text:
XQuery/XML to RDF

For the Emp-DEPT case study, RDF must be generated from underlying XML files. An XQuery script generates the RDF. It uses a configuration file to define how columns of a table should be mapped into RDF and the namespaces to be used. This mapping needs a little more work to allow composite keys and allow user defined transformations. An interactive tool to create this map would be useful.

Issues in mapping to RDF
The main guide to publishing linked data on the web is How to Publish Linked Data on the Web. This work connected with the Wikibook entry consists in progressively applying the principles enunciated there.

This conversion illustrates a few of the differences between local datasets, whether SQL or XML, and a dataset designed to fit into a global database. Some decisions remain unclear.
 * tables are implicitly within an organisational context. This context has to be added in RDF by creating a namespace for the local properties and identifiers
 * the scope of queries is implicitly within organisational boundaries, but in RDF this scope needs to be explicit. In the SQL query select * from emp; emp is ambiguously either the class of employees or the set of employees in the company.  In RDF this needs to be explicit, so that two kind of tuples need to be added:
 * tuples to type employees to a company definition of employee
 * tuples to relate the employee to the company (to be added)
 * linkage to the global database requires two kinds of links:
 * local properties need to be mapped to global predicates. Here the employee name is mapped to foaf:surname (but the case probably needs changing). Alternatively a local predicate f:name could be defined, which is equated to the foaf predicate with owl:samePropertyAs.
 * local identifiers of resources to be replaced by global URIs. Here location is mapped to a dbpedia  resource URI. Alternatively, the local URI f:location/Dallas  could be equated to the dbPedia resource with owl:sameAs. (where? and why delay this?)
 * foreign keys are replaced by full URIs, pointing directly to the linked resource. The name of this property is no longer the name of the foreign key (e.g. MgrNo but rather the name of the related resource (Manager). However, the foreign key itself might also need to be replaced.
 * primary keys are also replaced by URIs, but the local primary key value, for example the employee number, will need to be retained as a literal if it is not purely a surrogate key. This perhaps should be mapped to rdf:label.
 * datatypes are preferably explicit in the data to avoid conversion in queries although this increases the size of the RDF graph.
 * namespaces have been expanded in full where they occur in RDF attribute values. An alternative would be to define entities in an DTD prolog as shorthand for these namespaces, but not all processors of the RDF would do the expansion. xml:base can be used to default one namespace.

[The choices made here are those of a novice and review would be welcome. ]

Some issues not yet addressed:
 * meta-data about the dataset as a whole - its origin, when and how converted, - these can be DC properties of a document, with each entity tied to that document as a part?
 * an alternative approach to mapping would be to start with an ontology and add mapping information to it rather than generating it from the ad-hoc configuration file.

Configuration file
To facilitate the conversion from XML to RDF, a separate configuration file is defined. Here is the configuration file for the emp-dept data.

Data base conversion functions
One function row-to-rdf generates the RDF for a row of a table, another function map-to-schema generates RDFS descriptions of the predicates used in a table.

Full database conversion
The script to generate the RDF for the full database:

Links

 * Get RDF
 * Cached RDF
 * Validate RDF

Resource RDF
In addition each resource is retrieved as RDF. In this simple example, the request for a resource URI like:

http://www.cems.uwe.ac.uk/empdept/emp/7839

is re-written by Apache to http://www.cems.uwe.ac.uk/xmlwiki/RDF/empdeptrdf.xq?emp=7839

and the script retrieves the RDF:Description of the selected resource from the RDF file directly.

This mechanism does not conform to the recommended practice of distinguishing between information resources (such as the information about employee 7839) and the real world entity being represented. At present, the resource URI de-references directly to the RDF, rather than to indirect using the 303 mechanism recommended.

To Do

 * compound primary keys
 * conversion functions, for example to convert the case of strings, reformat dates
 * added resources and relationships - here the a company entity and links from departments to company

title: XQuery/XML to RDF


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XQuery/SPARQL interface

The following script provides, via a Joseki server at UWE, a query interface to RDF. Literal language and datatype are ignored in this representation. URIs link to the browse query and also directly to the resource.

A function converts the SPARQL XML Query result to a table, with links.

};

The SPARQL interface uses the configuration file to declare the namespaces.

Application
Query

The interface expands a query like select ?name ?job where { ?emp rdf:type f:emp. ?emp foaf:surname ?name. ?emp f:Job ?job. }

into:

prefix foaf:  prefix rdf:  prefix rdfs:  prefix f:  prefix xs:  select ?name ?job from  where {    ?emp rdf:type  f:emp.    ?emp foaf:surname ?name.    ?emp f:Job ?job.  }

and sends this to the Joseki service. The graph to query is actually passed as the default graph rather than in the from clause.

To do

 * handle language and datatype
 * local URIs as local names rather than full URIs#
 * better handling of default graph - should be able to reference the cached rdf defined in the config file

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: XQuery/SPARQL interface


text: User talk:216.46.154.8

title: User talk:216.46.154.8


text: File:Resize2 Trainz.jpg

title: File:Resize2 Trainz.jpg


text: User talk:190.64.82.201

title: User talk:190.64.82.201


text: User talk:207.255.3.5

title: User talk:207.255.3.5


text:
Talk:Blender 3D: Noob to Pro/Advanced Tutorials/Python Scripting/Import scripts

I'm new to this stuff, so I don't feel confident editing the main page. But I noticed that this imported uses the deprecated "NMesh" class. As an exercise, I updated it to use Mesh instead. Here's my version; if somebody else likes it and wants to stick it on the main page, great.

 * 1) !BPY

""" Name: 'NewWikibooks' Blender: 244 Group: 'Import' Tooltip: 'Better Wikibooks sample importer' """

import Blender import bpy

def import_obj(path): Blender.Window.WaitCursor(1) name = path.split('\\')[-1].split('/')[-1] mesh = Blender.Mesh.New( name ) # create a new mesh # parse the file file = open(path, 'r') for line in file.readlines: words = line.split if len(words) == 0 or words[0].startswith('#'): pass elif words[0] == 'v': x, y, z = float(words[1]), float(words[2]), float(words[3]) mesh.verts.extend(x, y, z)               elif words[0] == 'f': faceVertList = [] for faceIdx in words[1:]: faceVert = mesh.verts[int(faceIdx)-1] faceVertList.append(faceVert) mesh.faces.extend(faceVertList) # link the mesh to a new object ob = Blender.Object.New('Mesh', name) # Mesh must be spelled just this--it is a specific type ob.link(mesh) # tell the object to use the mesh we just made scn = Blender.Scene.GetCurrent for o in scn.getChildren: o.sel = 0 scn.link(ob) # link the object to the current scene ob.sel= 1 ob.Layers = scn.Layers Blender.Window.WaitCursor(0) Blender.Window.RedrawAll

Blender.Window.FileSelector(import_obj, 'Import')


text:
Muggles' Guide to Harry Potter/Magic/Ashwinder

Overview
An Ashwinder is a thin, ash-coloured serpent that is born from the embers of a magical fire.

Extended Description
The lifespan of an Ashwinder is short; they live for only an hour. Their primary purpose is to find a secluded area within the home to lay their eggs. Following the egg-laying, the parent ashwinder will collapse into dust. Ashwinder eggs are bright red and can give off intense heat. If not frozen with an appropriate charm, the eggs can ignite the dwelling within minutes. An ashy trail left by Ashwinders may assist in locating the eggs before any damage happens.

Frozen Ashwinder eggs are valuable. They are used in love potions, and can be eaten whole as a cure for ague.


text:
Fundamentals of Transportation/Trip Generation

Trip Generation is the first step in the conventional four-step transportation forecasting process (followed by Destination Choice, Mode Choice, and Route Choice), widely used for forecasting travel demands. It predicts the number of trips originating in or destined for a particular traffic analysis zone.

Every trip has two ends, and we need to know where both of them are. The first part is determining how many trips originate in a zone and the second part is how many trips are destined for a zone. Because land use can be divided into two broad category (residential and non-residential) we have models that are household based and non-household based (e.g. a function of number of jobs or retail activity).

For the residential side of things, trip generation is thought of as a function of the social and economic attributes of households (households and housing units are very similar measures, but sometimes housing units have no households, and sometimes they contain multiple households, clearly housing units are easier to measure, and those are often used instead for models, it is important to be clear which assumption you are using).

At the level of the traffic analysis zone, the language is that of land uses "producing" or attracting trips, where by assumption trips are "produced" by households and "attracted" to non-households. Production and attractions differ from origins and destinations. Trips are produced by households even when they are returning home (that is, when the household is a destination). Again it is important to be clear what assumptions you are using.

Activities
People engage in activities, these activities are the "purpose" of the trip. Major activities are home, work, shop, school, eating out, socializing, recreating, and serving passengers (picking up and dropping off). There are numerous other activities that people engage on a less than daily or even weekly basis, such as going to the doctor, banking, etc. Often less frequent categories are dropped and lumped into the catchall "Other".

Every trip has two ends, an origin and a destination. Trips are categorized by purposes, the activity undertaken at a destination location.

Some observations:
 * Men and women behave differently on average, splitting responsibilities within households, and engaging in different activities,
 * Most trips are not work trips, though work trips are important because of their peaked nature (and because they tend to be longer in both distance and travel time),
 * The vast majority of trips are not people going to (or from) work.

People engage in activities in sequence, and may chain their trips. In the Figure below, the trip-maker is traveling from home to work to shop to eating out and then returning home.

Specifying Models
How do we predict how many trips will be generated by a zone? The number of trips originating from or destined to a purpose in a zone are described by trip rates (a cross-classification by age or demographics is often used) or equations. First, we need to identify what we think the relevant variables are.

Home-end
The total number of trips leaving or returning to homes in a zone may be described as a function of:

$$ T_h = f(housing\ units,\ household\ size,\ age,\ income,\ accessibility,\ vehicle\ ownership). \,\!$$

Home-End Trips are sometimes functions of:
 * Housing Units
 * Household Size
 * Age
 * Income
 * Accessibility
 * Vehicle Ownership
 * Other Home-Based Elements

Work-end
At the work-end of work trips, the number of trips generated might be a function as below:

$$ T_w = f ( jobs(area\ of\ space\ by\ type,\ occupancy\ rate)) \,\!$$

Work-End Trips are sometimes functions of:
 * Jobs
 * Area of Workspace
 * Occupancy Rate
 * Other Job-Related Elements

Shop-end
Similarly shopping trips depend on a number of factors:

$$ \,\!T_s = f (number\ of\ retail\ workers,\ type\ of\ retail,\ area,\ location,\ competition) $$

Shop-End Trips are sometimes functions of:
 * Number of Retail Workers
 * Type of Retail Available
 * Area of Retail Available
 * Location
 * Competition
 * Other Retail-Related Elements

Input Data
A forecasting activity conducted by planners or economists, such as one based on the concept of economic base analysis, provides aggregate measures of population and activity growth. Land use forecasting distributes forecast changes in activities across traffic zones.

Estimating Models
Which is more accurate: the data or the average? The problem with averages (or aggregates) is that every individual’s trip-making pattern is different.

Home-end
To estimate trip generation at the home end, a cross-classification model can be used. This is basically constructing a table where the rows and columns have different attributes, and each cell in the table shows a predicted number of trips, this is generally derived directly from data.

In the example cross-classification model: The dependent variable is trips per person. The independent variables are dwelling type (single or multiple family), household size (1, 2, 3, 4, or 5+ persons per household), and person age.

The figure below shows a typical example of how trips vary by age in both single-family and multi-family residence types.

The figure below shows a moving average.

Non-home-end
The trip generation rates for both “work” and “other” trip ends can be developed using Ordinary Least Squares (OLS) regression (a statistical technique for fitting curves to minimize the sum of squared errors (the difference between predicted and actual value) relating trips to employment by type and population characteristics.

The variables used in estimating trip rates for the work-end are Employment in Offices ($$E_{off}\,\!$$), Retail ($$E_{ret}\,\!$$), and Other ($$E_{oth}\,\!$$)

A typical form of the equation can be expressed as:

$$T_{D,k} = a_1 E_{off,k} + a_2 E_{oth,k} + a_3 E_{ret,k}\,\!$$

Where:
 * $$ T_{D,k} \,\!$$ - Person trips attracted per worker in Zone k
 * $$E_{off,i} \,\!$$ - office employment in the ith zone
 * $$E_{oth,i} \,\!$$ - other employment in the ith zone
 * $$E_{ret,i} \,\!$$- retail employment in the ith zone
 * $$a_1,a_2,a_3 \,\!$$ - model coefficients

Normalization
For each trip purpose (e.g. home to work trips), the number of trips originating at home must equal the number of trips destined for work. Two distinct models may give two results. There are several techniques for dealing with this problem. One can either assume one model is correct and adjust the other, or split the difference.

It is necessary to ensure that the total number of trip origins equals the total number of trip destinations, since each trip interchange by definition must have two trip ends.

The rates developed for the home end are assumed to be most accurate,

The basic equation for normalization:

$$ T'_{D,j} = T_{D,j}\frac \,\!$$

Sample Problems

 * Problem (Solution)
 * Problem (Solution)
 * Problem (Solution)

Variables

 * $$T_O,i$$ - Person trips originating in Zone i
 * $$T_D,j$$ - Person Trips destined for Zone j
 * $$T_O,i ' $$ - Normalized Person trips originating in Zone i
 * $$T_D,j ' $$ - Normalized Person Trips destined for Zone j
 * $$T_h$$ - Person trips generated at home end (typically morning origins, afternoon destinations)
 * $$T_w$$ - Person trips generated at work end (typically afternoon origins, morning destinations)
 * $$T_s$$ - Person trips generated at shop end
 * $$H_i$$ - Number of Households in Zone i
 * $$E_{off,k}$$ - office employment in Zone k
 * $$E_{ret,k}$$ - retail employment in Zone k
 * $$E_{oth,k}$$ - other employment in Zone k
 * $$B_n$$ - model coefficients

Abbreviations

 * H2W - Home to work
 * W2H - Work to home
 * W2O - Work to other
 * O2W - Other to work
 * H2O - Home to other
 * O2H - Other to home
 * O2O - Other to other
 * HBO - Home based other (includes H2O, O2H)
 * HBW - Home based work (H2W, W2H)
 * NHB - Non-home based (O2W, W2O, O2O)

External Exercises
Use the ADAM software at the STREET website and try Assignment #1 to learn how changes in analysis zone characteristics generate additional trips on the network.

Additional Problems

 * Homework
 * Additional Problems

Videos

 * Trip Generation
 * Normalization


text: User talk:86.130.114.116

title: User talk:86.130.114.116


text:
Fundamentals of Transportation/Trip Generation/Problem

 Problem: Planners have estimated the following models for the AM Peak Hour

$$ T_{O,i} = 1.5*H_i \,\!$$

$$ T_{D,j} = (1.5*E_{off,j}) + (1*E_{oth,j}) + (0.5*E_{ret,j}) \,\!$$

Where:

$$T_{O,i}\,\!$$ = Person Trips Originating in Zone $$i\,\!$$

$$T_{D,j}\,\!$$ = Person Trips Destined for Zone $$j\,\!$$

$$H_i\,\!$$ = Number of Households in Zone $$i\,\!$$

You are also given the following data

A. What are the number of person trips originating in and destined for each city?

B. Normalize the number of person trips so that the number of person trip origins = the number of person trip destinations. Assume the model for person trip origins is more accurate.

 * Solution

/Problems


text:
Fundamentals of Transportation/Trip Generation/Solution

 Problem: Planners have estimated the following models for the AM Peak Hour

$$ T_{O,i} = 1.5*H_i \,\!$$

$$ T_{D,j} = (1.5*E_{off,j}) + (1*E_{oth,j}) + (0.5*E_{ret,j}) \,\!$$

Where:

$$T_{O,i}\,\!$$ = Person Trips Originating in Zone $$i\,\!$$

$$T_{D,j}\,\!$$ = Person Trips Destined for Zone $$j\,\!$$

$$H_i\,\!$$ = Number of Households in Zone $$i\,\!$$

You are also given the following data

A. What are the number of person trips originating in and destined for each city?

B. Normalize the number of person trips so that the number of person trip origins = the number of person trip destinations. Assume the model for person trip origins is more accurate.

 Solution: A. What are the number of person trips originating in and destined for each city?

B. Normalize the number of person trips so that the number of person trip origins = the number of person trip destinations. Assume the model for person trip origins is more accurate.

Use: $$ \quad T_{D,j}^' = T_{D,j} \frac =  > T_{D,j} \frac = T_{D,j} *1.0204 \,\!$$

/Solutions


text:
Active Server Pages/Protecting against user-input (XSS attacks)

To protect your users from Cross-site scripting (XSS) and similar attacks, you should escape both URLs and user-submitted text. In ASP this is done with two functions Server.HTMLEncode, and Server.URLEncode.

Server.HTMLEncode
Don't ever output non-escaped user data:

Instead do the following:

This method should also be used for all data that comes from SQL. Better safe than sorry.

Server.URLEncode
To encode URLs that you insert into the href attribute of A tags, use the Server.URLEncode function, like this:


text:
Fundamentals of Transportation/About

This book is aimed at undergraduate civil engineering students, though the material may provide a useful review for practitioners and graduate students in transportation. Typically, this would be for an Introduction to Transportation course, which might be taken by most students in their sophomore or junior year. Often this is the first engineering course students take, which requires a switch in thinking from simply solving given problems to formulating the problem mathematically before solving it, i.e. from straight-forward calculation often found in undergraduate Calculus to vaguer word problems more reflective of the real world.

How an idea becomes a road
One way to use this wikibook is through the lens of explaining "How an idea becomes a road." It begins with how ideas for roads are generated. This is followed by the analysis of ideas, first determining the origin and destination of a transportation facility (usually a road), then the width required to accommodate demand, and finally the design of the road, with a focus on curvature. The book is divided into three main parts: planning, operations, and design. These correspond to the three main types of practitioners in the transportation engineering community: transportation planners, traffic engineers, and highway engineers.

There are other topics provided as well, including Transit Planning and Operations.

Each page corresponds to the notes from one fifty-minute lecture.

Authors
Authors of this book include David Levinson, Henry Liu of the University of Michigan, William Garrison,Mark Hickman, Adam Danczyk, Michael Corbett, Brendan Nee. Karen Dixon at Oregon State University contributed Flash animations developed by herself and her students linked to in this book.

title: Fundamentals of Transportation/About


text:
Active Server Pages/Prerequisites

ASP (or Active Server Pages) is a scripting tool for dynamic webpages. It is a technology that can be compared to Cold Fusion, JSP, and PHP. While primarily made for the Microsoft Windows platform, there are implementations of ASP technology on other environments.

ASP is the technology that powers the dynamic websites, not the language that the pages are scripted in. There are a number of languages that can be used to script or program a dynamic website. However, most people assume that ASP and vbscript (one of the languages used) are the same.

With the release of the .Net platform, Microsoft also updated ASP to ASP.Net. There are a number of improvements to ASP that ASP.Net provides, but that would be a book unto itself. This textbook focuses on what is now called "classic" ASP. One important difference is that ASP.Net pages are named *.aspx and ASP 3.0 pages are named *.asp, and ASP 3.0 pages are interpreted and ASP.Net pages are compiled thus ASP.net pages work faster. ASP.Net uses the Microsoft .Net framework and can use any language that .Net supports. ASP 3.0 is limited to VBScript and JScript (Microsoft's version of Javascript).

Do I need to know HTML?
Yes and No... The output of ASP is usually HTML, so it is strongly recommended that you are familiar with at least HTML 4.01. While many programmers prefer visual editors like Macromedia's Dreamweaver and Ultradev, Microsoft's Frontpage and Visual InterDev, beginners will benefit more from using a plain text editor until comfortable with the basic concepts.

Do I need to know a programming language?
You should be familiar with at least one object-oriented programming language. This book will teach you how to program in ASP, but it will not teach you how to program. You should understand the following concepts:

 * variables
 * global variables, and how they differ from local variables
 * functions, and
 * how to pass parameters to functions
 * decision-making statements such as if-then and if-then-else
 * looping statements such as the for loop and the while loop

Do I need to install web server software on my computer?
There are sites such as 1asphost.com that provide free web sites with ASP capabilities. You can upload your ASP files, and the server will do all the ASP processing for you.

Find similar services by doing a Google search for "free asp hosting".

You may also install software on your computer to process ASP files locally. Internet Information Services will come in handy for users of Microsoft Windows operating system. And there are Apache webservers available for most of today's operating systems.

In order to execute ASP 3.0 locally, you will need Windows 2000 Professional or higher. All versions of Windows from 2000 include Internet Information Services with the exception of Windows XP Home. Installation is simple, just go to Add/Remove programs and then the Add/Remove Windows components section. Just keep in mind that just because you have IIS installed that does not mean that ASP files will execute.

title: Active Server Pages/Prerequisites


text: User talk:142.33.43.102

title: User talk:142.33.43.102


text: User talk:205.222.248.79

title: User talk:205.222.248.79


text:
Fundamentals of Transportation/Destination Choice

Everything is related to everything else, but near things are more related than distant things. - Waldo Tobler's 'First Law of Geography’

Destination Choice (or trip distribution or zonal interchange analysis), is the second component (after Trip Generation, but before Mode Choice and Route Choice) in the traditional four-step transportation forecasting model. This step matches tripmakers’ origins and destinations to develop a “trip table”, a matrix that displays the number of trips going from each origin to each destination. Historically, trip distribution has been the least developed component of the transportation planning model.

Where: $$T_{ij}\,\!$$ = Trips from origin i to destination j. Work trip distribution is the way that travel demand models understand how people take jobs. There are trip distribution models for other (non-work) activities, which follow the same structure.

Fratar Models
The simplest trip distribution models (Fratar or Growth models) simply extrapolate a base year trip table to the future based on growth, $$T_{ij,y+1} = g*T_{ij,y}\,\!$$

where:
 * $$T_{ij,y}\,\!$$ - Trips from $$i$$ to $$j$$ in year $$y$$
 * $$g\,\!$$ - growth factor

Fratar Model takes no account of changing spatial accessibility due to increased supply or changes in travel patterns and congestion.

Gravity Model
The gravity model illustrates the macroscopic relationships between places (say homes and workplaces). It has long been posited that the interaction between two locations declines with increasing (distance, time, and cost) between them, but is positively associated with the amount of activity at each location (Isard, 1956). In analogy with physics, Reilly (1929) formulated Reilly's law of retail gravitation, and J. Q. Stewart (1948) formulated definitions of demographic gravitation, force, energy, and potential, now called accessibility (Hansen, 1959). The distance decay factor of $$distance^{-1}$$ has been updated to a more comprehensive function of generalized cost, which is not necessarily linear - a negative exponential tends to be the preferred form. In analogy with Newton’s law of gravity, a gravity model is often used in transportation planning.

The gravity model has been corroborated many times as a basic underlying aggregate relationship (Scott 1988, Cervero 1989, Levinson and Kumar 1995). The rate of decline of the interaction (called alternatively, the impedance or friction factor, or the utility or propensity function) has to be empirically measured, and varies by context.

Limiting the usefulness of the gravity model is its aggregate nature. Though policy also operates at an aggregate level, more accurate analyses will retain the most detailed level of information as long as possible. While the gravity model is very successful in explaining the choice of a large number of individuals, the choice of any given individual varies greatly from the predicted value. As applied in an urban travel demand context, the disutilities are primarily time, distance, and cost, although discrete choice models with the application of more expansive utility expressions are sometimes used, as is stratification by income or auto ownership.

Mathematically, the gravity model often takes the form:

$$ T_{ij} = r_i s_j T_{O,i} T_{D,j} f(C_{ij} ) \,\!$$

$$ \sum_j {T_{ij} = T_{O,i} } ,\sum_i {T_{ij} = T_{D,j} } \,\!$$

$$ r_i = ({\sum_j {s_j T_{D,j} f(C_{ij} )} }) ^{-1} \,\!$$

$$ s_j = ({\sum_i {r_i T_{O,i} f(C_{ij} )} }) ^{-1} \,\!$$

where
 * $$T_{ij}\,\!$$ = Trips between origin $$i$$ and destination $$j$$
 * $$T_{O,i}\,\!$$ = Trips originating at $$i$$
 * $$T_{D,j}\,\!$$ = Trips destined for $$j$$
 * $$C_{ij}\,\!$$ = travel cost between $$i$$ and $$j$$
 * $$r_i, s_j\,\!$$ = balancing factors solved iteratively.
 * $$f\,\!$$ = impedance or distance decay factor

It is doubly constrained so that Trips from $$i$$ to $$j$$ equal number of origins and destinations.

Balancing a matrix
Balancing a matrix can be done using what is called the Furness Method, summarized and generalized below.

1. Assess Data, you have $$T_{O,i}\,\!$$,$$ T_{D,j}\,\! $$, $$ C_{ij} \,\!$$

2. Compute $$f(Cij)\,\!$$, e.g.

 * $$f(C_{ij}) = C_{ij}^{-2}\,\!$$
 * $$f(C_{ij}) = e^{-\beta C_{ij}}\,\!$$

3. Iterate to Balance Matrix

(a) Multiply Trips from Zone $$i\,\!$$ ($$T_i\,\!$$) by Trips to Zone $$j\,\!$$ ($$T_j\,\!$$) by Impedance in Cell $$ij\,\!$$ ($$f(C_{ij})\,\! $$) for all $$ij\,\!$$

(b) Sum Row Totals $$T'_{O,i}\,\!$$, Sum Column Totals $$T'_{D,j}\,\!$$

(c) Multiply Rows by $$N_{O,i}=T_{O,i}/T'_{O,i}\,\!$$

(d) Sum Row Totals $$T'_{O,i}\,\!$$, Sum Column Totals $$T'_{D,j}\,\!$$

(e) Compare $$T_{O,i}\,\!$$ and $$T'_{O,i}\,\!$$, $$T_{D,j}\,\!$$ $$T'_{D,j}\,\!$$ if within tolerance stop, Otherwise goto (f)

(f) Multiply Columns by $$N_{D,j}=T_{D,j}/T'_{D,j}\,\!$$

(g) Sum Row Totals $$T'_{O,i}\,\!$$, Sum Column Totals $$T'_{D,j}\,\!$$

(h) Compare $$T_{O,i}\,\!$$ and $$T'_{O,i}\,\!$$, $$T_{D,j}\,\!$$ and $$T'_{D,j}\,\!$$ if within tolerance stop, Otherwise goto (b)

Feedback
One of the key drawbacks to the application of many early models was the inability to take account of congested travel time on the road network in determining the probability of making a trip between two locations. Although Wohl noted as early as 1963 research into the feedback mechanism or the “interdependencies among assigned or distributed volume, travel time (or travel ‘resistance’) and route or system capacity”, this work has yet to be widely adopted with rigorous tests of convergence or with a so-called “equilibrium” or “combined” solution (Boyce et al. 1994). Haney (1972) suggests internal assumptions about travel time used to develop demand should be consistent with the output travel times of the route assignment of that demand. While small methodological inconsistencies are necessarily a problem for estimating base year conditions, forecasting becomes even more tenuous without an understanding of the feedback between supply and demand. Initially heuristic methods were developed by Irwin and Von Cube (as quoted in Florian et al. (1975) ) and others, and later formal mathematical programming techniques were established by Evans (1976).

Feedback and time budgets
A key point in analyzing feedback is the finding in earlier research by Levinson and Kumar (1994) that commuting times have remained stable over the past thirty years in the Washington Metropolitan Region, despite significant changes in household income, land use pattern, family structure, and labor force participation. Similar results have been found in the Twin Cities by Barnes and Davis (2000).

The stability of travel times and distribution curves over the past three decades gives a good basis for the application of aggregate trip distribution models for relatively long term forecasting. This is not to suggest that there exists a constant travel time budget.

In terms of time budgets:
 * 1440 Minutes in a Day
 * Time Spent Traveling: ~ 100 minutes + or -
 * Time Spent Traveling Home to Work: 20 – 30 minutes + or -

Research has found that auto commuting times have remained largely stable over the past forty years, despite significant changes in transportation networks, congestion, household income, land use pattern, family structure, and labor force participation. The stability of travel times and distribution curves gives a good basis for the application of trip distribution models for relatively long term forecasting.

Example 1: Solving for impedance
 Problem:

You are given the travel times between zones, compute the impedance matrix $$f(C_{ij})\,\! $$, assuming $$f(C_{ij})=C_{ij}^{-2}\,\!$$.

Compute impedances ($$f(C_{ij}) \,\!$$)

 Solution:

Example 2: Balancing a Matrix Using Gravity Model
 Problem:

You are given the travel times between zones, trips originating at each zone (zone1 =15, zone 2=15) trips destined for each zone (zone 1=10, zone 2 = 20) and asked to use the classic gravity model $$f(C_{ij})=C_{ij}^{-2}\,\!$$

 Solution:

(a) Compute impedances ($$f(C_{ij}) $$)

(b) Find the trip table

...

So while the matrix is not strictly balanced, it is very close, well within a 1% threshold, after 16 iterations. The threshold refers to the proximity of the normalizing factor to 1.0.

Additional Questions

 * Homework
 * Additional Questions

Variables

 * $$T_{O,i}$$ - Trips leaving origin $$i$$
 * $$T_{D,j}$$ - Trips arriving at destination $$j$$
 * $$T'_{D,j}$$ - Effective Trips arriving at destination $$j$$, computed as a result for calibration to the next iteration
 * $$T_{ij}$$ - Total number of trips between origin $$i$$ and destination $$j$$
 * $$r_i$$ - Calibration parameter for Origins
 * $$s_j$$ - Calibration parameter for Destinations
 * $$f(C_{ij})$$ - Cost function between origin $$i$$ and destination $$j$$

Videos

 * Destination Choice
 * Matrix Math
 * Solving for Impedance
 * Balancing a Matrix


text:
User:Shirleyom

Hi everybody, Welcome to my WikiBooks user page. By the way, my name is Shirley and I am 16 years old. I am from Ghana in West Africa. It is nice to meet you all.

Have a nice day.

~Shirley~

title: User:Shirleyom


text:
Talk:How To Build a Pinewood Derby Car/Physics

This paragraph has a couple of problems:

"Now consider an 8.53 m (28 foot) track that consists of a 30“ ramp followed by a flat portion to the finish. The ramp section is 2.43 m (8 feet) long and the flat section is 6.1 m (20 feet) long. The travels the 2.43 m ramp at an average velocity of v / 2 = ..."

1) A 30" ramp? Ealier the article claims the ramp is four feet high. Which is it?

2) "The travels ...". What travels? The car, perhaps?

I would leave my id but some moronic entity deleted it, so you will have to make do with my IP.

 * Thank you 71.117.209.73 - 1) thirty degree ramp - hypotenuse is double the base, which makes life easier (8 feet of track for a four foot rise) and 2) car of course. --Kkmurray (talk) 03:03, 6 March 2008 (UTC)

Angular velocity?
Isn't it v = r omega, not omega = r v?

Tread pattern affects rolling resistance, but raising a wheel doesn't?
A "V" or "H" tread pattern reduces CRF because it "limits the contact area," but raising a wheel doesn't because the same weight is redistributed elsewhere? I don't know enough about rolling resistance to know which is correct, but if rolling resistance is independent of the contact area, then the "V" or "H" tread shouldn't affect it; conversely, if Crr does depend on the contact area, then raising a wheel will certainly reduce it.

Normal forces impact on friction
The normal force on the axle is not affected by the slope because the wheel always rides on the same contact area of the axle so there is no cos(theta) term in the equation.

Further, putting the weight off center (in the back) cause the normal force on the rear axles to be greater than that on the front axles, increasing the frictional force. So there is a trade-off between increased potential energy and frictional forces during the inclined ramp and the linear track. So the equation for the normal force N per axle is not just N/4. It must reflect the location of the center of mass.


text: Wikibooks:Requests for deletion/Transwiki:Holden Astra


text: Wikibooks:Requests for deletion/Teaching Assistant in France Survival Guide


text:
Muggles' Guide to Harry Potter/Magic/Augurey

Overview
An Augurey, or Irish Phoenix, is a small greenish-black bird that resembles a vulture and can emit a distinctive low cry. Being shy creatures, they stay primarily within their tear-shaped nests and fly only in periods of heavy rain.

Extended Description
Though native to Britain and Ireland, the Augurey has also been spotted throughout northern Europe. They make their nests in bramble and thorn and their diet consists mostly of large insects and fairies.

In the past, wizards associated the cry of the Augurey with death, and a few early wizards are believed to have succumbed to a heart attack upon being surprised by the wail of an unseen augurey. Later it was determined that, instead of foretelling death, the augurey's cry signalled an impending rain shower.

The Augurey has been used as a home weather forecaster, though its persistent moaning during the winter months can be unbearable for some. As Augurey feathers repel ink, they are ineffective for quills.


text: Category:Book:Fundamentals of Transportation


text:
Talk:Introduction to Crochet/Simple projects

Other potential projects
Most crochet instruction books include several dozen projects. A few ideas:
 * A hook case
 * A yarn catcher
 * A beverage insulator (koozie)
 * A water bottle carrier (with shoulder strap)
 * A backpack
 * A headband
 * Placemats
 * An afghan blanket
 * A table runner
 * A purse
 * A sweater
 * A baby blanket

Projects

 * Clothing
 * Hats
 * Scarves
 * Sweaters
 * Skirts

 * Jewelry

 * Satchels

 * Household
 * Afghans
 * Pillows
 * Floormats
 * Bowls
 * Toys


text:
User:Pinkbuffers87

Creating Equity in the Classroom

By: Jessi Buffkin

INTRODUCTION
Equity in schools is a necessity and this should be a main focus. Classrooms need to have a secure environment. This is the role of the teachers and schools to make sure the students have environment that is easily able to learn in. Teachers need to be well prepared when entering the classroom when it comes to different race, ethnicity, sexual preference and disability. There are different actions that the school and teacher can take to accomplish creating equity. This is a matter of social justice.

What is racisms effect on creating equity in the classroom?
Racism spreads through schools all the time. Today in school there are many teachers who teach foreign languages and other classes where students can learn culture. The teachers teach the students about culture by cooking the foods of that ethnicity and having festivals. Racism is still occurring, and these foreign language classes are not helping this factor. Many respectable results can come from a student learning in a multicultural school. One is being able to adjust to different environments when not in school. While the students are in school they get to meet all different kinds of people so that when they go out in the real world the students will have open mind to the world. This results in not being stereotypical. It also prepares the child to deal with situations that might occur due to racism. The student also gets to learn about many different cultures. These are all many rewards that come out of having a child in a multicultural environment. All these things can lead to equity in schools, because maybe then there would not be such a large extent of racism in schools (Shehata). There are different minorities in schools; of them African Americans are the majorities. According to Wright, “The dilemmatic issue regarding the lack of achievement by African-American children may conceivably be changed if equal and quality educational opportunities are provided through instruction in the classroom.” Some teachers refuse to change the way they teach, regardless if there teaching technique is effective or not for all a students. Anderson says, “Those who dare to teach must never cease to learn.” To create equity in the classroom the teacher has to learn the techniques of all the students. (Young)

Should teachers have an open minds about sexual preference?
Students with different sexual preferences are very common in schools today. It is the teacher’s responsibility to make the child feel secure in the school environment. Teachers can do this by not allowing name calling whether the teacher agrees or disagrees. The teacher can also allow no assault or violence to these students (Stereotypes, Silence, and Speaking Out).This all has to do with “preventing youth crime.” Hate crime is defined as an attack on an individual or his or her property. Since this is a learned behavior teachers can try there best to prevent this. There are some steps that a school can take to try to prevent this kind of behavior. One is to give the teachers and the people who work at the school some type of preparation for how to handle certain situations. The teachers need to learn how to report a problem if one occurs like this. The school needs to make sure the students receive the same type of advising. This teaches students why being hateful towards certain types of people is wrong (Preventing Youth Hate Crime).

Is stereotyping a good idea for teachers in schools?
Stereotyping is not a good thing when you are a teacher. You need to come into a classroom with an open mind and someone might surprise you. For example Asian Americans, are typically stereotyped as submissive and hardworking. When stereotyping, usually you separate those children into another category which is not creating equity among the students (Preventing Youth Hate Crime). There was a study on, “effects of gender of teacher, gender of student, and classroom subject on teacher-student interactions.” There were 597 students being used for this experiment, almost equally distributed between girls and boys. There were 28 teachers involved in this experiment. The result in this experiment were most of the teachers interacted with the males more. Today in society males and females are treated differently. When it comes to the classroom it has been shown that male teachers have higher expectations for boys in math, and girls in English. According to this journal, (classroom interactions: gender of teacher, gender of student) “One way to study classroom interactions is through the use of the interactions for sex equity in classroom teaching (INTERSECT) observational instrument developed by Sadker et al (1984).” The final outcome demonstrated that male students were applauded, corrected, managed, and disapproved interactions. The boys got more teacher responses than the girl students. This was in junior high and in high school. This research shows that teachers seem to pay more attention to the males than the females which does not create equity in the classroom. These are some things that you try to avoid when in the classroom. (Duffy) There was a club that was brought together in Ontario schools. This club was brought together to discuss history of racism, and racism now in society. It states that in the curriculum for Ontario there are no courses that teach about equity. Only teachers who want to learn about this will. George Dei, chair of-sociology and equity studies in education at the Ontario Institute For Studies in Education, says there are a number of teachers who should be recognized for their anti-racism work. "But there are also many who have closed their minds," he adds. "We cannot wish racism away. We must acknowledge and respond to it." Which they did, stating that some of the practice in there schools are racist. Now there has to be fact about discrimination in text books today. Ontario is institute for studies in education (Black).

How should teachers create equity in classrooms?
There are many things that you can do to create equity in the classroom. Women can feel discouraged at times because they can feel as though they are being undermined. When a teacher will focus on a certain type of group of people this is not creating equity. Maybe the teacher would focus on the men because he or she thinks the men can succeed more. Focusing on any type of minority or race excludes the other classmates to respond. There are many things that someone can do to create equity. The first thing to do is state your expectations and stating that it is possible for anyone to do well in your class, even if they need some additional help. Make sure you give a proper wait-time when you are asking a question. Students need a proper amount of time to answer the question and this gives all students an equal opportunity to answer the question (Sandler). Also learn you’re Students' Names, and try to create a Safe Environment and lastly Be Aware of your Audience. Equity is defined as, “the state, quality, or ideal of being just, impartial, and fair.” (Houghton)

Conclusion
All this can lead to creating equity in the classroom. The teacher mostly has to make sure this occurs. The teacher has to have an open mind when entering the classroom, trying to avoid all types of stereotyping toward racism sexual preference and any minority group.

Multiple Choice Questions

1. What is the teacher responsible for creating when in the classroom? A.Making sure all students receive an A B.Creating a safe environment for students C.Making sure students copy down there homework D.Creating friendship among the students

2. What is one step a teacher can make to create equity in the classroom? A.Researching all the students different backgrounds B.Asking the children what ethnicity they are C.Making sure the teacher states all expectations D.Condemning the child for bad grades

3. When a teacher stereotypes what is she doing? A.Having an open mind to all students B.Having a closed mind and making prejudgments C.Telling the children to separate D.Creating fairness

4. When does the teacher need to state his or her expectations of the class? A.At the end of the semester B.In the middle of the semester C.When report cards come out D.On the first day of school

Answers to the multiple choice questions B. C. B. D.

Essay Question: What does a school do when allowing discrimination, racism, and stereotyping into the school? The school is not doing its job. The schools job is to create a safe environment for all the students. It is not the schools job to allow this kind behavior to continue. The school needs to take proper actions when these situations occur. When this is not allowed the school is then creating equity in the classroom.

title: User:Pinkbuffers87


text:
User talk:Pinkbuffers87

Welcome, !

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 20:21, 5 March 2008 (UTC)

title: User talk:Pinkbuffers87


text:
Fundamentals of Transportation/Choice Modeling

Mode choice analysis is the third step in the conventional four-step transportation forecasting model, following Trip Generation and Destination Choice but before Route Choice. While trip distribution's zonal interchange analysis yields a set of origin destination (OD) tables which tells where the trips will be made, mode choice analysis allows the modeler to determine what mode of transport will be used.

Disaggregate Travel Demand models
Travel demand theory was introduced in the appendix on traffic generation. The core of the field is the set of models developed following work by Stan Warner in 1962 (Strategic Choice of Mode in Urban Travel: A Study of Binary Choice). Using data from the CATS, Warner investigated classification techniques using models from biology and psychology. Building from Warner and other early investigators, disaggregate demand models emerged. Analysis is disaggregate in that individuals are the basic units of observation, yet aggregate because models yield a single set of parameters describing the choice behavior of the population. Behavior enters because the theory made use of consumer behavior concepts from economics and parts of choice behavior concepts from psychology. Researchers at the University of California, Berkeley (especially Daniel McFadden, who won a Nobel Prize in Economics for his efforts) and the Massachusetts Institute of Technology (Moshe Ben-Akiva) (and in MIT associated consulting firms, especially Cambridge Systematics) developed what has become known as choice models, direct demand models (DDM), Random Utility Models (RUM) or, in its most used form, the multinomial logit model (MNL).

Choice models have attracted a lot of attention and work; the Proceedings of the International Association for Travel Behavior Research chronicles the evolution of the models. The models are treated in modern transportation planning and transportation engineering textbooks.

One reason for rapid model development was a felt need. Systems were being proposed (especially transit systems) where no empirical experience of the type used in diversion curves was available. Choice models permit comparison of more than two alternatives and the importance of attributes of alternatives. There was the general desire for an analysis technique that depended less on aggregate analysis and with a greater behavioral content. And, there was attraction too, because choice models have logical and behavioral roots extended back to the 1920s as well as roots in Kelvin Lancaster’s consumer behavior theory, in utility theory, and in modern statistical methods.

The Logit Model
The Logit Model, widely used for transportation forecasting in various forms, was first theorized by Daniel McFadden. The Logit model says, the probability that a certain mode choice will be taken is proportional to $$e$$ raised to the utility over the sum of $$e$$ raised to the utility.

$$ P_m {\rm{ }} = {\rm{ }}\frac{\rm{ }} \,\!$$

For any Logit Model the sum of the probability of all modes will equal 1.

$$ 1{\rm{ }} = {\rm{ }}\sum{P_{m}}{\rm{ }} \,\!$$

The Logit Model also says that if a new mode of transportation is added to a system (or taken away) then the original modes will lose (or gain) an amount of travels proportional to their share originally.

Steps for the Logit Model:
 * Compute the Utility for each OD pair and mode
 * Compute Exponentiated utilities for each OD pair and mode
 * Sum Exponentiated utilities for each OD pair
 * Compute Probability for each mode by OD pair
 * Multiply Probability for OD pair by number of trips for each OD pair

Psychological roots

Early psychology work involved the typical experiment: Here are two objects with weights, $$w_1$$ and $$w_2$$, which is heavier? The finding from such an experiment would be that the greater the difference in weight, the greater the probability of choosing correctly. Graphs similar to the one on the right result. Louis Leon Thurstone proposed (in the 1920s) that perceived weight,

$$ w = v + e $$,

where $$v$$ is the true weight and $$e$$ is random with $$E(e) = 0. $$

The assumption that $$e$$ is normally and identically distributed (NID) yields the binary probit model.

Econometric formulation
Economists deal with utility rather than physical weights, and say that

 * observed utility = mean utility + random term.

Utility in this context refers to the total satisfaction (or happiness) received from making a particular choice or consuming a good or service.

The characteristics of the object, x, must be considered, so we have

 * u(x) = v(x) + e(x).

If we follow Thurston's assumption, we again have a probit model.

An alternative is to assume that the error terms are independently and identically distributed with a Weibull, Gumbel Type I, or double exponential distribution (They are much the same, and differ slightly in their tails (thicker) from the normal distribution). This yields the multinomial logit model (MNL). Daniel McFadden argued that the Weibull had desirable properties compared to other distributions that might be used. Among other things, the error terms are normally and identically distributed. The logit model is simply a log ratio of the probability of choosing a mode to the probability of not choosing a mode.

\log \left( {\frac } \right) = v(x_i ) \,\!$$

Observe the mathematical similarity between the logit model and the S-curves we estimated earlier, although here share increases with utility rather than time. With a choice model we are explaining the share of travelers using a mode (or the probability that an individual traveler uses a mode multiplied by the number of travelers).

The comparison with S-curves is suggestive that modes (or technologies) get adopted as their utility increases, which happens over time for several reasons. First, because the utility itself is a function of network effects, the more users, the more valuable the service, higher the utility associated with joining the network. Second, because utility increases as user costs drop, which happens when fixed costs can be spread over more users (another network effect). Third, technological advances, which occur over time and as the number of users increases, drive down relative cost.

An illustration of a utility expression is given:

\log \left( {\frac } \right) = \beta _0 + \beta _1 \left( {c_A  - c_T } \right) + \beta _2 \left( {t_A  - t_T } \right) + \beta _3 I + \beta _4 N = v_A \,\!$$

where
 * Pi = Probability of choosing mode i.
 * PA = Probability of taking auto
 * cA,cT = cost of auto, transit
 * tA,tT = travel time of auto, transit
 * I = income
 * N = Number of travelers

With algebra, the model can be translated to its most widely used form:

\frac = e^{v_A } \,\!$$

P_A = e^{v_A }  - P_A e^{v_A } \,\!$$

P_A \left( {1 + e^{v_A } } \right) = e^{v_A } \,\!$$

P_A = \frac \,\!$$

It is fair to make two conflicting statements about the estimation and use of this model:

 * 1) It's a "house of cards", and
 * 2) Used by a technically competent and thoughtful analyst, it's useful.

The "house of cards" problem largely arises from the utility theory basis of the model specification. Broadly, utility theory assumes that (1) users and suppliers have perfect information about the market; (2) they have deterministic functions (faced with the same options, they will always make the same choices); and (3) switching between alternatives is costless. These assumptions don’t fit very well with what is known about behavior. Furthermore, the aggregation of utility across the population is impossible since there is no universal utility scale.

Suppose an option has a net utility ujk (option k, person j). We can imagine that having a systematic part vjk that is a function of the characteristics of an object and person j, plus a random part ejk, which represents tastes, observational errors, and a bunch of other things (it gets murky here). (An object such as a vehicle does not have utility, it is characteristics of a vehicle that have utility.) The introduction of e lets us do some aggregation. As noted above, we think of observable utility as being a function:

v_A = \beta _0  + \beta _1 \left( {c_A  - c_T } \right) + \beta _2 \left( {t_A  - t_T } \right) + \beta _3 I + \beta _4 N \,\!$$

where each variable represents a characteristic of the auto trip. The value β0 is termed an alternative specific constant. Most modelers say it represents characteristics left out of the equation (e.g., the political correctness of a mode, if I take transit I feel morally righteous, so β0 may be negative for the automobile), but it includes whatever is needed to make error terms NID.

Econometric estimation

Turning now to some technical matters, how do we estimate v(x)? Utility (v(x)) isn’t observable. All we can observe are choices (say, measured as 0 or 1), and we want to talk about probabilities of choices that range from 0 to 1. (If we do a regression on 0s and 1s we might measure for j a probability of 1.4 or -0.2 of taking an auto.) Further, the distribution of the error terms wouldn’t have appropriate statistical characteristics.

The MNL approach is to make a maximum likelihood estimate of this functional form. The likelihood function is:

L^* = \prod_{n = 1}^N {f\left( {y_n \left| {x_n ,\theta } \right.} \right)} \,\!$$

we solve for the estimated parameters

\hat \theta \,\!$$

that max L*. This happens when:

\frac = 0 \,\!$$

The log-likelihood is easier to work with, as the products turn to sums:

\ln L^* = \sum_{n = 1}^N {\ln f\left( {y_n \left| {x_n ,\theta } \right.} \right)} \,\!$$

Consider an example adopted from John Bitzan’s Transportation Economics Notes. Let X be a binary variable that is gamma and 0 with probability (1- gamma). Then f(0) = (1- gamma) and f(1) = gamma. Suppose that we have 5 observations of X, giving the sample {1,1,1,0,1}. To find the maximum likelihood estimator of gamma examine various values of gamma, and for these values determine the probability of drawing the sample {1,1,1,0,1} If gamma takes the value 0, the probability of drawing our sample is 0. If gamma is 0.1, then the probability of getting our sample is: f(1,1,1,0,1) = f(1)f(1)f(1)f(0)f(1) = 0.1*0.1*0.1*0.9*0.1=0.00009. We can compute the probability of obtaining our sample over a range of gamma – this is our likelihood function. The likelihood function for n independent observations in a logit model is

L^* = \prod_{n = 1}^N {P_i ^{Y_i } } \left( {1 - P_i } \right)^{1 - Y_i } \,\!$$

where: Yi = 1 or 0 (choosing e.g. auto or not-auto) and Pi = the probability of observing Yi=1

The log likelihood is thus:

\ell = \ln L^*  = \sum_{i = 1}^n {\left[ {Y_i \ln P_i  + \left( {1 - Y_i } \right)\ln \left( {1 - P_i } \right)} \right]} \,\!$$

In the binomial (two alternative) logit model,

P_{auto} = \frac

\,\!$$, so

\ell = \ln L^*  = \sum_{i = 1}^n {\left[ {Y_i v(x_{auto} ) - \ln \left( {1 + e^{v(x_{auto} )} } \right)} \right]} \,\!$$

The log-likelihood function is maximized setting the partial derivatives to zero:

\frac = \sum_{i = 1}^n {\left( {Y_i - \hat P_i } \right) = } 0 \,\!$$

The above gives the essence of modern MNL choice modeling.

Independence of Irrelevant Alternatives (IIA)
Independence of Irrelevant Alternatives is a property of Logit, but not all Discrete Choice models. In brief, the implication of IIA is that if you add a mode, it will draw from present modes in proportion to their existing shares. (And similarly, if you remove a mode, its users will switch to other modes in proportion to their previous share). To see why this property may cause problems, consider the following example: Imagine we have seven modes in our logit mode choice model (drive alone, carpool 2 passenger, carpool 3+ passenger, walk to transit, auto driver to transit (park and ride), auto passenger to transit (kiss and ride), and walk or bike). If we eliminated Kiss and Ride, a disproportionate number may use Park and Ride or carpool.

Consider another example. Imagine there is a mode choice between driving and taking a red bus, and currently each has 50% share. If we introduce another mode, let's call it a blue bus with identical attributes to the red bus, the logit mode choice model would give each mode 33.3% of the market, or in other words, buses will collectively have 66.7% market share. Logically, if the mode is truly identical, it would not attract any additional passengers (though one can imagine scenarios where adding capacity would increase bus mode share, particularly if the bus was capacity constrained.

There are several strategies that help with the IIA problem. Nesting of choices allows us to reduce this problem. However, there is an issue of the proper Nesting structure. Other alternatives include more complex models (e.g. Mixed Logit) which are more difficult to estimate.

Returning to roots
The discussion above is based on the economist’s utility formulation. At the time MNL modeling was developed there was some attention to psychologist's choice work (e.g., Luce’s choice axioms discussed in his Individual Choice Behavior, 1959). It has an analytic side in computational process modeling. Emphasis is on how people think when they make choices or solve problems (see Newell and Simon 1972). Put another way, in contrast to utility theory, it stresses not the choice but the way the choice was made. It provides a conceptual framework for travel choices and agendas of activities involving considerations of long and short term memory, effectors, and other aspects of thought and decision processes. It takes the form of rules dealing with the way information is searched and acted on. Although there is a lot of attention to behavioral analysis in transportation work, the best of modern psychological ideas are only beginning to enter the field. (e.g. Golledge, Kwan and Garling 1984; Garling, Kwan, and Golledge 1994).

Example 1: Mode Choice Model
 Problem:

You are given this mode choice model $$U_{ijm} = -0.412 (C_c/w) -0.0201* C_{ivt} - 0.0531* C_{ovt} -0.89*D_1 - 1.78 D_3 - 2.15 D_4 \,\!$$

Where:

 * $$C_c/w\,\!$$ = cost of mode (cents) / wage rate (in cents per minute)
 * $$C_{ivt}\,\!$$ = travel time in-vehicle (min)
 * $$C_{ovt}\,\!$$ = travel time out-of-vehicle (min)
 * $$D\,\!$$ = mode specific dummies: (dummies take the value of 1 or 0)
 * $$D_1$$ = driving,
 * $$D_2$$ = transit with walk access, [base mode]
 * $$D_3$$ = transit with auto access,
 * $$D_4$$ = carpool

With these inputs:

What are the resultant mode shares?

 Solution:

Interpretation

Value of Time:

$$.0411/2.24 = \$0.0183/min = $1.10/hour $$

(in 1967 $, when the wage rate was about $2.85/hour)

implication, if you can improve the travel time (by more buses, less bottlenecks, e.g.) for less than $1.10/hour/person, then it is socially worthwhile.

Example 2: Mode Choice Model Interpretation
What mode would a perfectly rational, perfectly informed traveler choose in a deterministic world given these facts:

 Case 1

Car always wins (independent of parameters as long as all are < 0)

 Case 2

Under observed parameters, bus always wins, but not necessarily under all parameters.

It is important to note that individuals differ in parameters. We could introduce socio-economic and other observable characteristics as well as a stochastic error term to make the problem more realistic.

Sample Problem

 * Problem ( Solution )
 * Problem ( Solution )

Additional Questions

 * Homework
 * Additional Questions

Variables

 * $$U_{ijm}$$- Utility of traveling from i to j by mode m
 * $$D_n$$ = mode specific dummies: (dummies take the value of 1 or 0)
 * $$P_m$$ = Probability of mode m
 * $$C_c/w$$ = cost of mode (cents) / wage rate (in cents per minute)
 * $$C_{ivt}$$ = travel time in-vehicle (min)
 * $$C_{ovt}$$ = travel time out-of-vehicle (min)
 * $$D_n$$ = mode specific dummies: (dummies take the value of 1 or 0)

Abbreviations

 * WCT - walk connected transit
 * ADT - auto connect transit (drive alone/park and ride)
 * APT - auto connect transit (auto passenger/kiss and ride)
 * AU1 - auto driver (no passenger)
 * AU2 - auto 2 occupants
 * AU3+ - auto 3+ occupants
 * WK/BK - walk/bike
 * IIA - Independence of Irrelevant Alternatives

Key Terms

 * Mode choice
 * Logit
 * Probability
 * Independence of Irrelevant Alternatives (IIA)
 * Dummy Variable (takes value of 1 or 0)

Videos

 * Mode Choice
 * Mode Choice Problem


text: User talk:205.125.173.22

title: User talk:205.125.173.22


text: User talk:190.138.82.110

title: User talk:190.138.82.110


text:
Fundamentals of Transportation/Mode Choice/Problem

 Problem: You are given the following mode choice model.

$$U_{ijm} = -1 C_{ijm} + 5 D_T\,\!$$

Where:
 * $$C_{ijm}$$ = travel cost between $$i$$ and $$j$$ by mode $$m$$
 * $$D_T$$ = dummy variable (alternative specific constant) for transit

and Travel Times

A. Using a logit model, determine the probability of a traveler driving.

B. Using the results from the previous problem (#2), how many car trips will there be?

 * Solution

/Problems


text:
Fundamentals of Transportation/Mode Choice/Solution

 Problem: You are given the following mode choice model.

$$U_{ijm} = -1 C_{ijm} + 5 D_T\,\!$$

Where:
 * $$C_{ijm}$$ = travel cost between $$i$$ and $$j$$ by mode $$m$$
 * $$D_T$$ = dummy variable (alternative specific constant) for transit

 Solution:  Part A

A. Using a logit model, determine the probability of a traveler driving.

Solution Steps

 * 1) Compute Utility for Each Mode for Each Cell
 * 2) Compute Exponentiated Utilities for Each Cell
 * 3) Sum Exponentiated Utilities
 * 4) Compute Probability for Each Mode for Each Cell
 * 5) Multiply Probability in Each Cell by Number of Trips in Each Cell

Part B

B. Using the results from the previous problem (#2), how many car trips will there be?

Recall

/Solutions


title: User:Blackwatch21


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User talk:Blackwatch21

Please send me a message here: http://en.wikipedia.org/wiki/User_talk:Blackwatch21

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Technical Theatre/Lighting/Controls

Introduction to Lighting Control
Lighting control refers of any changes made in the light produced by one or more lighting instruments. This includes (but is by no means limited to) changes in intensity, color, direction, diffusion, polarization, and pattern. Though various methods of controlling these variables have evolved over time, it is common to manipulate them all from a central control board. The control board typically communicates with a system of dimmers, which control how much electricity flows to each light, as well as with any individual lights that can mechanically move/change color/rotate/etc. Such lights are usually referred to as intelligent lights.

title: Technical Theatre/Lighting/Controls


text:
User talk:Ewr2

'''Eric Wilson TR: 11:00- 12:15

Effective Schools

Table of Contents: I.	Introduction II. Philosophy III. The Role of the Teacher IV. The Role of the Administration V.	The Pole of the Parents VI. Cultural-Immersion VII. Six Dimensions of Transformational Leadership VIII. Literacy IX. Conclusion X.	Multiple Choice and Essay Questions XI. Reflection XII. Work Cited I.	Introduction'''

Much debate has gone into what exactly makes up an effective school. Some believe that instruction is the most important element in an effective school and others feel that the administrators that keep the schools in order are what make up an effective school. This section will uncover the question: What makes up an effective school?” '''II. Philosophy''' The first task that a school must face is its philosophy. This tells the students what the school expects from them. Many schools tell their students to be respectful and kind. This helps to build a harmonious en vironment in the school. '''III. The Role of the Teacher''' Posed with this question, the first answer that many people will probably give is the teacher. The teacher is a vital part of the school; after all, the teacher controls the classroom and decides the pace and the direction of the class. The teacher has the power to spark inspiration and make the students ask question about this complicated world that they live in. Research done by Maryann Manning and Janice Patterson performed research on eight teachers taking notes on what types of instruction would be helpful for the school. Their research indicated a few areas: 1.) Remove barriers to help communication with parents, 2.) Provide the right books for the child that are up to date, and 3.) Give the students more access to topics that are relevant to the curriculum that the students are more interested in. IV.	The Role of the Administration	The administration has another big role in determining the effectiveness of the schools. The administration’s job is to make sure that the school is in order.  The principal has to discipline the troublemakers in the school.  Administration deals with the student’s parents when a conflict is present.  They deal with the political side of the school.  	Both administration and teachers help to create a safe learning environment that allows the students to concentrate on the work and make good grades.  That is why schools in a nicer part of town seem to do better on standardized tests than students who live in a not so desirable part of town. This evidence can be seen in the motion picture “Lean on Me” with Morgan Freeman. Freeman plays the role of a high school principal who takes a job at a school with some of the worst test scores in the state of New Jersey. Freeman along with the other faculty members helps to change the culture in the school and helps the students to achieve higher test scores and increase their self- esteem. They turned an ineffective school into an effective school. V.	The Role of Parents Parents are also a factor in helping schools become effective. The PTA (Parent Teacher Association) has encouraged the involvement of parents in the schools. The parents are given information on the school’s programs and are encouraged to help with fund raisers. The money brought in from the fundraisers help pay for school functions such as the prom. Besides the PTA, parents can also encourage the kids to do well. Students may have a question about their homework and the parent can help teach the student. Based on the research entitled: Parent Involvement and Educational Outcomes for Latino Students (Marschall, 2006), the student’s parents that were most involved performed better in school compared to the students whose parents were not able to participate as much. '''VI. Cultural-Immersion''' Effective schools also need to show the world to their students. Being able to share ideas from a wide variety of cultures from around the world may help to “break down” cultural differences in this country. “Evidence suggests that community cultural-immersion activities incorporated in teacher- preparation programs can not only help preservice teachers correct misperceptions about, but build relationships with their learners that can potentially impact student achievement.’ (Cooper, 2007). '''VII. Six Dimensions of Transformational Leadership''' Research done by John Ross for the Journal of Education Research (Effects of Running Records Assessment on Early Literacy Achievement) provides these six dimensions of transformational leadership relevant to schools:

1.	Symbolize good professional practice. 2.	Provide individualized support. 3.	Provide intellectual stimulation. 4.	Hold high performance expectations 5.	Foster a vision. 6.	Collaborate on decision making. '''VIII. Literacy''' Literacy is the most important part of an individual’s education, because it allows the student to research and get a great deal of information. A research study was done at the Center for the Improvement of Early Reading Achievement took a look at how the teacher, school, community, and home effect the child’s reading abilities. The research showed that the collaboration with all of these factors were very helpful to the student. This allows the student to get more practice outside of school. '''IX. Conclusion''' This section shows what goes into effective schools and hopefully one day these materials and needs will be available to all of America’s students. If all of the parts of the school can work together, then the school can be an effective one.

X.	Multiple Choice Questions

1.	What is a teacher’s philosophy? a.	The way the teacher teaches. b.	The way the teacher wants the students to learn c.	Both A and B. 2.	What is the role of the administration? a.	Boss everyone around b.	Make the student’s miserable c.	Be a friend d.	Maintain order in the school. 3.	A student that starts out in an undesirable environment can… a.	Do poorly in school b.	Do well in school c.	Stay the same 4.	The parents who are more involved make their kid… a.	More likely to do well in school. b.	 Less likely to do well in school. c.	Stay the same. d.	Brag about their cool parents. 5.	What makes a school effective? a.	Good teachers b.	A good principal c.	Helpful parents d.	All the above

Answer Key: 1.) C., 2.) D., 3.)B., 4.)A., 5.)D.

Essay Question: Describe in your own words what makes up an effective school.

'''XI. Reflection on Effective Schools''' In my reflection on the topic of effective schools, I have realized that a lot of aspects go into making an effective school. I did not realize that so much research goes into this area of education. I found the research on the six dimensions of transformational leadership relevant to schools to be very straight forward and very achievable for schools to adopt and put into motion. This paper has also taught me that students have the potential to be very successful contributors to society, no matter where they come from. Schools have a power to spark inspiration into the lives of kids and help them see that the world has a lot to offer them and get the kids excited about the role that they will have once they finish school. Teachers are always looking for better ways of instructing their students. This is great because teachers are always looking for a new way of engaging their students’ interest. Administration, teachers, and staff all need to work together to keep the environment of the school a safe one. This allows the students the chance to focus on the instruction and not worry about troublesome students interfering with the learning process. The role of the parent in the school is very important to the success of the student. The research showed that the more the parent was willing to be involved with the school, the better the student did in school. This was a very rewarding experience for me.

'''XII. Work Cited''' Cooper, J E (May-June 2007). Strengthening the case for community-based learning in teacher education. Journal of Teacher Education. , 58, 3. p.245(11). Retrieved March 03, 2008, from General OneFile via Gale: http://find.galegroup.com/itx/inf omark.do?&contentSet=IAC-Documents&type=retrieve&tabID=T002&prodId=ITOF&docId=A163544643&source=gale&userGroupName=viva2_tncc&version=1.0 Manning, M., & Patterson, J. (Winter 2003). Taking Action with Teacher Research. Childhood Education. , 80, 2. p.104(1). Retrieved March 04, 2008, from General OneFile via Gale: http://find.galegroup.com/itx/infomark.do?&contentSet=IAC-Documents&type=retrieve&tabID=T002&prodId=ITOF&docId=A112165951&source=gale&userGroupName=viva2_vccs&version=1.0 Marschall, M. (Sept 2006). Parent involvement and educational outcomes for Latino students. The Review of Policy Research. , 23, 5. p.1053(24). Retrieved March 03, 2008, from General OneFile via Gale: http://find.galegroup.com/itx/infomark.do?&contentSet=IAC-Documents&type=retrieve&tabID=T002&prodId=ITOF&docId=A153691883&source=gale&userGroupName=viva2_tncc&version=1.0

Ross, J A (March-April 2004). Effects of running records assessment on early literacy achievement. The Journal of Educational Research. , 97, 4. p.186(9). Retrieved March 04, 2008, from General OneFile via Gale: http://find.galegroup.com/itx/infomark.do?&contentSet=IAC-Documents&type=retrieve&tabID=T002&prodId=ITOF&docId=A115346127&source=gale&userGroupName=viva2_vccs&version=1.0

Taylor, B M, & Pearson, P. D. (Nov 2004). Research on learning to read--at school, at home, and in the community. The Elementary School Journal. , 105, 2. p.167(15). Retrieved March 03, 2008, from General OneFile via Gale: http://find.galegroup.com/itx/infomark.do?&contentSet=IAC-Documents&type=retrieve&tabID=T002&prodId=ITOF&docId=A125954997&source=gale&userGroupName=viva2_tncc&version=1.0

title: User talk:Ewr2


text:
Fundamentals of Transportation/Route Choice

Route assignment, route choice, or traffic assignment concerns the selection of routes (alternative called paths) between origins and destinations in transportation networks. It is the fourth step in the conventional transportation forecasting model, following Trip Generation, Destination Choice, and Mode Choice. The zonal interchange analysis of trip distribution provides origin-destination trip tables. Mode choice analysis tells which travelers will use which mode. To determine facility needs and costs and benefits, we need to know the number of travelers on each route and link of the network (a route is simply a chain of links between an origin and destination). We need to undertake traffic (or trip) assignment. Suppose there is a network of highways and transit systems and a proposed addition. We first want to know the present pattern of travel times and flows and then what would happen if the addition were made.

Link Performance Function
The cost that a driver imposes on others is called the marginal cost. However, when making decisions, a driver only faces his own cost (the average cost) and ignores any costs imposed on others (the marginal cost).
 * $$Average Cost = S_T/ Q$$
 * $$Marginal Cost = \delta S_T/ \delta Q$$

where $$S_T$$ is the total cost, and $$Q$$ is the flow.

BPR Link Performance Function
Suppose we are considering a highway network. For each link there is a function stating the relationship between resistance and volume of traffic. The Bureau of Public Roads (BPR) developed a link (arc) congestion (or volume-delay, or link performance) function, which we will term Sa(Qa)

$$ S_a \left( {Q_a } \right) = t_a \left( {1 + 0.15\left( {\frac } \right)^4 } \right) \,\!$$

''ta = free-flow travel time on link a per unit of time

Qa = flow (or volume) of traffic on link a per unit of time (somewhat more accurately: flow attempting to use link a'')

''ca = capacity of link a per unit of time

Sa(Qa) is the average travel time for a vehicle on link a There are other congestion functions. The CATS has long used a function different from that used by the BPR, but there seems to be little difference between results when the CATS and BPR functions are compared.

Can Flow Exceed Capacity?
On a link, the capacity is thought of as “outflow.” Demand is inflow.

If inflow > outflow for a period of time, there is queueing (and delay).

For Example, for a 1 hour period, if 2100 cars arrive and 2000 depart, 100 are still there. The link performance function tries to represent that phenomenon in a simple way.

User Equilibrium
Each user acts to minimize his/her own cost, subject to every other user doing the same. Travel times are equal on all used routes and lower than on any unused route.

System optimal
Each user acts to minimize the total travel time on the system.

Price of Anarchy
The reason we have congestion is that people are selfish. The cost of that selfishness (when people behave according to their own interest rather than society's) is the price of anarchy.

The ratio of system-wide travel time under User Equilibrium and System Optimal conditions.

Price of Anarchy = $$ UE/SO > 1 $$

For a two-link network with linear link performance functions (latency functions), Price of Anarchy is < 4/3.

Is this too much? Should something be done, or is 33% waste acceptable? [The loss may be larger/smaller in other cases, under different assumptions, etc.]

Conservation of Flow
An important factor in road assignment is the conservation of flow. This means that the number of vehicles entering the intersection (link segment) equals the number of vehicles exiting the intersection for a given period of time (except for sources and sinks).

Similarly, the number of vehicles entering the back of the link equals the number exiting the front (over a long period of time).

Long-standing techniques
The above examples are adequate for a problem of two links, however real networks are much more complicated. The problem of estimating how many users are on each route is long standing. Planners started looking hard at it as freeways and expressways (motorways) began to be developed. The freeway offered a superior level of service over the local street system and diverted traffic from the local system. At first, diversion was the technique. Ratios of travel time were used, tempered by considerations of costs, comfort, and level of service.

The Chicago Area Transportation Study (CATS) researchers developed diversion curves for freeways versus local streets. There was much work in California also, for California had early experiences with freeway planning. In addition to work of a diversion sort, the CATS attacked some technical problems that arise when one works with complex networks. One result was the Moore algorithm for finding shortest paths on networks.

The issue the diversion approach didn’t handle was the feedback from the quantity of traffic on links and routes. If a lot of vehicles try to use a facility, the facility becomes congested and travel time increases. Absent some way to consider feedback, early planning studies (actually, most in the period 1960-1975) ignored feedback. They used the Moore algorithm to determine shortest paths and assigned all traffic to shortest paths. That’s called all or nothing assignment because either all of the traffic from i to j moves along a route or it does not.

The all-or-nothing or shortest path assignment is not trivial from a technical-computational view. Each traffic zone is connected to n - 1 zones, so there are numerous paths to be considered. In addition, we are ultimately interested in traffic on links. A link may be a part of several paths, and traffic along paths has to be summed link by link.

An argument can be made favoring the all-or-nothing approach. It goes this way: The planning study is to support investments so that a good level of service is available on all links. Using the travel times associated with the planned level of service, calculations indicate how traffic will flow once improvements are in place. Knowing the quantities of traffic on links, the capacity to be supplied to meet the desired level of service can be calculated.

Heuristic procedures
To take account of the affect of traffic loading on travel times and traffic equilibria, several heuristic calculation procedures were developed. One heuristic proceeds incrementally. The traffic to be assigned is divided into parts (usually 4). Assign the first part of the traffic. Compute new travel times and assign the next part of the traffic. The last step is repeated until all the traffic is assigned. The CATS used a variation on this; it assigned row by row in the O-D table.

The heuristic included in the FHWA collection of computer programs proceeds another way.
 * Step 0: Start by loading all traffic using an all or nothing procedure.
 * Step 1: Compute the resulting travel times and reassign traffic.
 * Step 2: Now, begin to reassign using weights. Compute the weighted travel times in the previous two loadings and use those for the next assignment. The latest iteration gets a weight of 0.25 and the previous gets a weight of 0.75.
 * Step 3. Continue.

These procedures seem to work “pretty well,” but they are not exact.

Frank-Wolfe algorithm
Dafermos (1968) applied the Frank-Wolfe algorithm (1956, Florian 1976), which can be used to deal with the traffic equilibrium problem.

Equilibrium Assignment
To assign traffic to paths and links we have to have rules, and there are the well-known Wardrop equilibrium (1952) conditions. The essence of these is that travelers will strive to find the shortest (least resistance) path from origin to destination, and network equilibrium occurs when no traveler can decrease travel effort by shifting to a new path. These are termed user optimal conditions, for no user will gain from changing travel paths once the system is in equilibrium.

The user optimum equilibrium can be found by solving the following nonlinear programming problem

$$ \min \sum_a {\int_0^{v_a} {S_a \left( Q_a \right)} } dx \,\!$$

subject to:

$$ Q_a = \sum_i {\sum_j {\sum_r {\alpha _{ij}^{ar} Q_{ij}^r } } } \,\! $$

$$ \sum_r {Q_{ij}^r = Q_{ij} } \,\!$$

$$ Q_a \geq 0,\;Q_{ij}^r \geq 0 \,\!$$

where $$ Q_{ij}^r \,\!$$ is the number of vehicles on path r from origin i to destination j. So constraint (2) says that all travel must take place: ''i = 1 ... n; j = 1 ... n''

$$\alpha _{ij}^{ar} \,\!$$ = 1 if link a is on path r from i to j ; zero otherwise.

So constraint (1) sums traffic on each link. There is a constraint for each link on the network. Constraint (3) assures no negative traffic.

Transit assignment
There are also methods that have been developed to assign passengers to transit vehicles. In an effort to increase the accuracy of transit assignment estimates, a number of assumptions are generally made. Examples of these include the following:

 * All transit trips are run on a set and predefined schedule that is known or readily available to the users.
 * There is a fixed capacity associated with the transit service (car/trolley/bus capacity).

Thought Questions

 * How can we get drivers to consider their marginal cost?
 * Alternatively: How can we get drivers to behave in a “System Optimal” way?

Sample Problem

 * Problem (Solution)
 * Problem (Solution)

Variables

 * $$ C_T$$ - total cost
 * $$ C_k$$ - travel cost on link $$k$$
 * $$ Q_k$$- flow (volume) on link $$k$$

Abbreviations

 * VDF - Volume Delay Function
 * LPF - Link Performance Function
 * BPR - Bureau of Public Roads
 * UE - User Equilibrium
 * SO - System Optimal
 * DTA - Dynamic Traffic Assignment
 * DUE - Deterministic User Equilibrium
 * SUE - Stochastic User Equilibrium
 * AC - Average Cost
 * MC - Marginal Cost

Key Terms

 * Route assignment, route choice, auto assignment
 * Volume-delay function, link performance function
 * User equilibrium
 * System optimal
 * Conservation of flow
 * Average cost
 * Marginal cost

External Exercises
Use the ADAM software at the STREET website and try Assignment #3 to learn how changes in network characteristics impact route choice.

Additional Questions

 * Homework
 * Additional Questions

Videos

 * Route Choice
 * User Equilibrium
 * Route Choice User Equilibrium Problems


text:
Fundamentals of Transportation/Route Choice/Problem

 Problem: Given a flow of six (6) units from origin “o” to destination “r”. Flow on each route ab is designated with Qab in the Time Function. Apply Wardrop's Network Equilibrium Principle (Users Equalize Travel Times on all used routes)

A. What is the flow and travel time on each link? (complete the table below) for Network A

B. What is the system optimal assignment?

C. What is the Price of Anarchy?

 * Solution

/Problems


text:
Fundamentals of Transportation/Route Choice/Solution

 Problem: Given a flow of six (6) units from origin “o” to destination “r”. Flow on each route ab is designated with Qab in the Time Function. Apply Wardrop's Network Equilibrium Principle (Users Equalize Travel Times on all used routes)

A. What is the flow and travel time on each link? (complete the table below) for Network A

B. What is the system optimal assignment?

C. What is the Price of Anarchy?

 Solution:  Part A

What is the flow and travel time on each link? Complete the table below for Network A:

These four links are really 2 links O-P-R and O-Q-R, because by conservation of flow Qop = Qpr and Qoq = Qqr.

By Wardrop's Equilibrium Principle, the travel time (cost) on each used route must be equal. Therefore $$C_{opr} = C_{oqr}$$.

OR

$$25+ 6*Q_{opr}= 20+7*Q_{oqr}$$

$$5+ 6*Q_{opr}= 7*Q_{oqr}$$

$$Q_{oqr} = 5/7 + 6*Q_{opr}/7$$

By the conservation of flow principle

$$Q_{oqr}+Q_{opr} = 6$$

$$Q_{opr} = 6 - Q_{oqr}$$

By substitution

$$Q_{oqr} = 5/7 + 6/7 (6 - Q_{oqr}) = 41/7 -6*Q_{oqr}/7$$

$$13*Qoqr = 41$$

$$Q_{oqr} = 41/13 = 3.15$$

$$Q_{opr}=2.84$$

Check

$$42.01 = 25+6(2.84)$$

$$42.05 = 20+7(3.15)$$

Check (within rounding error)

or expanding back to the original table:

User Equilibrium: Total Delay = 42.01 * 6 = 252.06

 Part B

What is the system optimal assignment?

Conservation of Flow:

$$Q_{opr}+Q_{oqr} = 6 \,\!$$

$$Total Delay = Q_{opr}(25+ 6*Q_{opr}) + Q_{oqr}(20+7*Q_{oqr}) \,\!$$

$$25 Q_{opr} + 6 Q_{opr}^2 + (6-Q_{opr})( 20 + 7(6-Q_{opr}))\,\!$$

$$25 Q_{opr} + 6 Q_{opr}^2 + (6-Q_{opr})( 62 - 7Q_{opr}))\,\!$$

$$25 Q_{opr} + 6 Q_{opr}^2 + 372 - 62 Q_{opr} - 42 Q_{opr} + 7 Q_{opr}^2\,\!$$

$$13 Q_{opr}^2 - 79 Q_{opr} + 372\,\!$$

Analytic Solution requires minimizing total delay

$$\delta C/\delta Q = 26 Q_{opr} - 79 = 0\,\!$$

$$Q_{opr} = 79/26 = 3.04\,\!$$

$$Q_{oqr} = 6-Q_{opr}=2.96\,\!$$

And we can compute the SO travel times on each path

$$ C_{opr,SO} = 25+ 6*3.04 = 43.24 \,\!$$

$$ C_{oqr,SO} = 20+7*2.96 = 40.72 \,\!$$

Note that unlike the UE solution, $$ C_{opr,SO} > C_{oqr,SO} \,\!$$

Total Delay = 3.04(25+ 6*3.04) + 2.96(20+7*2.96) = 131.45+120.53= 251.98

Note: one could also use software such as a "Solver" algorithm to find this solution.

 Part C

What is the Price of Anarchy?

User Equilibrium: Total Delay =252.06 System Optimal: Total Delay = 251.98

Price of Anarchy = 252.06/251.98 = 1.0003 < 4/3

/Solutions


text:
User:TheSwami

Visit my Wikipedia profile at User:TheSwami

Enjoy!

73

title: User:TheSwami


text: Adventist Youth Honors Answer Book/Recipes/Hominy Grits


text: Adventist Youth Honors Answer Book/Recipes/Butternut Squash


text: Adventist Youth Honors Answer Book/Recipes/Hot Apple Cider


text:
User talk:Ck209

Welcome!
Welcome, !

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard  | talk 23:23, 5 March 2008 (UTC)

Copyright problem with Image:Buddy fishing (crop).jpg

 * As well, please sign your posts with four tildes ( ~ ), which will produce a signature and timestamp; this makes it easy to read discussions by making it clear who said what and when. Thanks. – Mike.lifeguard  | talk 00:00, 6 March 2008 (UTC)

title: User talk:Ck209


text:
User talk:Kdv2754

Welcome!
Welcome, !

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard  | talk 23:23, 5 March 2008 (UTC)

title: User talk:Kdv2754


text:
User talk:Atimmer

Welcome!
Welcome, !

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard  | talk 23:24, 5 March 2008 (UTC)

title: User talk:Atimmer


text:
Technical Theatre/Lighting/Dimmers

Dimmers are mechanical or electromechanical devices used to vary the amount of electrical power being sent to each lighting instrument. In most modern theaters, changing the dimmers' output is the primary means of controlling the intensity of the lighting on stage.

The construction of dimmers has evolved considerably over time. Some of the oldest dimmers used in the theater, known as 'salt water dimmers,' consisted of a glass jar filled with salt water with two metal leads placed inside. When this was wired in series with the light to be controlled, an operator could control the light's output by varying the distance between the leads. This was a difficult (and often hazardous) process.

Modern dimmers are much more technically complex, and a great deal safer. They control the amount of voltage in the circuit using thyristors, simple electronic circuits that rapidly turn themselves on and off, allowing precisely the amount of current needed to pass through.

title: Technical Theatre/Lighting/Dimmers


text:
User talk:198.168.229.12

Join Us!
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title: User talk:198.168.229.12


text:
User:Katterjohn~enwikibooks

Kris Katterjohn

PGP key: 0x57625DFA

title: User:Katterjohn~enwikibooks


text:
User talk:216.221.91.101

– Mike.lifeguard  | talk 01:02, 6 March 2008 (UTC)

title: User talk:216.221.91.101


text:
User talk:Alliyson

Welcome!
Welcome, !

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally.-- – Mike.lifeguard  | talk 01:01, 6 March 2008 (UTC)

title: User talk:Alliyson


text:
User:Tmiller

School Funding: Are all schools created equal?

--

title: User:Tmiller


text:
User:Neoptolemus/Reading list

The following is a list of existing books on topics I find interesting, created for my own use so that I can quickly find something fascinating to read and/or edit. Νεοπτόλεμος ( talk | email | contribs ) 01:13, 6 March 2008 (UTC)

title: User:Neoptolemus/Reading list


text:
User talk:Tmiller

Welcome, !

Come introduce yourself at the new users page. If you have any questions, you can ask there or contact me personally. – Mike.lifeguard  | talk 01:24, 6 March 2008 (UTC)

title: User talk:Tmiller


text:
User talk:190.86.35.152

Join Us!
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title: User talk:190.86.35.152


text: User:Neoptolemus/Userboxes

title: User:Neoptolemus/Userboxes


text:
User talk:68.59.80.111

Join Us!
-- – Mike.lifeguard  | talk 01:42, 6 March 2008 (UTC)

Cookbook
G'day, please do join us, and place your recipe pages in the Cookbook by starting the page names with "Cookbook:". cheers, Webaware talk 03:16, 6 March 2008 (UTC)

title: User talk:68.59.80.111


text: User talk:70.237.142.74

title: User talk:70.237.142.74


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text:
User talk:67.87.51.255

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text:
User:Neoptolemus/To do list

 * Improve Ancient History (especially this section) -- recent changes in this book
 * Improve World History (especially this entry) -- recent changes in this book
 * Write History of Greece -- recent changes in this book
 * Write Spanish/Tenses -- recent changes in this appendix

title: User:Neoptolemus/To do list


text: User talk:76.65.21.244

title: User talk:76.65.21.244


text:
Bartending/Cocktails/Virgin Strawberry Daiquiri

This page is to be used as reference to making Virgin Strawberry Daiquiris. Also known as "The Rik", this drink is for those who go out once per month. For regular (alcoholic), just add 2 cups of rum (or other liqueur) to this recipe. Please keep in mind that this is only one recipe used for mixing Daiquiris, and it is always fun to try different methods to pick your favorite.

Ingredients

 * 1 cup of cold milk, cream, or combination of the two
 * 8 halved strawberries or other fruit if preferred
 * 1/4 cup water
 * 4 cups sugar
 * 1/2 cup ice
 * 1 Tablespoon of whipped cream (optional)

Directions

 * Add all ingredients to blender.
 * Blend until smooth and creamy.
 * Freeze for 2 minute.
 * Serve in shallow, chilled glass


text: User talk:142.179.27.219

title: User talk:142.179.27.219


text:
C++ Programming/Code/Standard C Library/String & Character

Standard C String & Character
The Standard C Library includes also routines that deals with characters and strings. You must keep in mind that in C, a string of characters is stored in successive elements of a character array and terminated by the NULL character.

Even if outdated this C string and character functions still appear in old code and more so than the previous I/O functions.