SONG: Simulator of Network Growth 1.0
Introduction
Simulation
Models
Interface
Parameters
List
Statistics
Outputs
User Instructions
FAQs
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Introduction
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SONG 1.0 is a simulator designed for simulating the process
of transportation network growth. The growth or decline of transportation
networks is normally treated as the result of top-down decision making in the
long-range planning efforts of metropolitan planning organizations (MPOs). However, changes to transportation
networks are essentially the results of numerous small decisions by property
owners, firms, developers, towns, cities, counties, state department of
transportation districts, MPOs, and states in response to market conditions and
policy initiatives. These system behaviors demonstrate the characteristics of decentralized
systems, where organized patterns and structures can emerge not because of
centralized control, but because of the interactions among decentralized system
components. This phenomenon of
decentralization and self-organization occurs in many circumstances, such as
bird flocks, ant colonies, life evolutions, neural networks. Increasingly research
is applying decentralized models in different domains as a new way of viewing
the world.
In SONG 1.0, transportation networks are treated as
decentralized systems that demonstrate self-organizing patterns. By design, the
simulator models behavior of individual system components and small decisions, and
then demonstrates the patterns resulting from interactions of component models.
The idea is that it is the actions
of the components, not the whole that are controlled by the designer; the
resulting patterns or structures, which often behave very differently than the
elements that compose them, are not designed.
It is worth to notice that SONG 1.0 shows a different kind
of simulation, called "soft simulation", which "provides qualitative
understanding of a complex system by constructing a simple one that shares the
same principle (Papert, 1992)." By developing
the simulator, the focus is not on perfect reproductions of the real world, but
rather to help people explore the "microworld" of transportation network
systems and to stimulate new ways of thinking about the network growth process.
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Simulation Models
-----------
SONG 1.0 simulates behaviors of individual links to explore
the patterns of resulting network forms. In particular, each link is treated as
autonomous agent and the simulation models individual link behaviors based on
certain rules that determine link revenue, costs and investment decision. The
model flowchart in Figure 1 provides a global view of the model structure;
detailed descriptions of components models are followed after the flowchart.
Figure 1: Simulation flowchart
1. Land Use and Network Settings
The land use and network are treated as initial conditions
input into the model. The land use is modeled as a layer of a grid of land
blocks called land use cells. Transportation networks are modeled as directed
graphs overlaying a land user layer.
The main objective of setting initial land use is to provide
input to transportation models. Information contained in the land use layer
includes: location, population density, and market density. It is assumed in
the simulation model that trips produced from a land use cell are directly
proportional to population density and trips attracted to a land use cell are
directly proportional to market density.
The model considers three land use patterns: (1) random initial land use, where trips
produced and attracted are randomly distributed; (2) uniform initial land use,
where trips are uniformed distributed, and it is a conceptual condition
designed to control the effect of land use on the formation of network; and (3)
bell-shaped land use, which is designed to replicate the distribution of land
use patterns with a Central Business District (CBD).
The transportation network is represented as a directed
graph that connects nodes with directional arcs, links. The simulator applies a
grid network structure.
2. Travel Demand Model
The travel demand model converts land use information
(population and employment data) into link flows on a given transportation
network through trip generation, trip distribution and route assignment models.
The trip generation model divides geographical area into
zones centered on network nodes and converts land use properties of the zones
into trips produced and attracted. The land use layer is modeled as a square,
and it is assumed that the land use layer is static throughout the
simulation.
The trip distribution model matches the generated trips by
purpose between origin (O) and destination (D). Trips produced are differentiated
according to destination; trips attracted to a zone are differentiated
according to origins.
The
traffic assignment model predicts the travelers’ choices of routes by the
relationship between flow and travel time. In particular, it converts the OD
matrix, from the trip distribution step, into flows on the links depending on
the way travelers choose routes. By
assumption, every traveler tries to optimize his travel time by choosing the
quickest route to reach the destination.
3. Revenue Model
The network revenue model determines the revenue road
providers can collect by providing the road services, depending on link speed,
flow, and length. (From travelers’ perspective, it is the toll they pay for
using the road.) The revenue model
is a link-based model that calculates revenue for each link. Revenue is calculated by multiplying the
toll and flow. Therefore, the higher the flow on the link, the higher is the
revenue.
4. Cost Model
This
model calculates the cost that is required to keep a link in its present usable
condition depending on the flow, speed, and length.
where, Cia is the cost of maintaining the
road at its present condition,
m
is the (annual) unit cost of maintenance for a link,
a1, a2,
a3 are
coefficients indicating economies or diseconomies of scale
5. Investment Model
Depending on the available revenue, and
maintenance costs link changes its speed.
If the revenue generated by a link is insufficient to meet its maintenance
requirements its speed drops. If
the link has revenue left after maintenance it invests that remaining amount in
capital improvements, increasing its speed. A major assumption in this model is
that a link uses all the available revenue in a time step without saving for
the next time step.
With the new speed on the links the travel time changes and
the whole process from the travel demand model is repeated to grow the
transportation network.
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Interface
As shown in Figure 2, the
Interface of SONG 1.0 contains three portions of information: the parameter
panel, the visualization panel, and the output panel.
Figure 2: Interface of
SONG 1.0
1. Parameter panel
The parameter panel is
located in the left side of the interface. It is where users can make changes
to the values of certain variables and see the consequences on the network
form. In doing so, users are able to examine the implications of alternative
policies as represented by different values of the parameters.
The parameters shown on
the interface include network types, speed, land use distributions, and sets of
parameters contained in the component models for simulating travel demand,
revenue, cost, and investment behaviors. Detailed description of each parameter
will be provided in "parameters" section of this file.
Figure 3: Parameter Panel of SONG 1.0
2. Visualization panel
The simulator is
designed to visualize network forms based on either different link flows or
different link speeds. Visualization of the simulation is demonstrated on the
right hand side of the interface, including the graph output, legend, running
button, and status information.
Figure 4: Visualization
panel of SONG 1.0
·
Graphic output
Graphic output is shown
on the grid network graph with different colors and thickness on each link
representing different link speed or link flow.
·
Legend
Different link flows
and different link speeds of the network are represented with different colors
of the links. In particular, the simulator follows the Red, Orange, Yellow,
Green, Blue, Indigo, and Violet (ROYGBIV)
spectrum with "Red" representing the highest speed or flow and "Blue"
representing lowest values in speed or flow. The particular value of speed or
flow for each color is indicated in the legend below the graph panel.
·
Running button and status information
To run the simulation,
users need to hit "evolve" button, and the running status will be displayed
below the legend indicating the model running status. The simulation process
stops either when equilibrium is reached, or when it reaches its 20th
iteration.
3. Output panel
The output panel is
located on the lower right hand side of the interface. It includes the following
information:
·
Speed and volume scroll down options
·
Iteration period
·
Statistics button for MOEs output
Figure 5: Output panel
of SONG 1.0
Figure 6: MOEs output
window
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Parameters List
-----------
SONG 1.0 contains a set of variables that allow users to
make adjustments. These include initial network
types, network speed distribution, land use distribution and some model parameters. Figure 2 shows the interface
of SONG 1.0 where users can adjust the parameters. A brief description of the
variable default values, range, and real world interpretation is given in Table
1. Additionally, the full list of underlying model parameters (including those
that are not shown in the interface) are also explained in this document.
Figure 2: Parameter panel of SONG 1.0
Table 1: SONG 1.0 Variable Table
|
|
Variable ID
|
Default value
|
Adjustable Range
|
Interpretationa
|
|
Land
use, network settings
|
|
|
|
|
Network
types
|
0
|
10x10
|
5x5~25x25
|
network
sizes
|
|
|
|
|
network
with river
|
|
|
Speed
distribution
|
1
|
uniform
|
uniform
|
no
differentiation in link speeds cross the network
|
|
|
|
|
random
|
randomly
distribute speed
|
|
|
|
|
prespecified
random
|
repeat the
"same" random distribution
|
|
Speed
multiplier
|
|
100%
|
20% - 220%
|
network
speed level
|
|
Land
use distribution
|
2
|
uniform
|
uniform
|
|
|
|
|
|
random
|
|
|
|
|
|
urban
|
land use
with downtown
|
|
|
|
|
prespecified
random
|
repeat the
"same" random distribution
|
|
Land
use multiplier
|
|
100%
|
20% - 220%
|
land use
density
|
|
Travel
Demand
|
|
|
|
|
|
Value
of time
|
5.1
|
1.0
|
0 - 5.0
|
hourly
time value
|
|
Friction
Factor
|
5.2
|
0.01
|
0 - 1.0
|
willingness
to travel
|
|
Revenue
|
|
|
|
|
|
Toll
rate
|
6.1
|
1.0
|
0.5 - 1.5
|
toll
|
|
Length
coefficient
|
6.2
|
1.0
|
0 - 1.5
|
revenue
responsiveness to distance traveled
|
|
Speed
coefficient
|
6.3
|
0.0
|
0 - 1
|
revenue
responsiveness to road speeds
|
|
Link
Maintenance Cost
|
|
|
|
|
|
Length
coefficient
|
 7.1
|
1.0
|
0 - 1.2
|
elasticity
of cost in response to road length
|
|
Flow
coefficient
|
7.2
|
0.75
|
0 - 1.2
|
elasticity
of cost in response to link flow
|
|
Speed
coefficient
|
7.3
|
0.75
|
0 - 1.2
|
elasticity
of cost in response to road speed level
|
|
Investment
|
|
|
|
|
|
Speed
improvement factor
|
8.1
|
1.0
|
0 - 1
|
responsiveness
of link improvement (investment) to link performance (such as revenue/cost
ratio)
|
a Detailed variable interpretations can also be
found from the model variable description below.
Initial Network Types, Speed
Distribution, and Land Use Distribution
1. Network types include options representing different sizes and types of
networks, e.g. users can choose grid networks with varying sizes from 5x5 to
25x25 as demonstrated in Figure 2; or network with a river crossing as
demonstrated in Figure 7.
Figure 7: Network with river crossing
2. Speed
distributions in the initial network can be set as random or uniform to see
how different (or similar) the evolved network form can be compared to the
initial one. Uniform speed
distribution means link speeds are uniform across the network; Random speed distribution distributes
the initial link speeds randomly across the network; and Pre-specified random speed distributes links speed randomly in a
pre-specified way, so that users can control the effects of speed distribution
and test the impacts of other variables. Speed
multiplier allows users to adjust the level of speeds across the whole
network. e.g. a value of 135% indicates the speed level is 135% of the default
speed level.
3. Land use
distributions at the initial stage of network development can be set as
random, uniform, pre-specified random, or with a CBD (call urban land
use). The idea is to explore if
orderly network structure can emerge from different initial land use
conditions. Additionally, a land use multiplier in the program
allows users to adjust the level of initial land use density cross the whole
network.
Model parameters
Corresponding to the simulation components models, simulation
parameters will be explained in this section. Note that not all of the parameters
explained below are visible in the interface, the user adjustable variables, as
shown in the interface, will be marked with "***" sign.
1. Parameters from
travel demand model
The models
User adjustable parameters are associated two models
simulating how trips are distributed in the network.
(a) Gravity model: 
, where 
=
is friction factor,
indicating people’s willingness to travel, and 
is the generalized cost of commuting between two locations;
and
(b) Generalized travel cost model:
, where costs of commute are generalized to consist of: travel time in monetary value and toll (or user fees):
Description of parameters:
, friction factor ***
- Default
value: 0.01
- Range:
0~1
- Real
world interpretation: w
represents the sensitivity of travel behavior to travel costs. In another word, w reflects
people’s willingness to travel.
Particularly, A w of 0, means willingness to travel is independent
of travel costs; lower values of w (e.g. 0.02), represent a society where
longer trips are preferred; and higher values of w (e.g. 0.9), represent areas where shorter trips are
preferred.
Value of time ***
- default:
1.0 per unit time
- range:
user define arbitrarily
- Interpretation:
e.g. by default, value of time is $1.0 an hour. Value of time is assigned
to convert travel time into monetary value by multiplying it with travel
time.
2. Parameters from revenue
model
The model:
[
], or its simplified version: [
], assuming no relationship (
=0) between revenue and speed, and linear relationship
between link length and revenue (
=1)
From services providers’ perspective, toll paid by travelers
equals to revenues made by the providers. So revenues are calculated in the
same way that toll is calculated in the generalized travel cost model in the
last section. Hence, parameters in the generalized cost model have the same
values as defined in the revenue model here.
Description of parameters:
, a model parameter to scale flow annually (not shown on the interface)
- Default
value:=365
- Range:
hidden from user adjustment
- Interpretation:
the model applies to scale daily revenue into annual revenue.
, Tax (toll) rate ***
- Default
value: 1.0
- Range:
user define between 0~10
- Interpretation:
tax rate determine how much tax providers charge travelers for traveling
on the road based on the distance traveled (link length,
) and road speed or standard (link speed,
).
, Length power in revenue model ***
- Default
value:1.0
- Range:
Users define between 0~10, indicating economy or diseconomy of scale of
revenue regarding road distances provided for travelers.
- Interpretation:
=1.0 means one unit increase in link length generates
one unit of additional revenue; >1.0 means one unit increase in link length generates
more than one unit additional revenue; <1.0 means one unit increase in link length generates
less than one unit additional revenue; =0 means change in link length will not affect revenue
made by the providers.
, Speed power in revenue model ***
- Default
value: 1.0
- Range:
Users define between 0~1.0, indicating economy or diseconomy of scale of
revenue regarding road speed provided for travelers.
- Interpretation:
=1.0 means one unit increase in speed (e.g. upgrade the
road section) generates on unit of additional revenue; if <1.0, one unit increase in speed leads to less than
one unit rise in revenue; if =0, then speed change has no effects on revenue; if >1.0, one unit increase in speed leads to more than
one unit increase in revenue.
3. Parameters from cost
model
The model:
[
]: the model calculates
, the cost of maintaining the road at its present condition
in time step t. This cost depicts the threshold cost of maintaining a link.
Description of parameters
, annual unit cost of maintenance for a link (Not shown on the interface)
- default
value: 365
- range:
fixed from user adjustment; or hide it
- Interpretation:
use to convert
daily link maintenance costs to annual costs.
, coefficients for length, indicating (dis)economies of scale
to road providers ***
- default:
1.0
- Range:
User define to determine the (dis)economy of scale link maintenance costs
regarding link length.
- Interpretation:
represents the way how link maintenance costs change as
link length changes. If =1.0, then link maintenance increase one percent wit
