• …
• Drop by (room 4.14), or mail me at lbrederode@dat.nl