My talk on "Transportation Networks" at the Urban Systems and Network Science (UrbanNets) satellite workshop at NetSci 2017, Indianapolis organized by Marta Gonzalez (MIT)

1. Transportation
Networks
Meead Saberi
meead.saberi@monash.edu

2. 2
§ Transportation networks are
complex, large-scale, and
come in a variety of forms
(e.g. road, rail, air, and
waterway networks.)
§ Transportation network
modeling research goes back
to 1950s.
§ Seminal work of Wardrop and
Whitehead (1952).
History

3. 3
§ From an economic perspective,
the supply in transportation
systems is represented by the
underlying network topology and
the cost characteristics whereas
the demand is represented by
the users of the transportation
system.
§ Network equilibrium models are
commonly used for the prediction
of traffic patterns in transportation
networks that are subject to
congestion
Network Modeling

4. 4
§ Origin-destination demand matrix
§ Multi-modal (car, public transport, taxi, walk, bike, etc.)
§ Time-dependent
§ Nodes are origins and destinations
§ Links are trips between origin and destination pairs
§ Traditionally difficult to observe, often through household
travel survey data
§ More recently observed using mobile phone data
§ Demand networks are spatial temporal weighted and
directed networks.
Network of transportation demand

5. 5
Chicago’s network of travel demand
Number of trips = 78,681
Number of nodes = 1,868
Number of links = 37,528

6. 6
Melbourne’s network of travel demand
Number of trips = 133,938
Number of nodes = 9,310
Number of links = 63,916

7. 7
Characterizing travel demand networks
(left) A zoomed in view of the complex network structure of trips in Melbourne aggregated
at Statistical Local Area (SLA) level. Node colors represent node degree changing from
blue (low) to red (high). The network exhibit a large variation in node degree with relation
to location. (right) Node degree distribution in Melbourne and Chicago mobility networks.
Dashed line represent the fitted power law.
Source: Saberi et al., 2016. Transportation.

8. 8
Travel demand as a network
§ The idea of viewing travel demand
as a graph is not new.
§ Understanding the spatial behavior
of individuals by studying human
activity spaces.
§ Traveler cognitive or mental map;
personal world; activity repertoire;
expectation space
§ Individual traveler activity space vs.
collective structure and properties
of combined individuals’ activity
spaces

9. 9
Characterizing travel demand networks
Spatial distribution of node degree in (left) Chicago and (right) Melbourne following a
heterogeneous pattern.
Source: Saberi et al., 2016. Transportation.

10. 10
Characterizing travel demand networks
Shortest path tree structure using the effective distance* concept from the perspective of a
node in (left) the CBD of Melbourne and (right) a northern suburb of Melbourne.
* Brockmann and Helbing, 2013. Science.

11. 11
Model evaluation and validation
Network structure of travel demand in Melbourne from (a and e) real world
observations, (b and f) Random Forest model, (c and g) Decision Tree model, and (d
and h) Modified Decision Tree model in 2007 and 2009.
Real world observations Modeled networks
Source: Saberi et al., 2017. (under review)

12. 12
§ Road infrastructure as a network
§ Nodes are junctions/intersections
§ Links are streets
§ Travelers (particles) flowing in the network
§ Time-dependent
§ Links have multi attributes (distance, travel time, volume,
density, speed, etc.)
§ Nodes have multi attributes (delay, capacity, etc.)
Transportation supply network

13. 13
Melbourne’s road network

14. 14
Network Traffic Flow Fundamental Variables
Q(t) is average network flow
K(t) is average network density
qi(t) is average link flow
ki(t) is average link density
li is link length
Network Fundamental
Diagram (NFD)
Traffic Flow
Fundamental
Diagram (FD)
Source: Geroliminis and Daganzo (2008)

15. 15
Network Traffic Flow Fundamental Variables
Q(V) is average network flow
K(V) is average network density
d(V) is the total distance traveled in V
t(V) is the total time traveled in V
Lxy(V) is total network length
tv is time interval

16. 16
Network Traffic Flow Fundamental Variables

17. 17
Network Exit Function
Source: Daganzo, 2007; Mahmassani et al., 2013
§ Relationship between vehicle
accumulation in the network
n(t) and output flow g(t), the
rate vehicles reach their
destinations.
§ γ is maximum output flow.
§ ω is jam accumulation.
§ What is gridlock? A state of
the system under which traffic
in the entire or a portion of the
network comes to a complete
standstill.
Equilibrium behavior
Non-equilibrium behavior

18. 18
Gridlock propagation and dissipation
Source: Mahmassani et al., 2013
Networks tend to jam at a range of
densities that are considerably smaller
than the theoretical network jam
density because of heterogeneous
distribution of congestion.

19. 19
Future Research Directions
§ Transportation networks as multi-layer networks
(multiplex) that are temporal, weighted and directed.
§ Definition of community in transportation networks?
§ Integration of demand and supply networks? Identifying
demand and supply mismatch.
§ How to integrate network measures with behavioral
models of transportation? Social discrete choice models?
§ Why and how a gridlock
forms? How it propagates in
the network? How it might
recover?
Source: Zhang et al. (2017)

20. Transportation
Networks
Meead Saberi
meead.saberi@monash.edu