One development, two proposals
A city expects about 1,200 new homes at Eastfield, on its eastern edge. One proposal widens Prairie Road from two lanes to three toward downtown. The other runs the bus every 10 minutes instead of every 30. Before choosing, the city wants to know how people might travel and where problems could appear.
Today Prairie Road flows freely. The model below describes the people and the network, represents their travel choices, and calculates the same outcomes for every scenario. Step from A to D, try a different amount of traffic today or a different number of homes, then open the calculation to see what produced each number.
Pause and think • slide 23Scenario C gives the new residents the lowest average trip time. Does that make the wider road the better project?Show answerHide answer
Not on that evidence alone. The average is dominated by drivers. At the default settings, scenario D cuts the trip for households without a car by more than 10 minutes, and the average hides that group. Costs, safety and long-term effects such as new development along the road are not in this toy model at all. Choosing the measures is part of the analysis.
Pause and think • slide 6A vendor demo shows smooth animated traffic. What would you ask to see before trusting it?Show answerHide answer
How the analyst changes an input such as the number of households or the network, runs the model, and compares the result with a reference scenario and with observed counts. Also where assumptions and error messages are recorded. Moving vehicles show how results are displayed, not whether they are right.
The four steps, run once
The traditional four-step process answers four questions in order. How many trips does each zone produce and attract? Which zones do those trips connect? Which mode do travelers use? Which routes carry them? Step through all four on a five-zone version of the city, then click a bridge to trace who uses it.
Pause and think • slide 14One desire line is much thicker than another. Does the road under the thick line carry more traffic?Show answerHide answer
No. A desire line joins two zones for display. Its trips may use several routes, and one road can carry trips from many origin–destination pairs. Compare the thick Riverside–Downtown line in step 2 with the roads in step 4.
Pause and think • slide 15We add a road to the network and leave the demand assumptions unchanged. What have we tested?Show answerHide answer
How that network change affects the demand already represented in the model. We have not forecast new development or every long-term response; those need further assumptions and model components.
Pause and think • slide 3How does selected-link analysis differ from subarea modeling?Show answerHide answer
Selected-link analysis traces a subset of trips: those whose paths use one link, such as a bridge. Subarea modeling cuts a smaller geographic area out of a larger network and needs consistent traffic entering and leaving its boundary.
Near a stop is not a short walk
A buffer marks everything within a straight-line distance of a stop. People walk on streets, and a highway with one footbridge can turn 100 meters on the map into a 900-meter walk. The walking view is also how an isochrone is built: a boundary of equal travel time from one place.
Pause and think • slide 10A new stop’s buffer overlaps an existing stop’s buffer. Do we know how many new riders the new stop will attract?Show answerHide answer
No. The overlap describes coverage. Ridership also depends on the people and activities in the area, the service provided and the alternatives travelers have.
Pause and think • slide 25A neighborhood shows low transit use on a mode-share map. Can the map tell us why?Show answerHide answer
No. We would look at service frequency, destinations, walking access and car ownership. Maps help us find patterns and form questions; data and a suitable model test them.
How big should a zone be?
Zones group homes and jobs so the model can count trips between areas. Large zones keep trip tables small but give every home in a zone the same access. Small zones show local differences, and every full trip table grows with the square of the number of zones.
Pause and think • slide 20We split every zone into smaller ones. What else must change?Show answerHide answer
Households and jobs must be allocated to the new zones, zone numbers updated, centroid connectors added, and trip tables and skims rebuilt. New boundaries alone change nothing in the model’s data.
Pause and think • slide 21A centroid connector for a neighborhood is placed on the far side of a river. The zone’s trip total is correct. What goes wrong?Show answerHide answer
The trips enter the network in the wrong place, so shortest paths and link volumes become unrealistic even though the totals are right. The connection structure deserves the same care as the boundary.
Nearest warehouse, cheapest system?
Planning software also solves logistics problems. In a distribution problem, warehouses are sources and stores are sinks. Sending each store to its nearest warehouse ignores capacity; the cheapest plan looks at all stores and all limits together.
Pause and think • slide 27If each store is assigned to its nearest warehouse, must the whole system have the lowest total cost?Show answerHide answer
No. A nearby warehouse may have limited capacity, and which store moves elsewhere changes the total. The lowest-cost plan depends on the complete set of constraints and on how cost is defined.
Solving the doubly constrained gravity model
The doubly constrained gravity model sets tij = Bi Dj Pi aj fij. Every row must add up to its productions Pi and every column to its attractions aj. Bi fixes the rows and Dj fixes the columns, but each formula contains the other unknown, so we solve by iteration: start with every Dj = 1, compute Bi, then Dj, and repeat.
This is Example 1 from the slide: two zones, four unknowns. Eastfield (zone 1) is mostly homes and Downtown (zone 2) mostly jobs. Press Next step and check each number by hand.
Pause and think • slide 23After the first step, with every Dj = 1, which constraint holds and which fails?Show answerHide answer
The rows hold. With Dj = 1 the model is the singly constrained gravity model, which always matches the productions. The columns generally miss the attractions, and Dj exists to fix them.
Pause and think • slide 23Double every Bi and halve every Dj. What happens to the trip table?Show answerHide answer
Nothing. Each tij depends only on the product BiDj, so the trip table is unique while B and D are fixed only up to a common factor. Starting from Dj = 1 picks one of those solutions. For the same reason, when total productions equal total attractions only three of the four equations in Example 1 are independent.
Pause and think • slide 23Madison has about 1,000 zones (2,000 unknowns) and Chicago about 33,000 (66,000 unknowns). Why iterate instead of solving the equations directly?Show answerHide answer
The equations are nonlinear, because B and D multiply each other. One round of this procedure needs only one pass over the trip table, about n2 multiplications, which a computer handles easily even at n = 33,000, and it usually settles within a few dozen rounds.