A macroscopic traffic model based on the Markov chain process is developed for urban traffic networks. The method utilizes existing census data rather than measurements of traffic to create parameters for the model. Four versions of the model are applied to the Philadelphia regional highway network and evaluated based on their ability to predict segments of highway that possess heavy traffic.
Application of a Markov chain traffic model to the Greater Philadelphia RegionJoseph Reiter
A macroscopic traffic model based on the Markov chain process is developed for urban traffic networks. The method utilizes existing census data rather than measurements of traffic to create parameters for the model. Four versions of the model are applied to the Philadelphia regional highway network and evaluated based on their ability to predict segments of highway that possess heavy traffic.
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.
IRJET- Traffic Study on Mid-Block Section & IntersectionIRJET Journal
This document summarizes a study on traffic patterns at mid-block sections and intersections in Borawan, India. Traffic volume data was collected over four days at five locations experiencing heavy traffic issues, including post office chouraha and gaaytri mandir tiraha. Both manual and automatic counting methods were used to collect data on vehicle types at different times of day. The results show peak traffic volumes during morning and evening rush hours. The study aims to improve traffic conditions and reduce accidents by examining the current levels of service and making recommendations for infrastructure improvements like expanding road dimensions or constructing flyovers. A literature review discusses previous research on pedestrian and vehicle behavior at crosswalks, and the impact of mid-block crosswalks on traffic
This document discusses developing a traffic simulation model to characterize heterogeneous or mixed traffic conditions in India. It reviews literature on quantifying the mix of different vehicle types and studying the impact of slow moving vehicles. The objective is to model traffic in Agartala, Delhi, Guwahati, and Kolkata on single lane urban roads. Field data will be collected using video cameras and analyzed using simulation software. The expected outcome is a simulation model that provides a better understanding of heterogeneous traffic flow to improve transportation infrastructure utilization and regulation.
This document summarizes a study of traffic flow characteristics for heterogeneous traffic in India. Speed, flow, and time headway data were collected from a six-lane urban road and analyzed. Headways between different vehicle combinations were found to best fit several statistical distributions. Speed-flow curves were plotted to determine the speed at which optimal flow occurs, though the study was limited by only using one hour of data. The results provide insight into modeling headways and understanding traffic flow in heterogeneous, mixed traffic conditions.
A Macroscopic Dynamic model integrated into Dynamic Traffic Assignment: advan...JumpingJaq
This document describes a dynamic macroscopic traffic model integrated into dynamic traffic assignment. The model uses continuous flow equations to model traffic flow on links between nodes. Nodes route traffic according to conservation and maximization principles. The model is calibrated using a case study network with over 500 zones, showing travel times comparable to a mesoscopic model but with faster computation. While coarse, the dynamic macroscopic model provides an efficient alternative for large-scale dynamic traffic assignment problems.
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.
Traffic assignment models are used to estimate traffic flows on a transportation network based on origin-destination flows and the network's topology, link characteristics, and performance functions. Traffic is assigned to paths between origin-destination pairs based on travel time or impedance. Traffic assignment is a key part of travel demand forecasting and is used to predict future network flows and performance under different planning scenarios. Common traffic assignment methods include all-or-nothing assignment, user equilibrium assignment, and system optimum assignment.
Application of a Markov chain traffic model to the Greater Philadelphia RegionJoseph Reiter
A macroscopic traffic model based on the Markov chain process is developed for urban traffic networks. The method utilizes existing census data rather than measurements of traffic to create parameters for the model. Four versions of the model are applied to the Philadelphia regional highway network and evaluated based on their ability to predict segments of highway that possess heavy traffic.
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.
IRJET- Traffic Study on Mid-Block Section & IntersectionIRJET Journal
This document summarizes a study on traffic patterns at mid-block sections and intersections in Borawan, India. Traffic volume data was collected over four days at five locations experiencing heavy traffic issues, including post office chouraha and gaaytri mandir tiraha. Both manual and automatic counting methods were used to collect data on vehicle types at different times of day. The results show peak traffic volumes during morning and evening rush hours. The study aims to improve traffic conditions and reduce accidents by examining the current levels of service and making recommendations for infrastructure improvements like expanding road dimensions or constructing flyovers. A literature review discusses previous research on pedestrian and vehicle behavior at crosswalks, and the impact of mid-block crosswalks on traffic
This document discusses developing a traffic simulation model to characterize heterogeneous or mixed traffic conditions in India. It reviews literature on quantifying the mix of different vehicle types and studying the impact of slow moving vehicles. The objective is to model traffic in Agartala, Delhi, Guwahati, and Kolkata on single lane urban roads. Field data will be collected using video cameras and analyzed using simulation software. The expected outcome is a simulation model that provides a better understanding of heterogeneous traffic flow to improve transportation infrastructure utilization and regulation.
This document summarizes a study of traffic flow characteristics for heterogeneous traffic in India. Speed, flow, and time headway data were collected from a six-lane urban road and analyzed. Headways between different vehicle combinations were found to best fit several statistical distributions. Speed-flow curves were plotted to determine the speed at which optimal flow occurs, though the study was limited by only using one hour of data. The results provide insight into modeling headways and understanding traffic flow in heterogeneous, mixed traffic conditions.
A Macroscopic Dynamic model integrated into Dynamic Traffic Assignment: advan...JumpingJaq
This document describes a dynamic macroscopic traffic model integrated into dynamic traffic assignment. The model uses continuous flow equations to model traffic flow on links between nodes. Nodes route traffic according to conservation and maximization principles. The model is calibrated using a case study network with over 500 zones, showing travel times comparable to a mesoscopic model but with faster computation. While coarse, the dynamic macroscopic model provides an efficient alternative for large-scale dynamic traffic assignment problems.
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.
Traffic assignment models are used to estimate traffic flows on a transportation network based on origin-destination flows and the network's topology, link characteristics, and performance functions. Traffic is assigned to paths between origin-destination pairs based on travel time or impedance. Traffic assignment is a key part of travel demand forecasting and is used to predict future network flows and performance under different planning scenarios. Common traffic assignment methods include all-or-nothing assignment, user equilibrium assignment, and system optimum assignment.
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.
2013 methodology for the calibration of vissim in mixed trafficDaniel Sitompul
This document describes a methodology for calibrating the microsimulation software VISSIM for modeling mixed traffic conditions. The methodology involves representing the unique characteristics of vehicles and geometry in mixed traffic, identifying calibration parameters through sensitivity analysis, setting parameter ranges heuristically, and using an optimization model like a genetic algorithm to determine parameter values that minimize the error between simulated and observed delays. The methodology is demonstrated through a case study of signalized intersections in Mumbai, India featuring mixed traffic.
This document summarizes a study that used a dual graph representation to simulate urban traffic from both a microscopic and macroscopic perspective. The study represented roads as nodes and intersections as links to form dual graphs of city networks. A traffic model was implemented on these dual graphs to simulate vehicle movement and analyze overall traffic flow patterns. Simulation results showed that regular lattice grid networks performed better than scale-free self-organized networks in terms of overall traffic capacity and individual vehicle traveling times. However, the model could be improved by incorporating more realistic traffic control methods and vehicle navigation strategies.
Beyond Level of Service – Towards a relative measurement of congestion in pla...JumpingJaq
This document discusses problems with using level of service (LOS) as the sole measure of congestion in transport planning. It proposes developing a relative measurement of congestion that considers additional factors like the subjective experience of drivers, prioritization of different road functions, and growing tolerance for congestion. The methodology involves: 1) Identifying a volume-capacity ratio where poor LOS is likely due to excess demand rather than capacity issues. 2) Developing indices that weight the importance of volume-capacity ratios based on factors like strategic importance, density of activity, amenity, and modal compatibility. The results would allow planners to more easily evaluate traffic LOS in context of the entire network.
This document describes a study that used an ARIMA time series model to estimate traffic arrival patterns at three signalized intersections on Route 18 in New Jersey. Simulation data from Paramics was used to collect vehicle counts and headways under different demand levels. The ARIMA model was found to predict arrival patterns more accurately than the conventional Poisson model, particularly for over dispersed and under dispersed traffic scenarios. Specifically, the ARIMA model had smaller deviations from the simulation data for metrics like headway distribution, vehicle counts per cycle, and variance-to-mean ratio. This indicates that the ARIMA time series model provides a better approach for estimating real-world traffic arrival patterns compared to traditional distributions like Poisson.
Chapter 6 Fundamentals of traffic flowFayaz Rashid
The document discusses fundamental principles of traffic flow, including the primary elements of traffic flow such as flow, density, speed, and headway. It describes flow-density relationships and the fundamental diagram of traffic flow. Mathematical models for describing macroscopic traffic flow relationships are presented, including the Greenshields model relating traffic density to speed. The primary elements, flow-density relationships, and Greenshields traffic flow model are summarized for understanding traffic flow characteristics.
TE004, A Study On Feasible Traffic Operation Alternatives At Signalized Inter...Saurav Barua
This study analyzed traffic operations at a busy signalized intersection in Dhaka, Bangladesh using traffic simulation software VISSIM. Four alternatives were considered: 1) banning right turns, 2) optimizing signal timing, 3) constructing a one-way overpass, and 4) constructing two overpasses. Traffic data was collected and used to calibrate the VISSIM model. The alternatives were then simulated and evaluated based on average speed, delay, and queue length. Constructing a single overpass was found to provide the greatest benefits, increasing average speed by 250% and reducing delays and queues by over 90%, making it the recommended alternative to improve traffic flow at the intersection.
Modeling business management systems transportationSherin El-Rashied
Introduction
How IT &Business Process Fit Together
What is modeling?
What is Simulation?
Modeling & Simulation in Business Process Management
The Seven-Step Model-Building Process
Transportation
An overview on transportation modeling
Transport model scope & structure
Car Traffic Jam Problem
Aim of Transportation Model
Types of Traffic Models
Microscopic Traffic model & Simulation
Cellular Automaton model
Conclusion
Solving Transportation Problem by Software Application
Class Example
The document discusses improvements to the modeling of right turns on red (RTOR) in the Highway Capacity Manual 2010 (HCM 2010). It summarizes the existing HCM 2010 procedures that do not adequately account for RTOR flows. A new proposed methodology is described that estimates maximum RTOR flow rates and incorporates them into flow profiles to generate more accurate performance measures. Experimental results demonstrate that the proposed logic improves the modeling accuracy of flow profiles, consistency with microscopic simulations, and control delay estimates compared to not accounting for RTOR.
Data driven public_transportation_operation_by_trips_jaehong_minJaehong MIN
This document summarizes the TRIPS (Travel Record based Integrated Public transport operation System) developed by KRRI (Korea Railroad Research Institute) to analyze and improve public transportation systems using smart card transaction data. The key points are:
1. TRIPS uses smart card data from public transit systems to analyze current demand and usage patterns, estimate demand under different operational scenarios, and evaluate the effects of service changes.
2. It has been applied to the public transit system in Seoul, analyzing over 12 million daily transactions to examine routes, ridership, transfers and more.
3. TRIPS has also been implemented in other local governments and can help optimize local transit networks and scheduling. Further development includes integrating
A New Paradigm in User Equilibrium-Application in Managed Lane PricingCSCJournals
Ineffective use of the High-Occupancy-Vehicle (HOV) lanes has the potential to decrease the overall roadway throughput during peak periods. Excess capacity in HOV lanes during peak periods can be made available to other types of vehicles, including single occupancy vehicles (SOV) for a price (toll). Such dual use lanes are known as “Managed Lanes.” The main purpose of this research is to propose a new paradigm in user equilibrium to predict the travel demand for determining the optimal fare policy for managed lane facilities. Depending on their value of time, motorists may choose to travel on Managed Lanes (ML) or General Purpose Lanes (GPL). In this study, the features in the software called Toll Pricing Modeler version 4.3 (TPM-4.3) are described. TPM-4.3 is developed based on this new user equilibrium concept and utilizes it to examine various operating scenarios. The software has two built-in operating objective options: 1) what would the ML operating speed be for a specified SOV toll, or 2) what should the SOV toll be for a desired minimum ML operating speed. A number of pricing policy scenarios are developed and examined on the proposed managed lane segment on Interstate 30 (I-30) in Grand Prairie, Texas. The software provides quantitative estimates of various factors including toll revenue, emissions and system performance such as person movement and traffic speed on managed and general purpose lanes. Overall, among the scenarios examined, higher toll rates tend to generate higher toll revenues, reduce overall CO and NOx emissions, and shift demand to general purpose lanes. On the other hand, HOV preferential treatments at any given toll level tend to reduce toll revenue, have no impact on or reduce system performance on managed lanes, and increase CO and NOx emissions.
A Framework for Traffic Planning and Forecasting using Micro-Simulation Calib...ITIIIndustries
This paper presents the application of microsimulation for traffic planning and forecasting, and proposes a new framework to model complex traffic conditions by calibrating and adjusting traffic parameters of a microsimulation model. By using an open source micro-simulator package, TRANSIMS, in this study, animated and numerical results were produced and analysed. The framework of traffic model calibration was evaluated for its usefulness and practicality. Finally, we discuss future applications such as providing end users with real time traffic information through Intelligent Transport System (ITS) integration.
This document summarizes a study on performance measures for two-way, two-lane highways. It discusses the measures and methodologies used over time in the Highway Capacity Manual (HCM), including their shortcomings identified in other research. Alternative performance measures proposed in other studies are also reviewed. The document aims to provide an extensive literature review on capacity and level of service for two-way, two-lane highways, comparing different performance measures and factors affecting capacity estimations.
This document discusses performance measures for two-way, two-lane highways and identifies shortcomings in the current Highway Capacity Manual methodology. It summarizes alternative performance measures that have been suggested in research to address the discrepancies, such as Percent Impeded and Average Travel Speed. The document also reviews empirical models that have been developed to predict level of service based on these alternative measures and identifies additional measures used in different studies and countries. It concludes by recommending further research is needed to determine the best headway threshold for differentiating platoons and to identify the most suitable level of service measure for different road environments as the HCM may not always be applicable.
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.
Accessibility Analysis and Modeling in Public Transport Networks - A Raster b...Beniamino Murgante
The document summarizes research on modeling accessibility in public transportation networks using a raster-based approach. The research aimed to create an accessibility indicator for jobs via public transit that had low data requirements to allow transfer to other regions. The study area was the capital region of Denmark. Accessibility was modeled using land use, transportation, and temporal components. The model calculated cost distances from population and job centers using rasterized transportation network data. Results showed variability in accessibility scores and generally aligned with commuting statistics. The raster approach allowed fast calculation with low data needs but did not fully account for travel time or mode changes.
Accessibility analysis of public transport networks in urban areasMayank Bansal
The document analyzes methodologies for assessing public transport accessibility in urban areas. It discusses objectives to study existing methods, applicability to India, impacts of accessibility, and future research scope. As a case study, it examines a study that measured public transport accessibility levels (PTAL) for different zones in Ahmedabad, India using a modified version of the UK methodology. Key findings were that accessibility was best in city centers and outskirts had poor accessibility. Improving access for all sections of society was recommended.
Application of finite markov chain to a model of schoolingAlexander Decker
This document discusses the application of finite Markov chains to model school progression. It begins by introducing key concepts of Markov chains including states, transition probabilities, and transition matrices. It then presents a model of school progression with states representing each year of school plus outcomes of graduating or dropping out. Transition probabilities between states are used to formulate the model. The document applies this model to secondary school data from Nigeria to predict academic progression. It analyzes the data using knowledge of finite Markov chains and finds the model provides an efficient way to predict student academic progress.
Immigration and Settlement Programming in SW OntarioJennifer Long
Community-based research: Qualitative investigation concerning newcomers' first-hand experiences of targeted, universal and mixed service provision in London Ontario. Recommendations and future research included.
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.
2013 methodology for the calibration of vissim in mixed trafficDaniel Sitompul
This document describes a methodology for calibrating the microsimulation software VISSIM for modeling mixed traffic conditions. The methodology involves representing the unique characteristics of vehicles and geometry in mixed traffic, identifying calibration parameters through sensitivity analysis, setting parameter ranges heuristically, and using an optimization model like a genetic algorithm to determine parameter values that minimize the error between simulated and observed delays. The methodology is demonstrated through a case study of signalized intersections in Mumbai, India featuring mixed traffic.
This document summarizes a study that used a dual graph representation to simulate urban traffic from both a microscopic and macroscopic perspective. The study represented roads as nodes and intersections as links to form dual graphs of city networks. A traffic model was implemented on these dual graphs to simulate vehicle movement and analyze overall traffic flow patterns. Simulation results showed that regular lattice grid networks performed better than scale-free self-organized networks in terms of overall traffic capacity and individual vehicle traveling times. However, the model could be improved by incorporating more realistic traffic control methods and vehicle navigation strategies.
Beyond Level of Service – Towards a relative measurement of congestion in pla...JumpingJaq
This document discusses problems with using level of service (LOS) as the sole measure of congestion in transport planning. It proposes developing a relative measurement of congestion that considers additional factors like the subjective experience of drivers, prioritization of different road functions, and growing tolerance for congestion. The methodology involves: 1) Identifying a volume-capacity ratio where poor LOS is likely due to excess demand rather than capacity issues. 2) Developing indices that weight the importance of volume-capacity ratios based on factors like strategic importance, density of activity, amenity, and modal compatibility. The results would allow planners to more easily evaluate traffic LOS in context of the entire network.
This document describes a study that used an ARIMA time series model to estimate traffic arrival patterns at three signalized intersections on Route 18 in New Jersey. Simulation data from Paramics was used to collect vehicle counts and headways under different demand levels. The ARIMA model was found to predict arrival patterns more accurately than the conventional Poisson model, particularly for over dispersed and under dispersed traffic scenarios. Specifically, the ARIMA model had smaller deviations from the simulation data for metrics like headway distribution, vehicle counts per cycle, and variance-to-mean ratio. This indicates that the ARIMA time series model provides a better approach for estimating real-world traffic arrival patterns compared to traditional distributions like Poisson.
Chapter 6 Fundamentals of traffic flowFayaz Rashid
The document discusses fundamental principles of traffic flow, including the primary elements of traffic flow such as flow, density, speed, and headway. It describes flow-density relationships and the fundamental diagram of traffic flow. Mathematical models for describing macroscopic traffic flow relationships are presented, including the Greenshields model relating traffic density to speed. The primary elements, flow-density relationships, and Greenshields traffic flow model are summarized for understanding traffic flow characteristics.
TE004, A Study On Feasible Traffic Operation Alternatives At Signalized Inter...Saurav Barua
This study analyzed traffic operations at a busy signalized intersection in Dhaka, Bangladesh using traffic simulation software VISSIM. Four alternatives were considered: 1) banning right turns, 2) optimizing signal timing, 3) constructing a one-way overpass, and 4) constructing two overpasses. Traffic data was collected and used to calibrate the VISSIM model. The alternatives were then simulated and evaluated based on average speed, delay, and queue length. Constructing a single overpass was found to provide the greatest benefits, increasing average speed by 250% and reducing delays and queues by over 90%, making it the recommended alternative to improve traffic flow at the intersection.
Modeling business management systems transportationSherin El-Rashied
Introduction
How IT &Business Process Fit Together
What is modeling?
What is Simulation?
Modeling & Simulation in Business Process Management
The Seven-Step Model-Building Process
Transportation
An overview on transportation modeling
Transport model scope & structure
Car Traffic Jam Problem
Aim of Transportation Model
Types of Traffic Models
Microscopic Traffic model & Simulation
Cellular Automaton model
Conclusion
Solving Transportation Problem by Software Application
Class Example
The document discusses improvements to the modeling of right turns on red (RTOR) in the Highway Capacity Manual 2010 (HCM 2010). It summarizes the existing HCM 2010 procedures that do not adequately account for RTOR flows. A new proposed methodology is described that estimates maximum RTOR flow rates and incorporates them into flow profiles to generate more accurate performance measures. Experimental results demonstrate that the proposed logic improves the modeling accuracy of flow profiles, consistency with microscopic simulations, and control delay estimates compared to not accounting for RTOR.
Data driven public_transportation_operation_by_trips_jaehong_minJaehong MIN
This document summarizes the TRIPS (Travel Record based Integrated Public transport operation System) developed by KRRI (Korea Railroad Research Institute) to analyze and improve public transportation systems using smart card transaction data. The key points are:
1. TRIPS uses smart card data from public transit systems to analyze current demand and usage patterns, estimate demand under different operational scenarios, and evaluate the effects of service changes.
2. It has been applied to the public transit system in Seoul, analyzing over 12 million daily transactions to examine routes, ridership, transfers and more.
3. TRIPS has also been implemented in other local governments and can help optimize local transit networks and scheduling. Further development includes integrating
A New Paradigm in User Equilibrium-Application in Managed Lane PricingCSCJournals
Ineffective use of the High-Occupancy-Vehicle (HOV) lanes has the potential to decrease the overall roadway throughput during peak periods. Excess capacity in HOV lanes during peak periods can be made available to other types of vehicles, including single occupancy vehicles (SOV) for a price (toll). Such dual use lanes are known as “Managed Lanes.” The main purpose of this research is to propose a new paradigm in user equilibrium to predict the travel demand for determining the optimal fare policy for managed lane facilities. Depending on their value of time, motorists may choose to travel on Managed Lanes (ML) or General Purpose Lanes (GPL). In this study, the features in the software called Toll Pricing Modeler version 4.3 (TPM-4.3) are described. TPM-4.3 is developed based on this new user equilibrium concept and utilizes it to examine various operating scenarios. The software has two built-in operating objective options: 1) what would the ML operating speed be for a specified SOV toll, or 2) what should the SOV toll be for a desired minimum ML operating speed. A number of pricing policy scenarios are developed and examined on the proposed managed lane segment on Interstate 30 (I-30) in Grand Prairie, Texas. The software provides quantitative estimates of various factors including toll revenue, emissions and system performance such as person movement and traffic speed on managed and general purpose lanes. Overall, among the scenarios examined, higher toll rates tend to generate higher toll revenues, reduce overall CO and NOx emissions, and shift demand to general purpose lanes. On the other hand, HOV preferential treatments at any given toll level tend to reduce toll revenue, have no impact on or reduce system performance on managed lanes, and increase CO and NOx emissions.
A Framework for Traffic Planning and Forecasting using Micro-Simulation Calib...ITIIIndustries
This paper presents the application of microsimulation for traffic planning and forecasting, and proposes a new framework to model complex traffic conditions by calibrating and adjusting traffic parameters of a microsimulation model. By using an open source micro-simulator package, TRANSIMS, in this study, animated and numerical results were produced and analysed. The framework of traffic model calibration was evaluated for its usefulness and practicality. Finally, we discuss future applications such as providing end users with real time traffic information through Intelligent Transport System (ITS) integration.
This document summarizes a study on performance measures for two-way, two-lane highways. It discusses the measures and methodologies used over time in the Highway Capacity Manual (HCM), including their shortcomings identified in other research. Alternative performance measures proposed in other studies are also reviewed. The document aims to provide an extensive literature review on capacity and level of service for two-way, two-lane highways, comparing different performance measures and factors affecting capacity estimations.
This document discusses performance measures for two-way, two-lane highways and identifies shortcomings in the current Highway Capacity Manual methodology. It summarizes alternative performance measures that have been suggested in research to address the discrepancies, such as Percent Impeded and Average Travel Speed. The document also reviews empirical models that have been developed to predict level of service based on these alternative measures and identifies additional measures used in different studies and countries. It concludes by recommending further research is needed to determine the best headway threshold for differentiating platoons and to identify the most suitable level of service measure for different road environments as the HCM may not always be applicable.
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.
Accessibility Analysis and Modeling in Public Transport Networks - A Raster b...Beniamino Murgante
The document summarizes research on modeling accessibility in public transportation networks using a raster-based approach. The research aimed to create an accessibility indicator for jobs via public transit that had low data requirements to allow transfer to other regions. The study area was the capital region of Denmark. Accessibility was modeled using land use, transportation, and temporal components. The model calculated cost distances from population and job centers using rasterized transportation network data. Results showed variability in accessibility scores and generally aligned with commuting statistics. The raster approach allowed fast calculation with low data needs but did not fully account for travel time or mode changes.
Accessibility analysis of public transport networks in urban areasMayank Bansal
The document analyzes methodologies for assessing public transport accessibility in urban areas. It discusses objectives to study existing methods, applicability to India, impacts of accessibility, and future research scope. As a case study, it examines a study that measured public transport accessibility levels (PTAL) for different zones in Ahmedabad, India using a modified version of the UK methodology. Key findings were that accessibility was best in city centers and outskirts had poor accessibility. Improving access for all sections of society was recommended.
Application of finite markov chain to a model of schoolingAlexander Decker
This document discusses the application of finite Markov chains to model school progression. It begins by introducing key concepts of Markov chains including states, transition probabilities, and transition matrices. It then presents a model of school progression with states representing each year of school plus outcomes of graduating or dropping out. Transition probabilities between states are used to formulate the model. The document applies this model to secondary school data from Nigeria to predict academic progression. It analyzes the data using knowledge of finite Markov chains and finds the model provides an efficient way to predict student academic progress.
Immigration and Settlement Programming in SW OntarioJennifer Long
Community-based research: Qualitative investigation concerning newcomers' first-hand experiences of targeted, universal and mixed service provision in London Ontario. Recommendations and future research included.
This short document promotes creating presentations using Haiku Deck, a tool for making slideshows. It encourages the reader to get started making their own Haiku Deck presentation and sharing it on SlideShare. In just one sentence, it pitches the idea of using Haiku Deck to easily create engaging slideshows.
Grafik menunjukkan persentase kejadian insiden DBD per 1000 jiwa di 5 daerah di Jawa Barat, dengan Kota Sukabumi memiliki persentase tertinggi yaitu 330,37 dan Cianjur terendah yaitu 16,99.
Differentiated instruction is an approach to teaching that aims to meet the needs of diverse learners by creating multiple paths to learning. Teachers can differentiate the content, process, and products based on students' readiness levels, interests, and learning profiles. Key strategies for differentiation include tiered instruction, anchoring activities, flexible grouping, and compacting the curriculum. While differentiation aims to be fair to students, it is not about giving all students the same instruction or having many different lesson plans - it is about creating an instructional approach that best serves the needs of each learner.
The document summarizes an upcoming conference titled "Schools of Architecture | Africa: Connecting Disciplines in Design + Development". The conference will bring together architects, scholars, and development planners from Africa and other parts of the world to discuss architectural education in Africa and the role of architecture in development on the continent. It will feature panel discussions on topics like African architectural education, the history and contemporary state of design and development, and the influence of popular architecture. The goal is to foster international collaboration and examine how architecture schools are adapting their approaches in Africa.
This document announces a summit on public-private partnerships (PPPs) in New Zealand infrastructure to be held on May 19-20, 2015 in Auckland. The summit will feature keynote speakers from the New Zealand Treasury, infrastructure organizations, and banks. Panel discussions will address funding local government infrastructure through PPPs and managing risks in PPP projects. Presentations will provide overviews of current and future PPP delivery in New Zealand, attracting international finance, and optimizing the PPP procurement process through developing best practices. The summit aims to bring together government and industry to discuss PPP delivery in New Zealand.
Timothy Seifrig has worked for Diamond Screw Products since 2013 as an Inventory Manager and IT professional. He has over 11 years of experience in warehouse management, vendor management, and strategic planning from his previous roles at Walmart. Seifrig served in the U.S. Army from 1999 to 2005 where he gained experience in communications, technology, and management. He is interested in various roles at Walmart related to safety, operations, inventory, and emergency preparedness.
This document provides an agenda and speaker list for the 7th annual New Zealand Rail Conference taking place on June 15-16, 2016 in Auckland. The conference will feature over 25 speakers from rail organizations in New Zealand and Australia discussing topics such as safety strategy, asset management, technology, and integrated transport solutions. Speakers include executives from KiwiRail, Sydney Trains, Metro Trains Melbourne, and the Australasian Railway Association. There will also be panel discussions and optional site tours of MetroPort Auckland on the second day.
A search result contains three distinct areas - ads, organic results, and local results. Learn more with this search guide from Titan Web Marketing Solutions.
The document provides information about the 10th International Harbour Masters' Association Congress taking place from May 30th to June 2nd, 2016 in Vancouver, Canada. The Congress will address the theme of "Port Expansion - The Challenges" and feature presentations and discussions on opportunities and challenges facing harbour masters related to balancing safety, environmental and economic responsibilities with increasing port and vessel sizes. The document outlines the schedule of events, speakers and technical site tour planned for the Congress.
Many business owners have the misconception that they need to focus on every social media channel. Not true! Learn how to leverage social media properly for your small business.
This document provides an agenda and details for the 2nd Annual Telecommunications & Train Control conference taking place on August 18-19, 2015 in Sydney, Australia. The conference will feature presentations and discussions on developments in telecommunications and train control technologies, network capacity and reliability, safety considerations, and innovations that can improve existing rail infrastructure performance. Speakers will address topics like new train control systems, spectrum management, communication network requirements, and technologies like CBTC. The event aims to discuss planning for future rail networks and leveraging telecommunications for increased safety and productivity.
The document provides details of the Rail Industry Safety and Standards Board's (RISSB) 16th annual Rail Safety Conference to be held on April 4-5, 2016 in Adelaide, Australia. It outlines the conference agenda, speaker line-up including representatives from regulatory bodies, rail operators and infrastructure managers, and topics such as safety culture, standards development and innovation. Pre-conference activities on April 4 include a site tour of Genesee & Wyoming Australia's maintenance facilities and the annual safety dinner in the evening.
University Efficiency and Shared Services Forum BrochureNiamh Horan
This document provides an agenda for the University Efficiency and Shared Services Forum taking place on April 28-29, 2015 in Sydney. The forum will feature presentations and panel discussions on topics related to improving efficiency and reducing costs in the university sector. Speakers will discuss audits of efficiency, challenges in meeting proposed higher education reforms, case studies of initiatives to improve processes and share services, and strategies to develop talent and capabilities to support more efficient operations. The goal is to help the higher education community work together to promote efficiency through sharing data, evidencing successes, and developing recommendations.
This document describes Joseph Reiter's analysis of unemployment data from the 2010 Census and 2008-2012 American Community Survey. It discusses: 1) reducing 559 variables down to 58 then selecting a 5-variable model to predict unemployment, 2) comparing models with different transformations of the response variable, 3) evaluating residuals and normality, and 4) concluding the selected model is robust but regional effects were less significant than expected and causation cannot be determined.
Not sure where to start with using Facebook to generate leads for your small business? Start right here with this quick how-to guide from Titan Web Marketing Solutions
This document provides an agenda for the 5th annual Heavy Haul Rail conference taking place in Perth, Australia on June 22-23, 2015. The conference will bring together international experts from heavy haul rail operations in countries like the US, Russia, and Canada to discuss topics like operational excellence, infrastructure for increased tonnage, scheduling and network efficiency, rolling stock technology, and maintenance. It will provide attendees with insights into heavy haul rail challenges, solutions, and innovations from major global operators such as Rio Tinto, BHP Billiton, and Aurizon.
This document provides a review of fuzzy microscopic traffic flow models. It discusses how fuzzy logic can be used to model traffic flow and driver behavior by introducing uncertainty into variables like speed and headway. It describes fuzzy cellular automata models that represent traffic as vehicles characterized by fuzzy numbers for position and velocity. It also covers fuzzy logic car-following models that use linguistic terms and rules to model car-following behavior, and fuzzy route choice models that calculate possibility indexes to determine the most likely route. The goal of these fuzzy models is to more realistically simulate traffic flow and account for the imprecise nature of traffic data.
This document provides an overview of a student's assignment reviewing fuzzy microscopic traffic flow models. It discusses how fuzzy logic can be used to introduce uncertainty into traffic simulation models to better reflect real-world conditions. It reviews different types of fuzzy microscopic models, including fuzzy cellular models that use fuzzy numbers to represent vehicle parameters and transitions between time steps, and fuzzy logic car-following models that use fuzzy reasoning and linguistic terms to describe driver behavior. The goal is to understand how these fuzzy microscopic models work.
Pergamon Transpn. Res.-B. Vol. 28B, No. 4, pp. 269-287, 19.docxkarlhennesey
Pergamon
Transpn. Res.-B. Vol. 28B, No. 4, pp. 269-287, 1994
Copyright 0 1994 Elsevier Science Ltd
Printed in the UK. All rights reserved
0191-2615194 $6.00 + .OO
0191-2615(93)E0002-3
THE CELL TRANSMISSION MODEL: A DYNAMIC
REPRESENTATION OF HIGHWAY TRAFFIC
CONSISTENT WITH THE HYDRODYNAMIC THEORY
CARLOS F. DAGANZO
Department of Civil Engineering and Institute of Transportation Studies,
University of California, Berkeley CA 94720, U.S.A.
(Received 23 October 1992; in revisedform 13 July 1993)
Abstract-This paper presents a simple representation of traffic on a highway with a single
entrance and exit. The representation can be used to predict traffic’s evolution over time and
space, including transient phenomena such as the building, propagation, and dissipation of
queues. The easy-to-solve difference equations used to predict traffic’s evolution are shown to be
the discrete analog of the differential equations arising from a special case of the hydrodynamic
model of traffic flow. The proposed method automatically generates appropriate changes in
density at locations where the hydrodynamic theory would call for a shockwave; i.e., a jump in
density such as those typically seen at the end of every queue. The complex side calculations
required by classical methods to keep track of shockwaves are thus eliminated. The paper also
shows how the equations can mimic the real-life development of stop-and-go traffic within moving
queues.
1. INTRODUCTION
Accurate descriptions of highway traffic flow over transportation networks, whether at
the planning or operations level, must recognize that the vehicles traveling on any section
of the network must be bound for specific destinations.
Static traffic assignment models used for transportation planning (see Sheffi, 1985,
for example) achieve this goal by describing the flow on a link of the network by its
components by final destination; e.g., by specifying a variable yid that represents the
amount of flow on link i that is ultimately bound for destination d. Unfortunately, this is
much more difficult to do for dynamic network flow problems (with time-dependent
origin-destination (O-D) flows) because the functional dependence of the link flows at
time t, yid(f), on the collection of all past flows is quite complex. This problem manifests
itself both at the planning level, where networks are quite complex, and at the operations
level, where networks are simpler, but more detail is sought about the system’s evolution.
Although dynamic traffic assignment models -planning level models involving large
networks- typically recognize that traffic travels to many destinations, the models are
based on simplistic flow relationships that are not perfectly consistent with the conserva-
tion laws of traffic. A planned sequel to this paper will discuss this in more detail.
Traffic operations models can be microscopic or macroscopic. Microscopic simula-
tions (e.g., Schw ...
This document provides an overview of traffic flow modeling and simulation methods for intelligent transportation systems. It discusses both macroscopic and microscopic modeling approaches. Macroscopic models view traffic as a continuous flow and use partial differential equations involving density, speed, and flow rate over time and space. Microscopic models treat each vehicle individually using ordinary differential equations to model driver behavior and car-following dynamics. The document also reviews several traffic simulation software tools and concludes that modeling and simulation can help design and evaluate new transportation control strategies before implementation.
A Cell-Based Variational Inequality Formulation Of The Dynamic User Optimal A...Joe Osborn
This summarizes a research paper that develops a cell-based dynamic traffic assignment formulation using a variational inequality approach. The formulation encapsulates the Cell Transmission Model to capture traffic dynamics like shockwaves and queues. It aims to precisely follow the ideal dynamic user optimal principle where all used routes between an origin-destination pair have equal travel times. An alternating direction method is used to solve the variational inequality problem. The paper evaluates the formulation using two scenarios to demonstrate traffic dynamics, interactions across links, and adherence to the dynamic user optimal principle.
This research article presents a linearized model for vehicle-track interactions. The key aspects are:
1) A wheel-rail interaction element is derived that considers both wheel-rail contact and separation conditions. It includes the effects of linear creepage and gravitational restoring forces.
2) Coupling matrices are developed to connect the wheel-rail interaction element to other vehicle and track components.
3) An equation of motion is established for the unified linearized vehicle-track system.
4) Numerical examples compare the linear model to a nonlinear model and evaluate using it for random vibration analysis to predict system response safety margins.
FOLLOWING CAR ALGORITHM WITH MULTI AGENT RANDOMIZED SYSTEMijcsit
We present a new Following Car Algorithm in Microscopic Urban Traffic Models which integrates some real-life factors that need to be considered, such as the effect of random distributions in the car speed,acceleration, entry of lane… Our architecture is based on Multi-Agent Randomized Systems (MARS) developed in earlier publications
A Computational Study Of Traffic Assignment AlgorithmsNicole Adams
The document summarizes a study comparing algorithms for solving traffic assignment problems. It classified algorithms as link-based (using link flows), path-based (using path flows), or origin-based (using link flows from origins). It reviewed literature on algorithms like Frank-Wolfe (link-based), path equilibration (path-based), and origin-based algorithm. It chose to implement representative algorithms from each class: Frank-Wolfe, conjugate Frank-Wolfe, bi-conjugate Frank-Wolfe (link-based), path equilibration, gradient projection, projected gradient, improved social pressure (path-based), and Algorithm B (origin-based) to compare their performance on benchmark problems.
A Computational Study Of Traffic Assignment AlgorithmsAlicia Buske
This document summarizes a research study that compares different algorithms for solving traffic assignment problems. The study performs a literature review of prominent traffic assignment algorithms, classifying them based on how the solution is represented (link-based, path-based, origin-based). It then implements representative algorithms from each class and conducts computational tests on benchmark networks of varying sizes. The results are analyzed to compare algorithm performance and identify the impact of different algorithm components on running time.
This document reviews several extensions and applications of the optimal speed traffic model. The original optimal speed model introduced in 1995 assumes that each vehicle has a legal velocity that depends on the following distance. Later models like the generalized force model and full velocity difference model address issues like unrealistic acceleration and deceleration in the original model. Other extensions examine the effects of next-nearest neighbor interaction and backward-looking behavior. Applications of optimal speed models include autonomous vehicle control, evaluating ITS strategies, and gaining insights into traffic congestion formation and flow stability. The conclusion recommends developing a more systematic "almighty model" that incorporates the various extensions and applications.
The document discusses traffic stream models. It describes two classes of traffic models: macroscopic models that examine average behaviors like density and speed, and microscopic models that examine individual behaviors like car-following models. The car-following model assumes cars cannot pass and a car's acceleration depends on the headway distance and speed difference of the car in front. Conservation laws state that the number of cars in a highway segment remains constant over time. Greenshield's model relates traffic speed to density, with free flow at low density and zero speed at maximum density. The document outlines concepts like flow rate, spacing, headway, density and speed-flow-density relationships.
This document provides a review and analysis of the optimal speed model. It discusses:
1) The theoretical models that support the optimal speed model including microscopic, mesoscopic, and macroscopic traffic flow models.
2) Problems with the original optimal speed model including unrealistic behavior, instability, and stop-and-go waves.
3) A proposed double boundary optimal velocity function model that allows vehicles to operate within a range of speeds and spacings rather than at a single optimal point. This addresses issues with the original model.
Vehicle Headway Distribution Models on Two-Lane Two-Way Undivided RoadsAM Publications
The time headway between vehicles is an important flow characteristic that affects the safety, level of service, driver behavior, and capacity of a transportation system. The present study attempted to identify suitable probability distribution models for vehicle headways on 2-lane 2-way undivided (2/2 UD) road sections. Data was collected from three locations in the city of Semarang: Abdulrahman Saleh St. (Loc. 1), Taman Siswa St. (Loc. 2) and Lampersari St. (Loc.3). The vehicle headways were grouped into one-second interval. Three mathematical distributions were proposed: random (negative-exponential), normal, and composite, with vehicle headway as variable. The Kolmogorov-Smirnov test was used for testing the goodness of fit. Traffic flows at the selected locations were considered low, with traffic volume ranged between 400 to 670 vehicles per hour per lane. The traffic volume on Loc.1 was 484 vehicles per hour, that on Loc. 2 was 405 vehicles per hour, and that on Loc. 3 was 666 vehicles per hour. Random distribution showed good fit at all locations under study with 95% confidence level. Normal distribution showed good fit at Loc. 1 and Loc. 2, whereas composite distribution fit only at Loc. 1. It was suggested that random distribution is to be used as an input in generating traffic in traffic analysis at highway sections where traffic volume are under 500 vehicles per hour.
A Biologically Inspired Network Design ModelXin-She Yang
This document summarizes a biologically inspired network design model based on the foraging behavior of the slime mold Physarum polycephalum. The model uses a gravity model to estimate traffic flows between cities and simulates the slime mold's development of a protoplasmic network to connect food sources. It applies this approach to design transportation networks for Mexico and China, comparing the results to existing networks. The networks are evaluated based on cost, efficiency, and robustness. The model converges to solutions that balance these factors in a flexible and optimized way inspired by biological networks.
A Biologically Inspired Network Design ModelXin-She Yang
This document summarizes a biologically inspired network design model based on the foraging behavior of the slime mold Physarum polycephalum. The model uses a gravity model to estimate traffic flows between cities and simulates the slime mold's development of a protoplasmic network to connect food sources. It applies this approach to design transportation networks for Mexico and China, comparing the results to existing networks. The networks are evaluated based on cost, efficiency, and robustness. The model converges to solutions that balance these factors in a flexible and optimized way inspired by biological networks.
1
Intermodal Autonomous Mobility-on-Demand
Mauro Salazar1,2, Nicolas Lanzetti1,2, Federico Rossi2, Maximilian Schiffer2,3, and Marco Pavone2
Abstract—In this paper we study models and coordination poli-
cies for intermodal Autonomous Mobility-on-Demand (AMoD),
wherein a fleet of self-driving vehicles provides on-demand
mobility jointly with public transit. Specifically, we first present
a network flow model for intermodal AMoD, where we capture
the coupling between AMoD and public transit and the goal is
to maximize social welfare. Second, leveraging such a model,
we design a pricing and tolling scheme that allows the system
to recover a social optimum under the assumption of a perfect
market with selfish agents. Third, we present real-world case
studies for the transportation networks of New York City and
Berlin, which allow us to quantify the general benefits of
intermodal AMoD, as well as the societal impact of different
vehicles. In particular, we show that vehicle size and powertrain
type heavily affect intermodal routing decisions and, thus, system
efficiency. Our studies reveal that the cooperation between AMoD
fleets and public transit can yield significant benefits compared
to an AMoD system operating in isolation, whilst our proposed
tolling policies appear to be in line with recent discussions for
the case of New York City.
I. INTRODUCTION
TRAFFIC congestion is soaring all around the world. Besidesmere discomfort for passengers, congestion causes severe
economic and environmental harm, e.g., due to the loss of
working hours and pollutant emissions such as CO2, partic-
ulate matter, and NOx [1]. In 2013, traffic congestion cost
U.S. citizens 124 Billion USD [2]. Notably, transportation
remains one of a few sectors in which emissions are still
increasing [3]. Governments and municipalities are struggling
to find sustainable ways of transportation that can match
mobility needs and reduce environmental harm as well as
congestion.
To achieve sustainable modes of transportation, new mobil-
ity concepts and technology changes are necessary. However,
the potential to realize such concepts in urban environments is
limited, since upgrades to available infrastructures (e.g., roads
and subway lines) and their capacity are often extremely costly
and require decades-long planning timelines. Thus, mobility
concepts that use existing infrastructure in a more efficient way
are especially attractive. In this course, mobility-on-demand
services appear to be particularly promising. Herein, two main
concepts exist. On the one hand, free floating car sharing
systems strive to reduce the total number of private vehicles
in city centers. However, these systems offer limited flexibility
and are generally characterized by low adoption rates that
result from low vehicle availabilities due to the difficulty of
1Institute for Dynamic Systems and Control ETH Zürich, Zurich (ZH),
Switzerland {samauro,lnicolas}@ethz.ch
2Department of Aeronautics and Astro.
This document reviews a fuzzy microscopic traffic model that uses fuzzy logic to simulate traffic streams at signalized intersections. The model represents vehicle parameters like position and velocity as fuzzy numbers. It combines aspects of cellular automata models and fuzzy calculus. Compared to traditional cellular automata models, the fuzzy microscopic model requires fewer simulation runs, stores less data, and estimates output distributions in a single run. Future work could explore a stochastic cellular automata model with fuzzy decision rules to analyze more complex traffic situations.
REVIEW OF OPTIMAL SPEED TRAFFIC FLOW MODELBashir Abdu
The document discusses optimal speed traffic flow models, which aim to more realistically model driver behavior compared to previous car following models. It describes several generations of optimal speed models that have been developed over time to address limitations. The models incorporate factors like desired optimal speed that is independent of the leader's speed, safe distance between vehicles, and asymmetric acceleration and deceleration behavior. The latest models presented in the document aim to produce realistic traffic dynamics like spontaneous jam formation and recover better delay time and kinematic wave properties.
Study of statistical models for route prediction algorithms in vanetAlexander Decker
This document summarizes and compares three statistical models for predicting vehicle routes in Vehicular Ad-Hoc Networks (VANETs): Markov models, Hidden Markov models (HMM), and Variable Order Markov models (VMM). It describes how each model works, including Markov models predicting the next road segment based on the current one, HMM using both transitions and observations to predict states, and VMM capturing longer dependencies while avoiding size increases of higher-order Markov models. The document also provides pseudocode for route prediction algorithms using each statistical model.
The document reviews optimal speed car-following models. It discusses macroscopic and microscopic traffic models, with a focus on microscopic optimal speed models. The optimal speed model defines a desired speed that is a function of headway distance and helps model traffic flow situations. The document also proposes enhancements to the optimal speed model, including a weighting factor dependent on relative speed and spacing to improve braking reactivity. In conclusion, it evaluates optimal speed models and their ability to realistically model traffic dynamics while avoiding collisions.
Discovering Digital Process Twins for What-if Analysis: a Process Mining Appr...Marlon Dumas
This webinar discusses the limitations of traditional approaches for business process simulation based on had-crafted model with restrictive assumptions. It shows how process mining techniques can be assembled together to discover high-fidelity digital twins of end-to-end processes from event data.
We are pleased to share with you the latest VCOSA statistical report on the cotton and yarn industry for the month of May 2024.
Starting from January 2024, the full weekly and monthly reports will only be available for free to VCOSA members. To access the complete weekly report with figures, charts, and detailed analysis of the cotton fiber market in the past week, interested parties are kindly requested to contact VCOSA to subscribe to the newsletter.
Did you know that drowning is a leading cause of unintentional death among young children? According to recent data, children aged 1-4 years are at the highest risk. Let's raise awareness and take steps to prevent these tragic incidents. Supervision, barriers around pools, and learning CPR can make a difference. Stay safe this summer!
1.
Application
of
a
Markov
chain
traffic
model
to
the
Greater
Philadelphia
Region
Joseph
Reiter,
Villanova
University
MAT
8435,
Fall
2013
ABSTRACT
A
macroscopic
traffic
model
based
on
the
Markov
chain
process
is
developed
for
urban
traffic
networks.
The
method
utilizes
existing
census
data
rather
than
measurements
of
traffic
to
create
parameters
for
the
model.
Four
versions
of
the
model
are
applied
to
the
Philadelphia
regional
highway
network
and
evaluated
based
on
their
ability
to
predict
segments
of
highway
that
possess
heavy
traffic.
2. Reiter
2
Table
of
Contents
INTRODUCTION
3
REVIEW
OF
TRAFFIC
MODELS
4
MICROSCOPIC
MODELS
4
MESOSCOPIC
MODELS
5
MACROSCOPIC
MODELS
6
MODEL
10
REPRESENTING
A
HIGHWAY
SYSTEM
AS
A
MATRIX
10
DETERMINING
POPULATIONS
12
TRAFFIC
DENSITY
14
HYPOTHETICAL
EXAMPLE
OF
THE
MODEL
16
APPLICATION
OF
MODEL
TO
THE
GREATER
PHILADELPHIA
REGION
18
ASSUMPTIONS
IN
THE
MODEL
18
DATA
ANALYSIS
20
POSITIVE
PREDICTIVE
VALUE
OF
MODELS
21
GRAPHS
OF
POSITIVE
PREDICTIVE
VALUE
22
CONCLUSION
24
APPENDIX
25
FIGURE
1
–
MAP
OF
EXIT
LOCATIONS
CHOSEN
FOR
THE
MODEL
25
FIGURE
2
–
NUMBER
OF
HOUSEHOLDS
AND
WORKERS
AROUND
EXITS
25
FIGURE
3
–
RELATIVE
VOLUME
OF
TRAFFIC
BY
HOUR
26
FIGURE
4
–
MATHEMATICA
CODE
USED
TO
DETERMINE
SHORTEST
PATH
IN
MODEL
27
WORKS
CITED
28
3. Reiter
3
Introduction
Traffic congestion in urban areas has been an issue since the beginning of the 20th
century, and it continues to be one of the most persistent problems facing urban planners.
The phenomenon has been extensively studied and several models have been used to
explain where, when, and how vehicles move through a network of roads. Limited
access highways changed how vehicles flowed in and around cities and across the
country. They allow vehicles to maintain constant speeds between exits and are partially
responsible for the expansion of cities (Rephann & Isserman, 1994).
The challenge in studying a road system populated with vehicles is that the number of
parts interacting at the same time is very large. Each individual vehicle in the system
must be considered on its own and also as a part of the system as a whole. In some ways,
this system acts like a complex economy; each vehicle acts to maximize its utility by
minimizing travel time, avoiding hazards, and seeking the least troublesome route to its
destination. Each constituent part of the system has some effect on all the other parts in
the system.
This paper looks at the issue of traffic congestion around cities and demonstrates a model
that predicts areas of traffic congestion based on census data along with statewide traffic
data. The model utilizes a Markov chain process in order to analyze the origin-
destination paths of vehicles in a network system. This method is applied to the Greater
Philadelphia Region and evaluated for its predictive value. The implications of this
model and possible extensions are also considered.
4. Reiter
4
Review
of
Traffic
Models
Microscopic
Models
Microscopic models focus on the individual interactions between vehicles and the
roadway. Vehicles follow specific rules outlined in the model that governs their
movement in the system (Velasco & Saayedra, 2008). These rules relate values such as
velocity, distance to nearby vehicles, and time. One common microscopic traffic model
is “follow-the-leader”, which utilizes a dynamical equation or system of differential
equations relating the motion of the (n+1)th vehicle following the nth vehicle in a single
lane (Gazis, Herman, & Rothery, 1961):
𝑥!!! 𝑡 + 𝑇 = 𝜆 𝑥! 𝑡 − 𝑥!!! 𝑡 ,
where xn is the position of the nth
vehicle, T is the time lag of response to the stimulus, λ
is the sensitivity, and the dots denote differentiation with respect to time t.
Nagel and Schreckenberg developed a cellular automata model that dictates rules for
traffic movements. These rules account for how vehicles accelerate with relation to each
other and move along the roadway. The product of the model is a time vs. space(road)
plot which tracks how dense traffic is at each point in the road during a time interval.
This plot shows how congestion patterns can travel in both time and space (Nagal &
Schreckenberg, 1992).
A model put forth by Indrei utilizes Markov chains to construct a theoretical traffic
system in a real space ℜ (Indrei, 2006). An object located in a particular element (i, j) of
5. Reiter
5
the configuration matrix transitions to a new location in discrete time. Each element of
this matrix represents a position on the roadway. Vehicle movements are defined as a
transition where rows represent highway lanes and columns represent length of the
highway segments:
𝑖, 𝑗 ⋈ 𝑓 𝑖 , 𝑗 + 𝜎 𝑜𝑏𝑗𝑒𝑐𝑡 ,
The symbol ⋈ represents a natural join between elements of two matrices A0 and A1. This
relation describes how an object in the (i, j)th slot in a matrix A0 ∈ ℜ will end up in the
(f(i), j + σ(object))th slot of another matrix A1 ∈ ℜ during one time step, where
𝜎 𝑜𝑏𝑗𝑒𝑐𝑡 =
1, with probability 𝑝
2, with probability 𝑞
3, with probability 𝑟
𝑝 + 𝑞 + 𝑟 = 1
and
𝑓: 𝑖 ↦ {𝑖, 𝑖 + 1, 𝑖 − 1}
Mesoscopic
Models
Another category of traffic models, called mesoscopic or kinetic traffic models, examines
vehicular movements as parts of a larger scale mechanism. Headway distribution models
focus on how much time passes between two successive vehicles. The time between
vehicles (headway) is described by a random variable with either a single distribution or
mix of different distributions. Some of these distributions are normal, gamma, and
exponential (Zhang, Wang, Wei, & Chen, 2007).
Cluster models are characterized by groups of vehicles that all exhibit the same property
such as velocity. This clustering effect may be due to how a roadway narrows to fewer
6. Reiter
6
lanes or other factors such as weather. The size of each cluster, which determines how
vehicles will flow on a highway, is dynamic and can grow or diminish over time
(Hoogendoorn & Bovy, 2001).
The gas-kinetic model of traffic flow comes from statistical mechanics and models
vehicles as particles in a traffic flow. Prigogine and Andrews developed this model
based on the Boltzmann-Maxwell equation that models the velocity of ideal gas particles.
The distribution of velocities f(x,v,t), where x is position on road, v is velocity, and t is
time (Prigogine & Andrews, 1960). This distribution function is described as:
𝜕𝑓
𝜕𝑡
+ 𝑣
𝜕𝑓
𝜕𝑥
=
𝜕𝑓
𝜕𝑡!"#
+
𝜕𝑓
𝜕𝑡!"##
where df/dtrel is the relaxation term (reflected by a desire to return to the ideal
distribution) and df/dtcoll is the ‘collision’ term, which in this case refers to the interaction
between vehicles ahead slowing down the ones behind.
Macroscopic
Models
Macroscopic models describe averaged quantities in traffic such as density, average
velocity, and velocity variance. Individual vehicles are not considered, but rather their
aggregate behavior is examined in order to understand the overall traffic flow on a
roadway. Lighthill and Whitham developed a theory that at any point of the road the
flow q (vehicles per hour) is a function of the concentration k (vehicles per mile), and that
the quantity in a small element of length (dk) changes at a rate equal to the difference
between inflow and outflow (dq) (Lighthill & Whitham, 1955):
7. Reiter
7
𝜕𝑘
𝜕𝑡
+
𝜕𝑞
𝜕𝑥
= 0
This partial differential equation describes a phenomenon from physics called a
kinematic wave. The dynamics of these waves describes how traffic jams can occur at
one point on a road and travel backwards through the traffic flow. A model built upon
the Lighthill/Whitham model that uses a system of partial differential equations was
proposed by Harold J. Payne and includes a convection, relaxation, and anticipation term
in the system (Hoogendoorn & Bovy, 2001):
𝑉 𝑥 𝑡 + 𝑇 , 𝑡 + 𝑇 = 𝑉!
(𝑟 𝑥 + 𝐷, 𝑡 ),
where x(t) is the location of the vehicle at time t, V(x,t) is velocity at x and t, Ve
is the
equilibrium velocity, and r(x,t) is the density, T is reaction time and D is gross-distance
headway with respect to the preceding vehicle. The equation describes how drivers will
adjust their velocity to an equilibrium velocity, which is affected by the traffic density.
The left and right sides of this equation can be expanded and combined to form a single
equation:
𝜕! 𝑉 + 𝑉𝜕! 𝑉 =
𝑉!
𝑟 − 𝑉
𝑇
− (
𝑐!
!
𝑟
)𝜕! 𝑟
where c0
2
= ξ/T > 0 is the anticipation constant, with ξ = -dVe
/dr the decrease in the
equilibrium velocity with increasing density. Other single and multi equation models
exist that extend the Lighthill/Whitham and Payne models to particular situations
(Hoogendoorn & Bovy, 2001).
8. Reiter
8
Two methods for describing traffic flow outlined by Sasaki and Myojin involve the use of
Markov chains (Sasaki & Myojin, 1968). The first is the branching probability matrix
method in which the highway is divided into m sections. A volume of traffic over each
section of highway is denoted xi , and a row vector of volumes can be constructed X =
(x1, x2, … , xm). Inflows and outflows are also denoted within a row vector; Ui = inflow
through ramp i (i = 1,2,3,…k), Vj = outflow through ramp j (j = 1,2,3,…r), and k = the
number of on-ramps and r = the number of off-ramps. The branching probability matrix
is written in canonical form:
𝑃 =
𝐼 0 0
𝑅! 0 𝑄!
𝑅! 0 𝑄!
where
R1= the probability of an inflow from on-ramp i to off-ramp
R2= the branching probability of traffic flow from section i to off-ramp j
Q1= the probability of an inflow from on-ramp i to section j
Q2= the branching probability of traffic flow from section i to section j
Traffic flows over sections are given by:
𝑋 = 𝑢𝑄!(𝐼 − 𝑄!)!!
and outflows through ramps are given by:
𝑣 = 𝑢 𝑅! + 𝑄!(𝐼 − 𝑄!)!!
𝑅!
9. Reiter
9
The second method described by Sasaki and Myojin is the route matrix method. If we
are given the distribution of trips between on-ramps and off-ramps, we can form a route
matrix which describes how a vehicle entering at on-ramp i will travel to off-ramp j. This
will be an (r × m) matrix in which the entry rim is equal to 1 if the route from on-ramp i to
off-ramp j includes section m, and equal to 0 otherwise. Each on-ramp will have its own
matrix Ri. The trip distributions can be denoted by row vector pi = (pi1,pi2,…,pir), where
pij = transition probability of a trip from on-ramp i to off-ramp j. The overall expected
traffic flow over the traffic network is:
𝑄 =
𝑝! 𝑅!
𝑝! 𝑅!
⋮
𝑝! 𝑅!
= 𝑄!" , (𝑘×𝑚)
and gross actual traffic flow:
𝑋 = 𝑢𝑄
Another article describes this process in detail and applies it to a hypothetical traffic
network (Crisostomi, Kirkland, Schlote, & Shorten, 2010). The literature refers to this
approach as the origin-destination (OD) matrix method. The estimation of these matrices
by various means is the subject of several articles (Van Zuylen & Willumsen, 1980)
(Perrakis, Karlis, Cools, Janssens, & Wets, 2012) (Youngblom, 2013).
10. Reiter
10
Model
The purpose of this model is to predict when and where heavy traffic is most likely to
occur in a highway network. Since the focus of this model is on particular segments of
highway rather than individual vehicles or traffic flow, it would need to be macroscopic
in its level of detail. Sasaki and Myojin’s model from the previous section provides a
good foundation on which to build this model since their model’s level of focus is on
highway segments. But we should first reexamine the situation we are trying to model.
Representing
a
highway
system
as
a
matrix
A road network can be looked at as a system of exits connected by segments of highway
that can be represented by a directed graph. The vertices of the graph represent exits and
edges represent highway segments:
For this example, there are 7 exits connected by highway segments. An adjacency matrix
A can be formed to describe this system:
11. Reiter
11
𝐀 =
0 1 0
1 0 1
0 1 0
0 0 0
0 1 0
1 1 0
1
1
0
0 0 1
0 1 1
0
1
0
1
0
0
0 0 1
0 0 1
1
0
1
0
0
1
0
0
1
0
A new matrix D representing the distance between exits in miles can be defined by
inserting the distances between exits instead of 1s, replacing the 0s that represent
unconnected exits with a very large number to simulate an infinite distance, and leaving
the 0s in place for elements where i = j:
𝐃 =
0 3 ∞
3 0 3
∞ 3 0
∞ ∞ ∞
∞ 2 ∞
2 3 ∞
4
5
∞
∞ ∞ 2
∞ 2 3
∞
4
∞
5
∞
∞
0 ∞ 2
∞ 0 1
2
∞
1
∞
0
1
∞
∞
1
0
The matrix D describes the relevant information about how the exits are connected to
each other, but we also need to know how many lanes of traffic there are on each segment
of highway. A matrix to describe the number of lanes between exits L is defined, where
elements representing segments that are not connected are given a value of -1 as a
placeholder (avoiding possible division by zero later in the model):
𝐋 =
−1 2 −1
2 −1 2
−1 2 −1
−1 −1 −1
−1 3 −1
2 3 −1
2
3
−1
−1 −1 2
−1 3 3
−1
2
−1
3
−1
−1
−1 −1 2
−1 −1 1
2
−1
1
−1
−1
3
−1
−1
3
−1
12. Reiter
12
The two matrices D and L together describe all the important information about the
geometry of the highway system.
Determining
Populations
Now that the road network is established, we can consider how vehicles travel on the
system. Assume that at any time t there are a particular number of vehicles in the area of
each exit. These populations can be represented by a row vector q = (q1, q2, …, qm),
where qi represents the population at exit i. So qt = (q1t, q2t, …, qmt) represents the
populations at each exit at time t.
For this model, time takes on discrete values of one-hour increments, so each hour a new
population must be determined. This new population consists of vehicles that came from
another exit and also vehicles that did not travel away from their exit. First, consider the
vehicles that come from another exit. Let the exit traveled from be ei and the exit
traveled to be ej, then there is a probability that a vehicle leaving ei goes to ej and it can
be expressed as pij. A matrix P can be formed from these probabilities:
𝐏 =
𝑝!,! 𝑝!,!
⋯ 𝑝!,!
𝑝!,! ⋱ ⋯ ⋮
⋮
𝑝!,!
⋮
⋯
⋱
⋯
⋮
𝑝!,!
This matrix represents a transition matrix that states the probabilities associated with
traveling from exit i to exit j. Each row of this matrix will be stochastic (sum to 1).
Another probability representing the relative volume of traffic on the highway network
during a particular hour must also be defined. Let v(t) be a function representing the
13. Reiter
13
relative volume of traffic using the network during time interval t, then the number of
vehicles leaving any particular exit during time interval t is given by v(t)qi, and the total
number of vehicles traveling to exit j is given by:
𝑣 𝑡 𝑞! 𝑝!,! + 𝑣 𝑡 𝑞! 𝑝!,! + 𝑣 𝑡 𝑞! 𝑝!,! + ⋯ + 𝑣 𝑡 𝑞! 𝑝!,! = 𝑣(𝑡) 𝑞! 𝑝!,!
!
!!!
The other portion of the new population consists of vehicles that did not leave their
position. Since the relative proportion of vehicle that didn’t travel during a time
increment is the complement of the proportion that did travel, the number of vehicles
remaining is the complementary probability times the number of vehicles at a particular
destination exit, given by:
[1 − 𝑣 𝑡 ]𝑞!
Combining these two expressions gives the new population for each exit:
𝑞(𝒕!𝟏)𝒊 = 𝑣 𝑡 𝑞! 𝑝!,!
!
!!!
+ [1 − 𝑣 𝑡 ]𝑞!
This equation can be expressed using matrices and vectors that have already been
defined:
𝐪𝒕!𝟏 = 𝑣 𝑡 𝐪𝒕 ∙ 𝐏 + 1 − 𝑣 𝑡 𝐪𝒕
14. Reiter
14
This process of finding the next population is similar to using a Markov chain, except that
there is an extra term for the proportion of a population not participating in the transition
process.
Traffic
Density
Since the goal of this model is to predict where and when heavy traffic occurs, it is
necessary to determine how many vehicles are traveling on each segment of the highway
system during each time interval. In order to determine how many vehicles are traveling
on a segment, we must determine which routes pass through each highway segment. A
complication occurs at this point in the process since there are several ways to go from
one exit to another. To simplify this, an assumption is made that vehicles will follow the
shortest path between two exits. It can be argued that this assumption is not completely
valid and that other way to determine a path may yield a more precise model. This paper
does not consider other path determining methods (Lim, Balakrishnan, Gifford, Madden,
& Rus, 2011), yet nothing in the general framework of this model prohibits using other
methods. An algorithm for finding the shortest paths on a graph between two vertices
was developed by EW Dijkstra and will be used in this model.
The number of vehicles traveling on a particular route from exit i to exit j was determined
from before as v(t)qipi,j. This value can be determined for each origin-destination pair
and a matrix constructed from them:
𝐑 =
𝑣(𝑡)𝑞! 𝑝!,! 𝑣(𝑡)𝑞! 𝑝!,! ⋯ 𝑣(𝑡)𝑞! 𝑝!,!
𝑣(𝑡)𝑞! 𝑝!,! ⋱ ⋯ ⋮
⋮
𝑣(𝑡)𝑞! 𝑝!,!
⋮
⋯
⋱
⋯
⋮
𝑣(𝑡)𝑞! 𝑝!,!
=
𝑟!,! 𝑟!,!
⋯ 𝑟!,!
𝑟!,! ⋱ ⋯ ⋮
⋮
𝑟!,!
⋮
⋯
⋱
⋯
⋮
𝑟!,!
15. Reiter
15
We can construct an (m × m) square matrix Q where each row is q:
𝐐 =
𝑞! 𝑞!
⋯ 𝑞!
𝑞! 𝑞!
⋯ 𝑞!
⋮
𝑞!
⋮
⋯
⋱
⋯
⋮
𝑞!
Then the route matrix R can be rewritten using matrices:
𝐑 = 𝑣 𝑡 𝐏 ⊙ 𝐐 𝐓
where the symbol ⊙ represents element by element multiplication of the matrices. The
transpose of Q is needed since each row of R is concerned with a single origin exit.
This matrix R show how many vehicles are traveling on a particular route, but our
interest is how many vehicles are traveling on a particular segment of highway. This can
be determined by taking the sum of all vehicles on all routes that pass through this
segment. A matrix C can be constructed to count the total number of vehicles passing
through each segment. An element of C can be described:
𝑐!,! = 𝑟!,!
!!!!!!!!!!
, for all 𝑟!,! which are shown to pass through segment (𝑖, 𝑗)
The routes rx,y that pass through segment (i, j) are determined by application of Dijkstra’s
Algorithm (Dijkstra, 1959) to the matrix D, which is the matrix that shows the distance
between exits. From the example above:
𝑐!,! = 𝑟!,! + 𝑟!,! + 𝑟!,! + 𝑟!,!
16. Reiter
16
Heavy traffic occurs in areas in which the traffic density passes above a certain limit, so it
is necessary to determine the density for each section of highway. Since the number of
vehicles per hour traveling on a particular segment is given by ci,j, the density (vehicles
per mile lane) can be determined from:
𝜌 =
𝑐!,!
𝑠 ∙ 𝑙!,!
where s is the average speed of vehicles in miles per hour and li,j is the number of lanes
from the matrix L on segment (i, j). This density can be compared to typical densities
that occur during heavy traffic to yield a prediction about what the traffic flow should be
like on this segment.
Hypothetical
Example
of
the
Model
Going back to the example from above, let’s define a population vector q =
(2000,3000,2500,4000,5000,3500,4500). The matrix Q is:
𝐐 =
20000 30000 25000
20000 30000 25000
20000 30000 25000
40000 50000 35000
40000 50000 35000
40000 50000 35000
45000
45000
45000
20000 30000 25000
20000 30000 25000
20000
20000
30000
30000
25000
25000
40000 50000 35000
40000 50000 35000
40000
40000
50000
50000
35000
35000
45000
45000
45000
45000
Let’s also declare P with equal probabilities that a vehicle will come from any exit, which
means that p1,j = p2,j = p3,j … :
17. Reiter
17
𝐏 =
0.1 0.15 0.15
0.1 0.15 0.15
0.1 0.15 0.15
0.2 0.25 0.05
0.2 0.25 0.05
0.2 0.25 0.05
0.1
0.1
0.1
0.1 0.15 0.15
0.1 0.15 0.15
0.1
0.1
0.15
0.15
0.15
0.15
0.2 0.25 0.05
0.2 0.25 0.05
0.2
0.2
0.25
0.25
0.05
0.05
0.1
0.1
0.1
0.1
and let v(t) = 0.1, then:
𝐑 =
200 300 300
300 450 450
250 375 375
400 500 100
600 750 150
500 625 125
200
300
250
400 600 600
500 750 750
350
450
525
675
525
675
800 1000 200
1000 1250 250
700
900
875
1125
175
225
400
500
350
450
so the number of vehicles traveling on highway section (6,7) during this hour is:
𝑐!,! = 250 + 400 + 400 + 350 = 1400
If the average speed is 65 miles per hour, then the density ρ(6,7) is:
𝜌!,! =
𝑐!,!
𝑠 ∙ 𝑙!,!
=
1400 vehicles/hr
65
miles
hr
∙ 3 lanes
≈ 7.179 vehicles/(mile ∙ lane)
Comparing this result to actual traffic densities would allow prediction of heavy traffic.
Notice that the only information needed besides the geometry of the road system was
number of vehicles around an exit, probability of destination, average speed, and relative
traffic volume for the entire road system during the time interval. Of note, individual
traffic volume measurements on each segment are not needed in this model.
18. Reiter
18
If we are interested in what traffic density is like at the next time interval, the formula for
qt+1 can be used:
𝐪𝒕!𝟏 = 𝑣 𝑡 𝐪𝒕 ∙ 𝐏 + 1 − 𝑣 𝑡 𝐪𝒕 = (2045, 3067, 2617.5, 4090, 5112.5, 3272.5, 4295)
This vector can be used to find the densities during the next time interval.
Application
of
Model
to
the
Greater
Philadelphia
Region
The highway system around the Philadelphia region is commonly plagued by heavy
traffic that can be difficult to anticipate. The model developed in this paper will now be
applied to the Philadelphia highway system. In order for the model to be applied, certain
assumptions about the region must be made. The level of validity of these assumptions
will affect the predictive value of the model, and are not absolute.
Assumptions
in
the
model
Instead of looking at all of the hundreds of highway exit in the region, this analysis only
looks at 46 strategically selected exits (see figure 1 in appendix). The implicit
assumption here is that only a certain number of exits need to be accounted for in order to
get a reasonably accurate prediction, as long as these exits are chosen in such a way that
they adequately cover the entire region being modeled.
To determine the initial values for the population vector q, an assumption is made that the
number of households (US Census Bureau, 2013) in an area is proportional to the number
of vehicles in this area during the early morning hours (approximately 1AM). The
19. Reiter
19
number of households within a 1 and 2 mile radius of each exit was obtained from census
data. This data is used as the population at time = 1AM. The rest of the populations are a
result of the iterative process in the model, which evolves dynamically.
The destination probabilities were derived from data about the number of workers in a
given radius of each exit (US Census Bureau, 2013). During the hours of 5AM to 10AM,
the proportion of workers in the area of an exit matches the probability that a vehicle will
travel to this exit. This produces a transition matrix in which each column contains
elements with the same probability. During the hours of 3PM to 4AM, the values of the
transition matrix switches to being proportional to the number of households around an
exit, which is what we assumed the initial population was. This should return the number
of vehicles around an exit return to the initial population at the end of each day. During
the hours of 11AM to 2PM, the transition matrix is assumed to be a combination of the
other two transition matrices. So the average of these probabilities is used during the
mid-day hours.
The average speed of vehicles on the highway is assumed to be 65 miles per hour. There
are two problems with this assumption. First, every section of highway may not have an
average speed of exactly 65 miles per hour. Second, during heavy traffic, the average
speed of vehicles will reduce. The first consideration will not drastically affect the
model, since dividing by a slightly different value, say 70 miles per hour, will only
decrease the density by a small percentage (7.1%). The second consideration has a
greater possibility of affecting the results of the density. Heavy traffic will decrease the
average speed and density will rise. Since detecting heavy traffic is the goal of this
20. Reiter
20
model, densities above the heavy traffic threshold will already be accounted for and an
increase in density value will not change the categorical classification as heavy traffic.
When applying the model to a real network, there will be highways that lead away from
the network and do not connect to another exit. These lengths of highway should be
considered when applying the model since incoming traffic will affect densities. In order
to account for these highways, exits were added at the end of these highway segments
and given a starting population = 9999 and number of workers = 10000. These false exits
provide a buffer to the road network to more realistically replicate traffic conditions at the
edge of the network. Also, these false exits provide a way to represent traffic coming
into or leaving the highway network at the edges.
Data
Analysis
Four versions of this model were executed and analyzed. These versions are a result of
manipulating the radius around exits in which population and number of workers were
considered. To evaluate the models’ ability to predict heavy traffic, the results of the
each model were compared to historical data (Google Maps, 2013). The Highway
Capacity Manual for 2010 describes levels of services, which relate the traffic densities to
relative heaviness of traffic flow (Transportation Reseach Board, 2011). The number of
lanes on each highway segment was determined in order to calculate vehicle density (ITO
Map, 2013). For this paper, levels of service of C (18 pc/mi/ln) or greater were
considered heavy for the models based on populations within 1 miles of exits and levels
of service D (26 pc/mi/ln) or greater were considered heavy for models based on
populations within 2 miles of exits.
21. Reiter
21
The positive predictive value (PPV) was determined for each hour between 7AM and
7PM for each weekday. Positive predictive value is obtained through application Bayes
theorem. The goal is to determine the conditional probability that there will be heavy
traffic given that the model predicts heavy traffic. Let H be the event that there is heavy
traffic on a highway segment, then:
PPV = P H Predict H) =
P Predict H H) ∙ P(H)
P Predict H H) ∙ P H + P Predict H Not H) ∙ P(Not H)
The positive predictive value is a measure of the true positive rate of heavy traffic
compared to the total number of predicted heavy traffic areas. This value allows the
models to be compared to each other and shows how likely their predictions are to be
correct.
The models will be referred to by the following for the rest of this paper:
1 miles population radius 2 mile population radius
1 mile workers radius Model A Model B
2 mile workers radius Model C Model D
Positive
Predictive
Value
of
Models
(see figure 2 and 3 in appendix for model data)
(pop, workers) Model A (1,1) Model B (2,1) Model C (1,2) Model D (2,2)
Overall 0.52086 0.42116 0.52319 0.41645
Monday 0.38129 0.30717 0.36957 0.29934
Tuesday 0.42446 0.35836 0.42029 0.34868
Wednesday 0.56835 0.44369 0.55797 0.43421
Thursday 0.58273 0.48805 0.60145 0.64748
Friday 0.64748 0.50853 0.66667 0.51974
7AM 0.3 0.44286 0.25714 0.4
8AM 0.76923 0.65714 0.8 0.60869
9AM 0.78333 0.71765 0.76364 0.67777
22. Reiter
22
10AM 0.31429 0.38824 0.31429 0.4125
11AM 0.22 0.22857 0.22222 0.2125
12PM 0.3 0.2625 0.3 0.23333
1PM 0.28 0.24706 0.28 0.23333
2PM 0.32 0.29412 0.3 0.28421
3PM 0.6 0.55 0.62 0.56
4PM 0.76923 0.63077 0.76923 0.65385
5PM 0.78462 0.68889 0.78462 0.66207
6PM 0.6 0.58519 0.69231 0.59286
7PM 0.52086 0.42116 0.52319 0.41645
Graphs
of
Positive
Predictive
Value
0
0.1
0.2
0.3
0.4
0.5
0.6
A
B
C
D
PPV
Model
Overall
Positive
Predictive
Value
23. Reiter
23
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Monday
Tuesday
Wednesday
Thursday
Friday
PPV
Day
Positive
Predictive
Value
By
Day
Model
A
Model
B
Model
C
Model
D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
7
8
9
10
11
12
13
14
15
16
17
18
19
PPV
Hour
Positive
Predictive
Value
By
Hour
Model
A
Model
B
Model
C
Model
D
24. Reiter
24
A comparison of the models indicates a greater sensitivity to the population radius than
the workers radius. This is most clearly observed when evaluating the day-to-day change
in PPV. In general, the predictive value was higher during times in which the relative
traffic volumes were higher. Models A and C performed well, with overall PPVs of
0.52086 and 0.52319 respectively. Both models considered populations within 1 mile.
These models mostly performed better during times of heavier traffic, where all models
performed about the same during non-peak hours.
Conclusion
The model presented here can be applied to any urban highway traffic network provided
that sufficient demographic data is available for the region being studied. This is an
economic advantage over other modeling methods that need to collect and update traffic
data to construct an origin-destination matrix. An evaluation of these other models’
predictive value may give insight into whether or not there is an advantage to using them.
Through the use of technology, vehicles are beginning to use an adaptive approach to
route selection, which looks at current traffic conditions along with predicted conditions.
Vehicles can now automatically be notified of changing traffic while on route and adjust
accordingly (Dragoi & Dobre, 2011). As traffic control technologies continue to
advance, our ability to avoid traffic congestion will improve and possibly change our
disposition towards navigating on urban highway systems.
25. Reiter
25
Appendix
Figure
1
–
Map
of
exit
locations
chosen
for
the
model
Figure
2
–
Number
of
households
and
workers
around
exits
(US
Census
Bureau,
2013)
Exit Households
within 1 mile
Households
within 2 miles
Workers
within 1 mile
Workers within
2 miles
Lat Lon
1 5913 23358 33101 50047 40.10611 -75.35119
2 2294 9692 11891 31020 40.11097 -75.28197
3 1281 8663 9393 20856 40.13131 -75.20159
4 4475 17685 20309 40049 40.16195 -75.11893
5 2623 11330 9034 27603 40.13125 -74.96899
6 1277 11074 9709 24403 40.19291 -74.87955
7 2446 13216 3289 13990 40.12042 -74.84316
8 1552 5491 556 3781 40.1025 -74.79157
10 229 2727 12 517 40.08346 -74.76093
11 3354 14490 7834 22614 40.08431 -74.93474
12 3730 19980 3532 17340 40.07006 -74.96135
27. Reiter
27
Figure
4
–
Mathematica
code
used
to
determine
shortest
path
in
model
For[x=1, x<74,x++,
spf = FindShortestPath[g,x,All];
a=Table[spf[v],{v,VertexList[g]}];
For[n=1,n<Length[a]+1,n++,
For[t=1,t<Length[a[[n]]],t++,
count[[a[[n,t]],a[[n,t+1]]]]+=R[[x,n]]
]
]
]; (* This loop finds shortest path using dijkstra's algorithm for
each route and adds the number of vehicles traveling on this path to
each segment along the shortest path; a mapping of R, which is
represented by g, to count matrix *)
28. Reiter
28
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