It is a research and programming (mathematica) project, about transportation (traffic) modeling.
I spent about 3 months (September - early December 2010) taking the trains, relying on my Baby-G's stop watch function to keep record of door open and close time for each stop and duration between stops.
After that the concentration went to testing the differential equation, and then expanded the original coding method with a different numerical approach, that's where the lag-time process came in.
Study: The Future of VR, AR and Self-Driving CarsLinkedIn
We asked LinkedIn members worldwide about their levels of interest in the latest wave of technology: whether they’re using wearables, and whether they intend to buy self-driving cars and VR headsets as they become available. We asked them too about their attitudes to technology and to the growing role of Artificial Intelligence (AI) in the devices that they use. The answers were fascinating – and in many cases, surprising.
This SlideShare explores the full results of this study, including detailed market-by-market breakdowns of intention levels for each technology – and how attitudes change with age, location and seniority level. If you’re marketing a tech brand – or planning to use VR and wearables to reach a professional audience – then these are insights you won’t want to miss.
This article (in French) explains how Geoflex has developed original PPP-RTK solutions (Precise Point Positioning with Real Time Kinematic capabilities) to reduce the convergence time of PPP (from 30 minutes to a few minutes) by adding a priori atmospheric data in the PPP calculation.
Study: The Future of VR, AR and Self-Driving CarsLinkedIn
We asked LinkedIn members worldwide about their levels of interest in the latest wave of technology: whether they’re using wearables, and whether they intend to buy self-driving cars and VR headsets as they become available. We asked them too about their attitudes to technology and to the growing role of Artificial Intelligence (AI) in the devices that they use. The answers were fascinating – and in many cases, surprising.
This SlideShare explores the full results of this study, including detailed market-by-market breakdowns of intention levels for each technology – and how attitudes change with age, location and seniority level. If you’re marketing a tech brand – or planning to use VR and wearables to reach a professional audience – then these are insights you won’t want to miss.
This article (in French) explains how Geoflex has developed original PPP-RTK solutions (Precise Point Positioning with Real Time Kinematic capabilities) to reduce the convergence time of PPP (from 30 minutes to a few minutes) by adding a priori atmospheric data in the PPP calculation.
Distributed Video Coding (DVC) has become increasingly popular in recent times among the researchers in video coding due to its attractive and promising features. DVC primarily has a modified complexity balance between the encoder and decoder, in contrast to conventional video codecs. However, Most of the reported DVC schemes have a high time-delay in decoder which hinders its practical application in real-time systems. In this work, we focus on speed up the Side Information(SI) generation module in DVC, which is a major function in the DVC coding algorithm and one of the time-consuming factor at the decoder. By applied it through Compute Unified Device Architecture (CUDA) based on General-Purpose Graphics Processing Unit (GPGPU), the experimental results show that a considerable speedup can be obtained by using the proposed parallelized SI generation algorithm.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Automated Piecewise-Linear Fitting of S-Parameters step-response (PWLFIT) for...Piero Belforte
An innovative full time-domain macromodeling
technique for general, linear multiport systems is described. The
methodology is defined in a digital wave framework and timedomain
simulations are performed via an efficient method called
Segment Fast Convolution (SFC). It is based on a piecewiseconstant
(PWC) model of the impulse response of scattering
parameters, computed starting from a piecewise-linear fitting
of their step response (PWLFIT). Such step response is directly
available from time-domain reflectometer measurements
(TDR/TDT) or equivalent simulations. The model-building phase
is performed in a fast automated framework and an analytic
formulation of computational efficiency of the SFC with respect to
the standard time-domain convolution is given. Two application
examples are used to verify the PWLFIT performance and to
perform a comparison with macromodeling methods defined in
the frequency-domain, such as Vector Fitting (VF).
Index Terms—Digital wave models, time-domain macromodeling,
S-parameters, step response.
COMPLEMENTARY VISION BASED DATA FUSION FOR ROBUST POSITIONING AND DIRECTED FL...ijaia
The present paper describes an improved 4 DOF (x/y/z/yaw) vision based positioning solution for fully 6
DOF autonomous UAVs, optimised in terms of computation and development costs as well as robustness
and performance. The positioning system combines Fourier transform-based image registration (Fourier
Tracking) and differential optical flow computation to overcome the drawbacks of a single approach. The
first method is capable of recognizing movement in four degree of freedom under variable lighting conditions, but suffers from low sample rate and high computational costs. Differential optical flow computation, on the other hand, enables a very high sample rate to gain control robustness. This method, however, is limited to translational movement only and performs poor in bad lighting conditions. A reliable positioning system for autonomous flights with free heading is obtained by fusing both techniques. Although the vision system can measure the variable altitude during flight, infrared and ultrasonic sensors are used for robustness. This work is part of the AQopterI8 project, which aims to develop an autonomous
flying quadrocopter for indoor application and makes autonomous directed flight possible.
Pipelining understandingPipelining is running multiple stages of .pdfarasanlethers
Pipelining understanding:
Pipelining is running multiple stages of the same process in parallel in a way that efficiently uses
all the available hardware while respecting the dependencies of each stage upon the previous
stages. In the laundry example, the stages are washing, drying, and folding. By starting a wash
stage as soon as the previous wash stage is moved to the dryer, the idle time of the washer is
minimized. Notice that the wash stage takes less time than the dry stage, so the wash stage must
remain idle until the dry stage finishes: the steady state throughput of the pipeline is limited by
the slowest stage in the pipeline. This can be mitigated by breaking up the bottleneck stage into
smaller sub-stages. For those less concerned with laundry-based examples, consider a video
game. The CPU computes the keyboard/mouse input each frame and moves the camera
accordingly, then the GPU takes that information and actually renders the scene; meanwhile, the
CPU has already begun calculating what\'s going to happen in the next frame.
How Pipelining will done:
In class, we mentioned that interpreting each computer instruction is a four step process: fetching
the instruction, decoding it and reading the register, executing it, and recording the results. Each
instruction may take 4 cycles to complete, but if our throughput is one instruction each cycle,
then we would like to perform, on average, $n$ instructions every $n$ cycles. To accomplish
this, we can split up an instruction\'s work into the 4 different steps so that other pieces of
hardware work to decode, execute, and record results while the CPU performs the fetch. The
latency to process each instruction is fixed at 4 cycles, so by processing a new instruction every
cycle, after four cycles, one instruction has been completed and three are \"in progress\" (they\'re
in the pipeline). After many cycles the steady state throughput approaches one completed
instruction every cycle.
An assembly line in a auto manufacturing plant is another good example of a pipelined process.
There are many steps in the assembly of the car, each of which is assigned a stage in the pipeline.
Typically the depth of these pipelines is very large: cars are pretty complex, so there need to be a
lot of stages in the assembly line. The more stages, the longer it takes to crank the system up to a
steady state. The larger the depth, the more costly it is to turn the system around: A branch
misprediction in an instruction pipeline would be like getting one of the steps wrong in the
assembly line: all the cars affected would have to go back to the beginning of the assembly line
and be processed again.
OnLive Example[Realtime]:
OnLive is a company that allows gamers to play video games in the cloud. The games are run on
one of the company\'s server farms, and video of the game is sent back to your computer. The
idea is that even the lamest of computers can run the most highly intensive games because all the
computer does .
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
Distributed Video Coding (DVC) has become increasingly popular in recent times among the researchers in video coding due to its attractive and promising features. DVC primarily has a modified complexity balance between the encoder and decoder, in contrast to conventional video codecs. However, Most of the reported DVC schemes have a high time-delay in decoder which hinders its practical application in real-time systems. In this work, we focus on speed up the Side Information(SI) generation module in DVC, which is a major function in the DVC coding algorithm and one of the time-consuming factor at the decoder. By applied it through Compute Unified Device Architecture (CUDA) based on General-Purpose Graphics Processing Unit (GPGPU), the experimental results show that a considerable speedup can be obtained by using the proposed parallelized SI generation algorithm.
International Journal of Engineering and Science Invention (IJESI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJESI publishes research articles and reviews within the whole field Engineering Science and Technology, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
Automated Piecewise-Linear Fitting of S-Parameters step-response (PWLFIT) for...Piero Belforte
An innovative full time-domain macromodeling
technique for general, linear multiport systems is described. The
methodology is defined in a digital wave framework and timedomain
simulations are performed via an efficient method called
Segment Fast Convolution (SFC). It is based on a piecewiseconstant
(PWC) model of the impulse response of scattering
parameters, computed starting from a piecewise-linear fitting
of their step response (PWLFIT). Such step response is directly
available from time-domain reflectometer measurements
(TDR/TDT) or equivalent simulations. The model-building phase
is performed in a fast automated framework and an analytic
formulation of computational efficiency of the SFC with respect to
the standard time-domain convolution is given. Two application
examples are used to verify the PWLFIT performance and to
perform a comparison with macromodeling methods defined in
the frequency-domain, such as Vector Fitting (VF).
Index Terms—Digital wave models, time-domain macromodeling,
S-parameters, step response.
COMPLEMENTARY VISION BASED DATA FUSION FOR ROBUST POSITIONING AND DIRECTED FL...ijaia
The present paper describes an improved 4 DOF (x/y/z/yaw) vision based positioning solution for fully 6
DOF autonomous UAVs, optimised in terms of computation and development costs as well as robustness
and performance. The positioning system combines Fourier transform-based image registration (Fourier
Tracking) and differential optical flow computation to overcome the drawbacks of a single approach. The
first method is capable of recognizing movement in four degree of freedom under variable lighting conditions, but suffers from low sample rate and high computational costs. Differential optical flow computation, on the other hand, enables a very high sample rate to gain control robustness. This method, however, is limited to translational movement only and performs poor in bad lighting conditions. A reliable positioning system for autonomous flights with free heading is obtained by fusing both techniques. Although the vision system can measure the variable altitude during flight, infrared and ultrasonic sensors are used for robustness. This work is part of the AQopterI8 project, which aims to develop an autonomous
flying quadrocopter for indoor application and makes autonomous directed flight possible.
Pipelining understandingPipelining is running multiple stages of .pdfarasanlethers
Pipelining understanding:
Pipelining is running multiple stages of the same process in parallel in a way that efficiently uses
all the available hardware while respecting the dependencies of each stage upon the previous
stages. In the laundry example, the stages are washing, drying, and folding. By starting a wash
stage as soon as the previous wash stage is moved to the dryer, the idle time of the washer is
minimized. Notice that the wash stage takes less time than the dry stage, so the wash stage must
remain idle until the dry stage finishes: the steady state throughput of the pipeline is limited by
the slowest stage in the pipeline. This can be mitigated by breaking up the bottleneck stage into
smaller sub-stages. For those less concerned with laundry-based examples, consider a video
game. The CPU computes the keyboard/mouse input each frame and moves the camera
accordingly, then the GPU takes that information and actually renders the scene; meanwhile, the
CPU has already begun calculating what\'s going to happen in the next frame.
How Pipelining will done:
In class, we mentioned that interpreting each computer instruction is a four step process: fetching
the instruction, decoding it and reading the register, executing it, and recording the results. Each
instruction may take 4 cycles to complete, but if our throughput is one instruction each cycle,
then we would like to perform, on average, $n$ instructions every $n$ cycles. To accomplish
this, we can split up an instruction\'s work into the 4 different steps so that other pieces of
hardware work to decode, execute, and record results while the CPU performs the fetch. The
latency to process each instruction is fixed at 4 cycles, so by processing a new instruction every
cycle, after four cycles, one instruction has been completed and three are \"in progress\" (they\'re
in the pipeline). After many cycles the steady state throughput approaches one completed
instruction every cycle.
An assembly line in a auto manufacturing plant is another good example of a pipelined process.
There are many steps in the assembly of the car, each of which is assigned a stage in the pipeline.
Typically the depth of these pipelines is very large: cars are pretty complex, so there need to be a
lot of stages in the assembly line. The more stages, the longer it takes to crank the system up to a
steady state. The larger the depth, the more costly it is to turn the system around: A branch
misprediction in an instruction pipeline would be like getting one of the steps wrong in the
assembly line: all the cars affected would have to go back to the beginning of the assembly line
and be processed again.
OnLive Example[Realtime]:
OnLive is a company that allows gamers to play video games in the cloud. The games are run on
one of the company\'s server farms, and video of the game is sent back to your computer. The
idea is that even the lamest of computers can run the most highly intensive games because all the
computer does .
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
Alt. GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using ...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Removing Uninteresting Bytes in Software FuzzingAftab Hussain
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
SAP Sapphire 2024 - ASUG301 building better apps with SAP Fiori.pdfPeter Spielvogel
Building better applications for business users with SAP Fiori.
• What is SAP Fiori and why it matters to you
• How a better user experience drives measurable business benefits
• How to get started with SAP Fiori today
• How SAP Fiori elements accelerates application development
• How SAP Build Code includes SAP Fiori tools and other generative artificial intelligence capabilities
• How SAP Fiori paves the way for using AI in SAP apps
GridMate - End to end testing is a critical piece to ensure quality and avoid...ThomasParaiso2
End to end testing is a critical piece to ensure quality and avoid regressions. In this session, we share our journey building an E2E testing pipeline for GridMate components (LWC and Aura) using Cypress, JSForce, FakerJS…
Encryption in Microsoft 365 - ExpertsLive Netherlands 2024Albert Hoitingh
In this session I delve into the encryption technology used in Microsoft 365 and Microsoft Purview. Including the concepts of Customer Key and Double Key Encryption.
Pushing the limits of ePRTC: 100ns holdover for 100 daysAdtran
At WSTS 2024, Alon Stern explored the topic of parametric holdover and explained how recent research findings can be implemented in real-world PNT networks to achieve 100 nanoseconds of accuracy for up to 100 days.
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
Sudheer Mechineni, Head of Application Frameworks, Standard Chartered Bank
Discover how Standard Chartered Bank harnessed the power of Neo4j to transform complex data access challenges into a dynamic, scalable graph database solution. This keynote will cover their journey from initial adoption to deploying a fully automated, enterprise-grade causal cluster, highlighting key strategies for modelling organisational changes and ensuring robust disaster recovery. Learn how these innovations have not only enhanced Standard Chartered Bank’s data infrastructure but also positioned them as pioneers in the banking sector’s adoption of graph technology.
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
1. Numerical Modeling of Train Traffic: Lexington 4, 5, 6 Trains,
Using Collocation Method with Chebyshev Interpolation
by
Kuoi “Lisa” Ueda
Department of Mathematics and Statistics
Hunter College (CUNY)
Adviser: Professor John Loustau
March 2011
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
2. Abstract
In this paper I simulate train traffic congestion on Lexington Avenue subway line by
using a numerical model derived from fluid flow. My numerical technique is collocation
method with Chebyshev polynomial interpolation. In addition, I use two separate
collocation implementations. Each highlights different aspects of the situation.
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
3. Table of Contents
§ References
§ Theory
§ Traffic Model
§ Findings
§ Collocation and Chebyshev-Gauss quadrature and Computational Results
§ Lag-Time Linearization and Computational Results
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
4. References
1. Bellomo, Nicola, Bertrand Lods, Roberto Revelli, Luca Ridolfi, "Generalized
Collocation Methods, Solutions to Nonlinear Problems", Birkhauser, 2002.
2. Hildebrand, F. B., "Introduction to Numerical Analysis", McGraw - Hill, 1956.
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
5. Theory
Traffic model developed in [1] is based on a fluid dynamic model obtained using the mass conservation equation
and Fick's law.
∑u/∑t + ∑q/∑x = 0
u = u(t, x) is the mass density
q = q(t, x) is the flow
Introducing a new variable, velocity v = v(t, x), writing q as a product of u and v,
and expressing velocity so that it varies inversely to density
v=1–u
∑u/∑t + ∑u(1-u)/∑x = 0
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
6. Traffic Model I
u* = u [1 + h (1 – u) ∑u/∑x]
is the "apparent local density" or "local fictitious density" proposed by Bellomo et al.
The coefficient h is intended to represent the driver's reaction to uncertainty.
Replacing u with u* in the equation for q
q = u*(1 – u*)
= u*– (u*)2
= u [ 1 + h – h u ∑u/∑x ] – ( u [ 1 + h - h u ∑u/∑x] )2
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
7. Traffic Model II
Inserting the last expression into the basic differential equation for the proposed variables u and v yields
∑u/∑t + ∑/∑x( u [ 1 + h – h u ∑u/∑x ] – ( u [ 1 + h - h u ∑u/∑x] )2 ) = 0
∑u/∑t + ∑/∑x( u [ 1 + h – h u ∑u/∑x ] ) = ∑ /∑x (u [ 1 + h - h u ∑u/∑x] )2)
∑u/∑t + ( 1 – 2 u ) ∑u/∑x = h u2 ( 1 – u ) (∑2u)/∑x2 + h u ( 2 – 3 u ) (∑u/∑x)2
fl
∂u/∂t = h u2 ( 1 – u ) (∂2u)/∂x2 + h u ( 2 – 3 u ) (∂u/∂x)2 – ( 1 – 2 u ) ∂u/∂x
By implementing the above differential equation numerically, we model the traffic density, u, for time t and
location x.
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
8. Traffic Model III
In a subway system –
§ Density can be measured via train arrival frequency at any station. The maximal density is governed by work
rules designating the minimum distance between trains.
§ Locations of trains in front or behind are unknown to train drivers. Drivers rarely, if ever, see another train.
§ Drivers rely on the control center's instruction to stop, go, slowdown, and speedup. Information is
transmitted by signal lights and radio communication.
A train driver at a fixed point in a tunnel feels the "apparent local density" or the "local fictitious density, when –
§ Told by the control center that train congestion is ahead.
§ Seeing large number of passengers on the platform when train is pulling into the station.
Drivers and controllers can over-react to the condition in the subway system by over-accelerating the train, or
breaking hard to maintain distance. Both drivers and controllers are subject to delayed responses to changing
conditions. A stopped train needs time to regain speed causing further delays in the trains that are behind.
The result of over-reaction would create a "stop and go" traffic pattern.
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
9. Findings (Summary)
Number of Arrivals Mean Arrival
Arvl. Frequency Mean Station Time Station Time
Uptown & Frequency (in
Variance (in seconds) Variance
Downtown minutes)
Local Peak 63 2 2.55 22.82 448.59
Local Off 26 5 11.36 21.09 35
Express Peak 19 2 3.5 25.85 64.78
Express Off 19 4 5.06 21.05 12.79
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
10. Findings (Express)
Express Peak
Date/Time Station 59th Street 42nd Street 14th Street Brooklyn Bridge Total Time
To 8:54 8:59 9:04 9:09 15 minutes
Back 9:26 9:23 9:17 9:11 15 minutes
11/19/10
8:54 am
25.02 23.81 17.54 30.65 -
Station Time
(in seconds)
18.26 32.92 20.65 19.50 -
Express Off Peak
Date/Time To 6:51 6:55 6:58 7:03 13 minutes
Back 7:16 7:13 7:08 7:04 13 minutes
11/17/10
17.98 25.14 23.37 14.36 -
6:51 pm Station Time
(in seconds)
20.99 24.63 21.42 20.54 -
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
11. Findings (Local)
Local Peak Local Express
10/21/10 10/27/10
Date/Time Date/Time
5:15 pm 12:16 pm
Station Time Station Time
Station To Back Station To Back
(in seconds) (in seconds)
68th St. 5:13 5:54 20.89 13.95 68th St. 12:16 13:00 17.62 19.94
59th St. 5:15 5:52 24.80 17.55 59th St. 12:17 12:58 23.25 20.10
st st
51 St. 5:16 5:51 24.88 15.37 51 St. 12:18 12:56 20.78 19.31
nd nd
42 St. 5:18 5:48 20.97 21.73 42 St. 12:21 12:55 22.21 20.76
33rd St. 5:20 5:46 14.39 15.16 33rd St. 12:23 12:53 17.18 14.69
th th
28 St. 5:22 5:45 20.27 13.18 28 St. 12:25 12:51 16.60 16.43
rd rd
23 St. 5:23 5:43 15.02 13.64 23 St. 12:26 12:50 17.75 17.85
th th
14 St. 5:26 5:42 21.03 19.76 14 St. 12:28 12:48 23.92 17.50
Astor Pl. 5:27 5:40 13.38 13.75 Astor Pl. 12:30 12:47 15.33 18.86
Bleeker St. 5:29 5:39 14.14 15.33 Bleeker St. 12:32 12:45 20.44 13.31
Spring St. 5:30 5:38 14.21 14.76 Spring St. 12:34 12:44 14.26 15.00
Canal St. 5:31 5:36 13.94 15.85 Canal St. 12:35 12:43 14.95 15.41
Brooklyn Brooklyn
5:34 5:35 - - 12:37 12:41 - -
Bridge Bridge
Total Time 21 minutes 19 minutes - - Total Time 21 minutes 19 minutes - -
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
12. Findings (Exceptional)
11/05/10 11/08/10
Date/Time
5:53 pm 6:20 pm
Station To Back Station Time To Back Station Time
*5:53 34.36
68th St. 6:40 25.28 6:20 7:02 22.22 25.70
5:55 25.28
59th St. 5:58 6:39 33.21 28.65 6:22 7:00 30.39 24.57
51st St. 6:00 6:36 35.68 27.19 6:24 6:58 36.26 26.49
42nd St. *6:03 6:33 50.16 227.66 6:27 *6:56 29.63 37.14
33rd St. 6:05 6:31 36.52 18.39 6:30 6:54 21.65 16.97
28th St. 6:07 6:30 42.17 19.51 6:31 6:53 20.83 14.76
23rd St. 6:09 6:28 40.12 17.41 6:33 6:51 23.04 17.57
14th St. 6:10 6:26 39.95 22.73 6:35 6:50 36.99 16.29
Astor Pl. Skipped 6:24 - 18.25 Skipped 6:48 - 17.68
Bleeker St. 6:13 6:23 30.96 17.17 6:38 6:47 21.53 15.66
Spring St. Skipped 6:22 - 15.20 Skipped 6:45 - 14.46
Canal St. Skipped 6:21 - 17.75 Skipped 6:44 - 14.32
Brooklyn
6:16 6:19 - - 6:42 6:43 - -
Bridge
Total Time 21 minutes 21 minutes 22 minutes 19 minutes
* On Nov. 8 2010: I documented two arrivals for 68th Street station, because I had to get on the 2nd train arrived at 5:55 PM after I failed to squeeze myself into the first train.
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
13. Findings (Conclusion)
Evidently, train dispatch control center decided to have the trains bypass less crowded stations. When trains run
smoothly during rush hour, the door open-close time is shorter in single line stations. Transfer hubs have a greater
door open-close time.
The findings confirm Bellomo et al's traffic modeling; MTA works hard to prevent the stop and go traffic
phenomenon. They use procedures such as the station skipping as mentioned above. Without that, trains would be
held in tunnels and would move at a slow speed.
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
14. Collocation
Assume track length = 1. Hence our spatial variable x lies in [0, 1]
§ Set of collocation points Z = {xi}, i = 1, . . ., 20.
§ pi[xj] = dij.
§ For any continuous function s, polynomial interpolation satisfies
PZ(s) = ∑i s(xi)pi in 19.
§ 0 = h u2[(1 – u)∑2u/∑x2 + h u(2 – 3u)(∑u/∑x)2 – (1 – 2u)∑u/∑x.
To simplify, we rewrite this as 0 = L(u).
Then the collocation solution to the equation is an element uP in 19 with the property that 0 = PZ(L(uP)).
PZ is zero on a function if and only if L(uP)(xi) = 0 for all i. This yields a system of equations.
§ ajn+1 = t [ L( ∑j ajn pj )](xi) + ajn
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
15. Chebyshev-Gauss quadrature
Designed for functions that have vertical tangents at the end points of the domain.
s(x) = u(x)/Sqrt[x(1-x)]
Select interpolation points (collocation points) that will minimize the error
xi = 1/2 – 1/2 Cos ((i - 1)/(n - 1))
§ Steep tangents at the boundary of the congested region
§ It is possible that s behaves like a polynomial function and may be approximated by a polynomial
But then up is an approximation of s, not u. Hence at the end we must multiply the result by Sqrt[x(1-x)] in order to
recover u.
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
16. Computational Results
i)
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
17. Computational Results
ii)
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
18. Lag-Time Linearization
§ Alternative implementation
§ A time step procedure where each time state is a linear function of the prior one.
Our differential equation given by
∑u/∑t = h u2[(1 – u)∑2u/∑x2 + h u(2 – 3u)(∑u/∑x)2 – (1 – 2u)∑u/∑x
is non-linear.
With the time lag process, we can linearize the differential equation by asserting prior state ajn-1 ,and then
calculate the next state ajn+1 as a linear transformation of the current state ajn.
§ ajn+1 = t [ N( ∑j ajn-1 pj ) ( ∑j ajn pj )](xi) + ajn
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
19. Lag-Time Computational Results
The following graphs show the output of the lag-time process.
Graph iii) shows a folding effect that is actually rubber-banding – between areas of relatively high density and
areas of relatively low density.
iii)
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
20. Lag-Time Computational Results
iv)
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.
21. Bellomo et al's Computational Results
This PDF file is Created by trial version of Quick PDF Converter Suite.
Please use purchased version to remove this message.