Recently in Topology Category


Just as we have cut the earth into a grid of latitude and longitude (and knowing that each "block" of 1 degree latitude by 1 degree longitude gets smaller and smaller as we approach the poles), we similarly cut our cities and rural areas into a finer mesh from that same grid. Much of this arises from the various large scale ordinance surveys that took places in the Americas, Australia, and India. There are of course grids dating much earlier, to Miletus and Mohenjo Daro among many others. Not all grids are aligned with longitude and latitude, sometimes they align with local landscape features, but most of the modern ones are. (Where grids of different alignments come together, interesting spaces are created). Not all grids are squares, most are more like rectangles.

So why should we have 90-degree rectilinear grids?

The arguments in favor are that it:

  1. simplifies construction and makes it easier to maximize the use of space in buildings,
  2. simplifies real estate by making the life of the surveyor easier,
  3. simplifies intersection management by reducing conflicts compared to a 6-way intersection,
  4. is embedded in existing property rights and so impossible to change.

We in the modern world need not be bound to the primitive tools of the early surveyor, the primitive signal timings of the 1920s traffic engineer, or the primitive construction techniques of early carpenters. And while for existing development we might be locked into existing property rights, for new developments that doesn't follow.

The arguments against the rectilinear include that it:

  1. is among the least efficient way to connect places from a transportation perspective,
  2. reduces opportunities for interesting architecture,
  3. wastes developable space by overbuilding roads.


There are many designs for non-rectilinear street networks. Ben-Joseph and Gordon (2000) (Hexagonal Planning in Theory and Practice (Journal of Urban Design 5(3) pp.237-265)) summarize a number of the 19th and 20th century designs. Most are simple aesthetic choices, as in Canberra, the planned capital city of Australia, and don't seem to relate to deeper urban organizational issues.

Muller

Rudolf Müller proposed The City of the Future: Hexagonal Building Concept for a New Division. Müller's plan offsets the 60-degree streets so that they come together in 4-way rather than 6-way intersections (though they are still at 60-degrees and not bent to make 90-degree intersections). This ensures that the cells in the plan are not bisected by roads, and that they are instead hexagonal blocks. This plan loses a lot of areas to ornamental parks in the middle of streets.

The circuity increase associated with a 90-degree rather than 60-degree network is obvious. Circuity (the ratio of Euclidean to Network distance) would be minimized if roads were at 0-degree angles. The downside is that this Euclidean network where everyone traveled in a straight-line would literally "pave the earth". Leaving aside the downsides for the environment of being so-paved, the more critical trade-off from a transportation perspective is construction costs. More roads are more expensive. So a network design trades-off travel costs accruing over time with the up-front construction and long-term maintenance costs. The optimal network design depends on the land use pattern it aims to serve. (And the land use pattern depends on the network design.) The City of Alonso or Von Thünen, with all jobs downtown merely requires a simple radial network to connect it. A polycentric or fully dispersed (homogeneous) city with everything spread uniformly across space begs for more cross-connections.


Charles Lamb's City Plan has the streets hexsect the hexagonal cells. In this case, the blocks are really triangles.


There is a large literature on the network design problem. One useful paper: Pierre Melut and Patrick O'Sullivan (1974) A Comparison of Simple Lattice Transport Networks for a Uniform Plain, Geographical Analysis 6(2) pp. 163–173, says:

The objective is to compare construction and transport costs for triangular [60-degree], orthogonal [90-degree], and hexagonal [120-degree] regular lattices as transport networks serving a uniform, unbounded plain. The lattices are standardized so that the average distance from the elementary area to the edge is the same for each. This standardization results in equal construction costs for the three networks; thus, the comparison can be made in terms of route factors [circuity], which favors the triangular lattice over the other two.


Lamb


Because the circuitous network is less efficient, more network pavement and track and vehicle mileage must be provided to enable the same amount of transportation. This wastes spaces that could be better allocated to non-transportation purposes.

The lattice itself comprises a single level in a hierarchical system. Selected links in a lattice can be reinforced to make them faster, attracting traffic. This process of reinforcement is natural with investment rules that favor more heavily trafficked routes and explains the hierarchy of roads. If it is based on simple reinforcement of existing links rather than creation of new links, that hierarchy will not affect the topology of the network.

Ask MetaFilter has an interesting thread on Comparing perimeters of arrays of hexagons vs. squares - geometry tiling resolved . A key point is that arranging hexagons into a square-like shape has a higher perimeter than arranging squares into a square-like shape.

 __    __    __    __    __
/  \__/  \__/  \__/  \__/  \
\__/  \__/  \__/  \__/  \__/
/  \__/  \__/  \__/  \__/  \
\__/  \__/  \__/  \__/  \__/
/  \__/  \__/  \__/  \__/  \
\__/  \__/  \__/  \__/  \__/
/  \__/  \__/  \__/  \__/  \
\__/  \__/  \__/  \__/  \__/
/  \__/  \__/  \__/  \__/  \
\__/  \__/  \__/  \__/  \__/
  Diagram 1. Sample hex map

Jellicle wrote:

I think your problem is this - to minimize the perimeter of n hexagons, when you add each new hexagon to the previously-existing group, you have to add it in such a way that touches the most neighbors possible. You would never add a hexagon that touches only on one face if you could add it somewhere else where it touches two faces or three faces, right? If you look at diagram 1 here (which is hexes in a grid shape), you see several hexes at the four corners which touch only on two faces, while there are areas on the outer surface at the top and bottom where those hexes could be placed where they would touch on three faces instead of two. So simply moving those four corner hexes would reduce the perimeter without changing the surface area.

Yet we know the hexagon is efficient, it replicates the closest packing of circles. (Take a penny, surround it with pennies so that they are all tangent. The central penny touches six others.) Thus following the closest-packing argument, the hexagon as geometrical shape is not sufficient for efficiency, we must also arrange those shapes into an efficient pattern, in this case, something more like the Glinski Chess Board:


Glinski

Much of the inspiration for thinking about hex-maps comes from the gaming community, where such maps have been used since the 1961, when a Hex map was used for the Avalon Hill game Gettysburg. It has since become a standard that is widely used to represent directions of movement in games.

So, although we talk about "grids" as being necessary for connectivity, we can get even more connectivity if we think about a variety of different geometries. It would be a shame if we got locked into grid geometries for new developments when there are so many alternatives to be had.

Network Structure and City Size

Betaville

Network structure varies across cities. This variation may yield important knowledge about how the internal structure of the city affects its performance. This paper systematically compares a set of surface transportation network structure variables (connectivity, hierarchy, circuity, treeness, entropy, accessibility) across the 50 largest metropolitan areas in the United States. It finds most of these measures vary with city size. A set of scaling parameters are discovered to show how network size and structure vary with city size. These results suggest that larger cities are physically more inter-connected.

Keywords: Connectivity, Network Structure, Transportation Geography, Network Science, City Size, Scaling Rules


Network Structure and Travel

Pavithra-JohnAdams

Congratulations to soon to be Dr. Pavithra Parthasarathi, who recently was awarded the 2011 John S Adams Award for Excellence in Transportation Research and Education, and who successfully defended her Ph.D. Thesis "Network Structure and Travel" (a draft of which is linked) on May 5, 2011. She accepted a job with the Hampton Roads Transportation Planning Organization (HRTPO) in Norfolk, VA, starting May 16th.

Abstract:

Changing the design aspects of urban form is a positive approach to improving transportation. Land use and urban design strategies have been proposed to not only to bring about changes in travel behavior but as a way of providing a better quality of life to the residents. While the research on the relationship between urban form and travel behavior has been pretty extensive, there is a clear gap in the explicit consideration of the underlying transportation network, even though researchers acknowledge its importance. This dissertation aims to continue on the research interest in understanding travel behavior while explicitly accounting for the underlying transportation network structure.

Transportation networks have an underlying structure, defined by the layout, arrangement and the connectivity of the individual network elements, namely the road segments and their intersections. The differences in network structure exist among and between networks. This dissertation argues that travelers perceive and respond to these differences in underlying network structure and complexity, resulting in differences in observed travel patterns. This hypothesized relationship between network structure and travel is analyzed in this dissertation using individual and aggregate level travel and network data from metropolitan regions across the U.S. Various measures of network structure, compiled from existing sources, are used to quantify the structure of street networks. The relation between these quantitative measures and travel is then identified using econometric models.

The underlying principle of this research is that while the transportation network is not the only indicator of urban form and travel, an understanding of the transportation network structure will provide a good framework for understanding and designing cities. The importance of such an understanding is critical due to the long term and irreversible nature of transportation network decisions. The comprehensive analyses presented in this dissertation provide a clear understanding of the role of network design in influencing travel.


A Numeric Topology of the United States Eisenhower Interstate Highway System

 

Hedberg Maps makes "A Numeric Topology of the United States Eisenhower Interstate Highway System " which looks quite cool, though is not quite free. A full discussion is here

 

The interstate system has another quality besides the creation of corridors, boundaries and districts: it orders and grids the country. In creating the basic numbering plan for the highways, its creators followed a tradition that includes not only previous highway systems (including the 1920’s U.S. Highway System), but street layouts dating back to William Penn’s Philadelphia, the initial “nine squares” of New Haven, and the very definition of United States territory, the 1785 Land Ordnance with its grid of 6 x 6 mile townships. It has become so common for American cities to lay out streets in a square grid with numerical names that it can be surprising to go to countries where this practice is unknown. Learning to navigate even older American cities like Boston, where what grids there are are haphazard and streets change names seemingly at whim, can be daunting to those raised in orderly Omaha or Chicago.

 

....

Some ground-rules quickly emerged:

  • I would try to keep the “5-roads” as my guideposts and conform everything else to them (but what do you do when 1-80 and 1-90 become one road in Ohio and Indiana?)
  • One roadway = one line.
  • Two-digit routes would be drawn with a heavier line weight than three-digit routes. Where they share a pathway, the heavier line takes priority.
  • State boundaries would be topologically correct: every road intersection and state boundary road crossing would be shown in the correct order.
  • Odd-prefix three-digit routes (i.e spurs like I-394) would be shown as straight lines, and even ones (i.e. loop roads like I-494/694) would be made of circular arcs.
  • As much as graphically feasible, routes would be encouraged to lie along their numbered place in the grid for as much of their length as was graphically feasible.
  • A minimum of 1⁄4 inch would fall between each major intersection. Mostly.
  • I would use only straight line segments and arcs. No other curvy bits.

Network Reliability on the Electric Grid (from Miller-McCune Debunking Theories of a Terrorist Power Grab

Hines and Blumsack's study ... shows that the most vulnerable points are the ones that have the most energy flowing through them -- like huge power stations or highly connected transformers.

Article Do topological models provide good information about electricity
infrastructure vulnerability?

I think there is something to learn about generalizing network reliability and vulnerability across fields (electricity, transportation, etc.). Network structure, and the underlying technology, matter.

Recent working paper: TheoryOfConnectivity.JPG
This paper develops a positive theory of network connectivity, seeking to explain the micro-foundations of alternative network topologies as the result of self-interested actors. By building roads, landowners hope to increase their parcels’ accessibility and economic value. A simulation model is performed on a grid-like land use layer with a downtown in the center, whose structure resembles the early form of many Midwest- ern and Western (US) cities. The topological attributes for the networks are evaluated. This research posits that road networks experience an evolutionary process where a tree-like structure first emerges around the centered parcel before the network pushes outward to the periphery. In addition, road network topology undergoes clear phase changes as the economic values of parcels vary. The results demonstrate that even without a centralized authority, road networks have the property of self-organization and evolution, and, that in the absence of intervention, the tree-like or web-like nature of networks is a result of the underlying economics.

Optical Flow Switching

Chan, Weichenberg, and Medard Optical Flow Switching. A proposed communications protocol, but one which has some insights for transportation (if not immediate applicability)

Motivated by the minimization of network management and switch complexity in the network core, flows are serviced as indivisible entities. That is, data cells comprising a flow traverse the network contiguously in time, along the same wavelength channel, and along the same spatial network path. This is in contrast to packet switched networks, where transactions are broken up into constituent cells, and these cells are switched and routed through the network independently. Note that in OFS networks, unlike packet switched networks, all queuing of data occurs at the end users, thereby obviating the need for buffering in the network core. Core nodes are thus equipped with bufferless optical cross-connects (OXCs). OFS is a centralized transport architecture in that coordination is required for logical topology reconfiguration. However, OFS traffic in the core will likely be efficiently aggregated and sufficiently intense to warrant a quasi-static logical topology that changes on coarse time scales. Hence, the centralized management and control required for OFS is not expected to be onerous. The network management and control carried out on finer time-scales will be distributed in nature in that only the relevant ingress and egress access networks will need to communicate.
(emphasis added)

So instead of storing and buffering (on-road queueing), they allocate the whole path between origin and destination to the flow (a trip).

Of course, since this is communications, there are some things they can do that transportation cannot:

If any errors are detected, a request for retransmission of the whole file is done via feedback to the transmitter.

(Sorry, your trip didn't work out, please have your clone repeat the trip).

From Gizmodo Is This the Craziest Bridge Ever Designed?

How to change from driving on the left to driving on the right:

Is This the Craziest Bridge Ever Designed?I don't know if the "Pearl River Necklace bridge is the craziest bridge ever designed, but it sure looks like the most twisted one. It's a clever solution to a very real and obvious problem, however.

The bridge is part of a proposal by NL Architects to connect Hong Kong with mainland China. To do that, they had to solve a problem: In Hong Kong, people drive on the left side of the road. In mainland China, they drive on the right side. Here's the solution: A road flipper that physically twists the roads over each other.

Is This the Craziest Bridge Ever Designed?

I hope the project goes forward, because I've always wanted to drive in a gigantic Scalextric. [Design Boom]"

Street grids

| 1 Comment

Human Transit has a nice post in praise of standard street grids.

Minneapolis Orbital Line

Continuing a series on circulatory transit routing, there is a difficulty providing services in the "suburb-to-suburb" market. The best markets will still be those with major attractions. This route connects a number of education, retail, and employment destinations, as well as connecting all of the radial transit routes emanating from Minneapolis (and some from St. Paul).

Starting on the east side, the line runs north to south from Rosedale Mall, down Snelling Avenue past HarMar, to the University of Minnesota St. Paul campus and State Fairgrounds, south to Energy Park, back to Snelling Avenue past Hamline University, intersecting the Central Corridor, down to Grand Avenue and Macalaster College, along Randolph to St. Kate's, down Fairview through Highland Park, down Edgcombe Avenue to 7th Street (intersecting, and sharing right-of-way with a 7th Street/Fort Road line), over to Hiawatha LRT, where it shares Right of Way under the Airport. Crossing the River will remain a costly proposition given the narrowness of the existing bridge.

On the south side, it leaves the Hiawatha LRT at Mall of America, and runs along American Boulevard south of I-494 in Bloomington. (the choice of above or below I-494 is tricky, but there seems to be more activity south of the beltway, and it better serves potential park-and-ride).

The line turns North at Edinborough Way and moves over to France Avenue, where it passes Southdale Mall and Fairview Hospital, serving Edina. It runs through the 50th and France district, and then cuts across to the Excelsior and Grand area, following 36th Street until it intersects with Wooddale Avenue, intersecting the Southwest LRT. It proceeds north on railroad RoW to the Cedar Lake trail. It turns north at Park Place Boulevard, with a stop at the new West End development. The line follows Xenia Avenue north to another railroad RoW, and crosses Theordore Wirth park. It runs along Plymouth Avenue until Penn Avenue (where it intersects the Inner Circle ), and turns north on Penn until Lowry Avenue.

The Orbital Line follows Lowry Avenue across the Mississippi River, turns south at RR RoW, and then east through Northeast Park and along Ridgway Parkway. It then follows frontage roads of I-35W until it reaches Rosedale Mall.


As with any hypothesized or "fantasy" transit line, all routings are first order approximations and many tens of millions of dollars in design will need to be spent to establish final alignments. There are an infinite number of possibilities (and a very large number of realistic possibilities), this seems from a cursory inspection to be some reasonable routes that have a shot at doing relatively well on an efficiency metric (benefits > costs), though I can make no guarantees of either absolute efficiency or optimality.


View Minneapolis Orbital Transit Line in a larger map

Saint Paul Circle Line

The Iron Law of the Twin Cities is that if Minneapolis has something, Saint Paul gets one too (and vice versa). The examples are numerous (arenas, campuses of the University of Minnesota, branches of I-35, chapters of the American Automobile Association, and so on).

In a previous post I posited a Minneapolis Circle Line . Of course Saint Paul would want to get in on the action.

I have drawn two possible fixed route, exclusive(ish) right-of-way transit lines (an Inner Circle and an Outer Circle), along with the already planned Central Corridor. I have not shown other possible lines, presumably radial, that would extend from Saint Paul (one imagines one on 7th Street/Fort Road to the southwest, a streetcar along Grand Avenue, something along Robert Street to the South, something to the west, northeast, and northwest.

The Inner Circle follows the Central Corridor line beginning at Marion Street but continues on University past the Capitol, past Regions Hospitalacross I-35E to Lafayette Road, goes south down Lafayette Road across I-94, and runs behind the proposed St. Paul Saints stadium through Lowertown, meets the Central Corridor again at Union Depot, and then jogs over to Kellogg Boulevard to run past RiverCentre, Xcel Energy Center, the Science Museum, the History Center, near the Cathedral, and up Marion Street back to University Avenue. It would serve re-developable areas near Lafayette road and Marion Street, and major attractions in the city.

The Outer Circle I have broken into two sections for convenience: North and South.

The Outer Circle (north) begins at the Dale Street station on the Central Corridor, runs north to the Pierce Butler route corridor, and goes east parallel the existing railroad tracks, behind the Minnesota Transportation Museum, across I-35E, and then south to University Avenue where it meets the Inner Circle alignment. It serves

The Outer Circle (south) also begins at the Dale Street station, runs south to Summit Avenue (I assume it would share right-of-way with the "Grand Avenue" streetcar should such a thing exist), proceed down Summit Avenue, to Ramsey Street, past United Hospital, serving the West Seventh area. It would turn south on Smith Avenue, cross the Mississippi River, to George Street, serving the West Side. It would proceed East on George Street to Cesar Chavez Street, and then Ada Street. It would cross the Lafayette Freeway and run along the edge of the St. Paul Airport. Here is the expensive part: a new river crossing would need to be constructed to get from the south to the north banks of the Mississippi River. The line would climb up Mounds Boulevard, serving Dayton's Bluff and Metropolitan State University, and then run southeast along 7th Street/Fort Road, to the Inner Circle.


Rings make the most sense in the context of existing (or future) radials, allowing cross-traffic in cities and shortening travel times for those not going downtown. Given that St. Paul CBD has about 3% of the region's employment (~40,000 jobs) (1990 statistics), new systems should not focus exclusively on such a small market, but should better help travelers reach diverse destinations across the city.


View Saint Paul Circle Lines in a larger map

Minneapolis Circle Line

| 4 Comments


I have recently been thinking about the backbone transit network of the Twin Cities.

The existing and soon-to-be-built LRT lines (Hiawatha, Central Corridor, Southwest Corridor) all radiate from downtown Minneapolis. The same is true of the one Commuter Rail line.

Examining the proposed Minneapolis Streetcar System one again sees the downtown orientation (aside from the Midtown Greenway Streetcar line).

Most Minneapolitans, do not work downtown. Most do not take shop, entertain themselves, or do other things downtown very often.

Many other cities have adopted Railway loop lines , which circle around downtown at some radius. These cities include Berlin, London, Sydney, Melbourne, Brisbane, Glasgow, Madrid, Beijing, Shanghai, Tokyo, Osaka, Oslo, Seoul, Chicago, and Moscow. The advantage is that travelers do not need to go all the way into the center to go to a destination on another spoke.

Thinking about network topology in the Minneapolis case, I hypothesize a Minneapolis Circle Line service. There are several objectives in mind
(1) Maximize destinations served outside of downtown.
(2) Minimize construction costs, use existing (or to be built) alignments where possible
(3) Minimize interference from traffic, avoid on-street rights-of-way where possible.
(4) As a service, it can utilize existing tracks but go to different destinations. It separates the requirement that the line and services on the line be identical.

To that end, there are several major sections of the service:
(A) The south-side runs on the proposed Midtown Greenway Streetcar
(B) The west-side runs along the proposed SW LRT right-of-way from the intersection of the Midtown Greenway to Penn Avenue.
(C) The Penn Avenue section runs from the SW LRT Penn Station to Plymouth Avenue
(D) The north-side runs on Plymouth Avenue across the Mississippi River
(E) The northeast section runs through Boom Island park to Main Street/St. Anthony Main. If done as a "Heritage" Transit line, it could add to the qualitative attractions of this largely pedestrian zone.
(F) The southeast section follows from Main Street along the Granary Road right-of-way across the north side of the Gopher Stadium. Part of this is the Northern Alignment from the Central Corridor studies. However it would take advantage of its location and have stops at the new developments in the University Bio-technology corridor.
(G) The east section follows 25th Ave SE south to the railroad right-of-way paralleling and crossing I-94 to 27th Ave.
(H) The section passes through the five-way intersection at Franklin Avenue and East River Road to cross the Mississippi River on the Franklin Avenue Bridge.
(I) The route follows Franklin Avenue to 26th Avenue S, turns south, to meet the Midtown Greenway extended just past the Lake Street Station on the Hiawatha Line.
(*) Some alternative routings have been drawn as well.

The route thus connects Seward, Midtown, Phillips, Uptown, Lake Calhoun, Kenwood, Bassetts Creek, Harrison,Sumner-Glenwood, Near North, North Loop, East Hennepin, St. Anthony Main and Nicollet Island, Marcy-Holmes, Dinkytown,the University of Minnesota, Stadium Village, and Prospect Park, and Cedar- Riverside.



View Minneapolis Circle Line Service in a larger map

I have not tested this hypothesis in terms of potential travel demand. I do not have a perfect routing that inherently beats all others, it is a question of trade-offs and values. However the notion of non-radial services needs to be raised as the Twin Cities go forth on the biggest rail construction boom since the 19th century.

Bill St. Arnaud finds: The Flattening Internet Topology: Natural Evolution, Unsightly Barnacles or Contrived Collapse? by Phillipa Gill, Martin Arlitt, Zongpeng Li, and Anirban Mahanti. The full article can be found here (pdf).


In this paper we collect and analyze traceroute measure- ments1 to show that large content providers (e.g., Google, Microsoft, Yahoo!) are deploying their own wide-area networks, bringing their networks closer to users, and bypassing Tier-1 ISPs on many paths. This trend, should it continue and be adopted by more content providers, could flatten the Internet topology, and may result in numerous other consequences to users, Internet Service Providers (ISPs), content providers, and network researchers.

From New Scientist: Designing highways the slime mould way

... Jeff Jones and Andrew Adamatzky, specialists in unconventional computing at the University of the West of England in Bristol, wondered if biology could provide an alternative to conventional road planning methods. To find out, they created templates of the UK using a sheet of agar on which they marked out the nine most populous cities, excluding London, with oat flakes. Then, in the place of London, the pair introduced a colony of P. polycephalum, which feeds by spawning tendrils to reach nutrients, and recorded the colony's feeding activity (see picture).

Most of the resulting "maps" mimicked the real inter-city road network, but some offered new routes. For instance, the motorway between Manchester and Glasgow passes along the west coast of the UK, but the slime mould preferred to travel east to Newcastle and then north to Glasgow ( /arxiv.org/abs/0912.3967 ). "This shows how a single-celled creature without any nervous system - and thus intelligence in the classical sense - can provide an efficient solution to a routing problem," says Jones.

Recently published:

Zhang, Lei, David Levinson, and Shanjiang Zhu (2008) Agent-Based Model of Price Competition and Product Differentiation on Congested Networks. . Journal of Transport Economics and Policy Sept. 2008 42(3) pp. 435-461. [download]

Using consistent agent-based techniques, this research explores the welfare consequences of product differentiation on congested networks. The economic analysis focuses on the source, evolution, measurement, and impact of product differentiation with heterogeneous users on a mixed ownership network. Path differentiation and space differentiation are defined and measured for a base scenario and several variants. The findings favour a fixed-rate road pricing policy compared to complete pricing freedom on toll roads. It is also shown that the impact of production differentiation on welfare is not always positive and depends on the level of user heterogeneity.

Recently published:

Xie, Feng and David Levinson (2008) The Weakest Link: A model of the decline of surface transportation networks. Transportation Research part E 44(1) 100-113. [doi]

This study explores the economic mechanisms behind the decline of a surface transportation network, based on the assumption that the decline phase is a spontaneous process driven by decentralized decisions of individual travelers and privatized links. A simulation model is developed with a degeneration process by which the weakest link is removed iteratively from the network. Experiments reveal how the economic efficiency of a network evolves during the degeneration process and suggest an "optimal" degenerated network could be derived during the decline phase in terms of maximizing total social welfare.

Keywords: Decline; Transportation network; Simulation; Welfare; Accessibility


New UK high-speed rail plan unveiled

From the BBC New UK high-speed rail plan unveiled

The line would serve Birmingham and Manchester, getting passengers from Glasgow to London in just two hours and 16 minutes, the rail firm said. It rejected several alternative routes, including the east of England.

Judging from the map (linked below), the architecture of the line is clearly to feed London, all of the ancillary cities are as if on a tree with the xylem and phloem oriented to London, it would not be terribly good for say Manchester to Edinburgh or Manchester to Birmingham.

"The firm said that the line would account for 43.7 million journeys per year by 2030, which would result in 3.8 million fewer vehicle journeys and fewer carbon dioxide emissions.".
In other words, more 90% of the trips are switching from rail or air to HSR. Providing better rail service to existing rail passengers is a good thing, but CO2 is hardly a rationale (as more CO2 has to be used going faster than going slower if the electricity is from the same place ... diesel to electric conversion is a separate matter).

Finally, the cost is esimated at $55B for 1500 miles of rail (presumably including triple or quadruple tracking in some sections. Planning will take 5 more years. It is hoped by the promoters the first section (London to Birmingham) will open in 2020. Speeds will max at 200 mph.


rail plan

Birmingham: 45mins, down from 1h 22mins

Liverpool: 1hr 23mins, down from 2hrs 8mins

Manchester: 1hr 6mins, down from 2hrs 7mins

Edinburgh: 2hrs 9mins, down from 4hrs 23mins

Glasgow: 2hrs 16mins, down from 4hrs 10 mins


Also see: London to Glasgow in five minutes, a video showing the West Coast Main Line (which this proposal seems to duplicate) and was recently modernized for 9 billion pounds.

Recently published:

Xie, Feng and David Levinson (2009) Jurisdictional Control and Network Growth. Networks and Spatial Economics 9(3) 459-483. [doi]

Transport infrastructure evolves over time in a complex process as part of a dynamic and open system including travel demand, land use, as well as economic and political initiatives. As transport infrastructure changes, each traveler may adopt a new schedule, frequency, destination, mode, and/or route, and in the long term may change the location of their activities. These new behaviors create demand for a new round of modifications of infrastructure. In the long run, we observe the collective change in the capacity, service, connectivity, and connection patterns (topology) of networks. This paper examines how a fixed set of places incrementally gets connected as transport networks are constructed and upgraded over time. A simulator of network incremental connection (SONIC) is constructed to model the process of incremental connections and examines how networks evolve differently under centralized versus decentralized jurisdictional initiatives. Exploring the mechanism underlying this dynamic process can answer questions such as how urban networks have developed into various topologies, which network patterns are more efficient, and whether and how transport engineers, planners, and decision makers can guide the dynamics of land uses and infrastructure in a desired direction.

Keywords Network growth - Transport economics - Incremental connection - Jurisdictional control

The following was recently published:

Xie, Feng and David Levinson (2009) Modeling the Growth of Transportation Networks: A comprehensive review. Networks and Spatial Economics. 9(3) 291-307. [doi]

This paper reviews the progress that has been made over the last half-century in modeling and analyzing the growth of transportation networks. An overview of studies has been provided following five main streams: network growth in transport geography; traffic flow, transportation planning, and network growth; statistical analyses of network growth; economics of network growth; and network science. In recognition of the vast advances through decades in terms of exploring underlying growth mechanisms and developing effective network growth models, the authors also point out the challenges that are faced to model the complex process of transport development.

The following was recently published:

Xie, Feng and David Levinson (2009) The Topological Evolution of Road Networks.
Topological evolution of surface transportation networks
Computers, Environment, and Urban Systems 33(3) 211-223 [doi]

This study explores the topological evolution of surface transportation networks, using empirical evidence and a simulation model validated on that data. Evolution is an iterative process of interaction, investment, and disinvestment. The temporal change of topological attributes for the network is also evaluated using measures of connectivity, density, heterogeneity, concentration, and connection patterns. The simulation model is validated using historical data from the Indiana interurban network. Statistical analyses suggest that the simulation model performs well in predicting the sequence of link abandonment in the interurban network as well as the temporal change of topological attributes. The simulation model is then applied on different idealized network structures. Typical connection patterns such as rings, webs, hub-and-spokes, and cul-de-sacs emerge in the networks; the spontaneous organization of network hierarchies, the temporal change of spacing between parallel links, and the rise-and-fall of places in terms of their relative importance are also observed, providing evidence for the claim that network topology is an emergent property of network dynamics.

PACS numbers: 89.75.Fb, 89.75.-k, 89.75Kd

The following was recently published:

Corbett, Michael, Feng Xie, and David Levinson (2009) Evolution of the Second-Story City: The Minneapolis Skyway System. Environment
and Planning b
36(4) 711-724 [doi]

This paper describes and explains the growth of the Minneapolis Skyway network. Accessibility is used as a major factor in understanding that growth (i.e. does the network connect to the location(s) with the highest accessibility, followed by the second highest, and so on). First, employment opportunities are used as the measure of activity and are based off of the square footage of buildings and/or ITE trip generation rates. Using information about the buildings located downtown for each year since the first skyway was built, the accessibilities of each of the connected and adjacent unconnected blocks were calculated for every time period the skyway system expanded. The purpose is to determine how often the expansion connected the block with the highest accessibility. The results show that though important, accessibility was rarely maximized, except in the early stages of development. A connect-choice logit model relating the probability of joining the network (in a given year) to accessibility and network size was employed. The results show accessibility does remain an important factor in predicting which links are connected. Physical difficulties in making connections may have played a role, as well as the potential for adverse economic impacts.



Keywords: Network growth, Skyways, Minneapolis

From WaPo New Virginia Rules Target Cul-de-Sacs

Virginia has adopted a new subdivision code requiring connecting neighborhoods and narrower streets in new developments. The aim is to save maintenance costs and promote accessibility.

I heard this a few years ago, and going through old notes, decided to post, from the CBC series: As It Happens

To listen: Real Audio file, go to minute 21m:20s

The introductory text: "For as long as most of us can remember, the citizens of North America have been firmly entrenched on the right. Now, a bold and shocking proposal in the state of Ohio may result in a wild shift to the left. And it will come as no surprise that the French are involved.

The Ohio Department of Transportation is currently mulling over an unprecedented traffic diversion. If a recent recommendation comes to fruition, drivers on U.S. Highway 224 may find themselves driving -- if only briefly -- on the left side of the road. The lane-reversal plan is a proposed import from the city of Versailles, France, where Gallic drivers have found it to be "la rue juste"."


This is a clever idea to avoid left-turn conflicts (or at least put them where you want them and make the crossovers seem like through movements. Wikipedia has an article.

My former classmate, Joe Bared, now at FHWA did a study with colleagues:
TechBrief: Drivers' Evaluation of the Diverging Diamond Interchange, FHWA-HRT-07-048


The Hwy 224 proposal in Ohio was rejected. The proposal for Kansas City seems alive.

Apparently, a number of important internet backbone cables serving India and Iran have been severed recently: It's 2008 -- Do You Know Where Your Internet Cables Are?.

This is similar in structure to highway network links being severed, except imagine there were only 3 links into the country, and they all failed in one week. Might this be Non-random?

Centers are edges

Centers are not nodes, in fact junctions are not nodes. In graphs (representation of transportation networks for modeling and analysis), nodes are aspatial representations of the intersection of links, which themselves are aspatial representations of the structure of network. However real nodes, i.e. centers and junctions, take space. As such they provide a spatial separation between areas that adjoin them. They serve as edges to adjoining areas (e.g. neighborhoods).

As Alfred Korzybski once said, "the map is not the territory". Similarly, the graph is not the place. Network elements separate as they connect.

updated August 25, 2009:

For those of you who doubt I am doing work over in London, I have completed two other papers (in addition to "Too Expensive to Meter" based on my research over here):

  • Levinson, David (2008) The Orderliness Hypothesis: Does Population Density Explain the Sequence of Rail Station Opening in London? Journal of Transport History 29(1) March 2008 pp.98-114.[download]
  • Network growth is a complex phenomenon. Some have suggested that it occurs in an orderly or rational way, based on the size of the places that are connected. David Levinson examines the order in which stations were added to the London surface rail and Underground rail networks in the nineteenth and twentieth centuries, testing the extent to which order correlates with population density. While population density is an important factor in explaining order, he shows that other factors were at work. The network itself helps to reshape land uses, and a network that may have been well ordered at one time may drift away from order as activities relocate.


  • Levinson, David (2008) Density and Dispersion: The Co-Development of Land use and Rail in London. Journal of Economic Geography 8(1) 55-57.
    JEG: [doi]
  • This article examines the changes that occurred in the rail network and density of population in London during the 19th and 20th centuries. It aims to disentangle the 'chicken and egg' problem of which came first, network or land development, through a set of statistical analyses clearly distinguishing events by order. Using panel data representing the 33 boroughs of London over each decade from 1871 to 2001, the research finds that there is a positive feedback effect between population density and network density. Additional rail stations (either Underground or surface) are positive factors leading to subsequent increases in population in the suburbs of London, while additional population density is a factor in subsequently deploying more rail. These effects differ in central London, where the additional accessibility produced by rail led to commercial development and concomitant depopulation. There are also differences in the effects associated with surface rail stations and Underground stations, as the Underground was able to get into central London in a way that surface rail could not. However, the two networks were weak (and statistically insignificant) substitutes for each other in the suburbs, while the density of surface rail stations was a complement to the Underground in the center, though not vice versa.


Perhaps more interesting for the non-academic, we (Ahmed El-Geneidy, Feng Xie, and myself of the Nexus group) have put together three quicktime movies


  • 1.The co-evolution of London population density and surface (National) rail

  • 2.The co-evolution of London population density and the Underground

  • 3.The co-evolution of London population density and surface (National) rail and the Underground


These can be accessed from here.

David Levinson

Network Reliability in Practice

Evolving Transportation Networks

Place and Plexus

The Transportation Experience

Access to Destinations

Assessing the Benefits and Costs of Intelligent Transportation Systems

Financing Transportation Networks

View David Levinson's profile on LinkedIn

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