Lecture 3 - General Mobility Modelling Metrics
20 Feb 2023
Mozhgan Pourmoradnasseri, Ph.D.
Supply; Road Network
Demand; Traffic Flow
Regulations; Signaling
For efficient management and informed decision making, cities need to know ...
Transportation network is a network or graph in geographic space, describing an infrastructure that permits and constrains movement or flow, such as road networks, railways, air routes.
Nodes: Junctions, stations, zones, airports, ...
Links: streets, lanes, shipping channels, flights, ...
Link charachtristics: Speed limit, travel time, cost, ...
Travels cause by people who need to perform activities at different geographic locations.
Therefore highly differentiated by time of the day, day of the week, purpose, type of cargo, importance of duration of traveling, etc.
Demand is traditionally represented by aggregated origin-destination (OD) matrices.
Hadachi, A., Pourmoradnasseri, M., & Khoshkhah, K. (2020). Unveiling large-scale commuting patterns based on mobile phone cellular network data. Journal of Transport Geography, 89, 102871.
Normalized OD matrix of trips between municipalities of Tartumaa.
To evaluate and track how well a city's transportation system (or any other mobility system) is meeting the needs of its residents and promoting environmental sustainability.
Suppose that I have two ways of getting home from work; by train or by car.
With train:
Travel time 50 minutes
With car:
11% of the time 60 minutes, and 89% of the time 30 minutes.
How and when should I go home if I want to be home at 6 pm?
I want to spend maximum possible time with family.
I want to go to cinema with family and want to be on time with probability of 90%
Average: (0.11*60+0.89*30 = 33 minutes)
Travel time is usually referred to as the period of time spent traveling from an origin location to a destination location.
Travel time = free flow time + systematic delay + unexplained delay
can be explained by observed characteristics of the trip
cannot be foreseen and taken into account
Systematic Delay Actors:
Higher demand \(\rightarrow\) Higher traffic density \(\rightarrow\) Higher travel time \(\rightarrow\) Higher variability
This is not an ad.
Understanding travel time is essential for reliable route choices and traffic management and control.
Computing reliable travel time is difficult.
Definition
Travel time variability is an indicator of the variability of travel time from an origin to destination in the transportation network (including any model transfer or en-route stops). It can be defined as the random variation in travel time, i.e. the variation in unexplained delay.
Variability Actors:
minimal and maximal travel time on 11.3 km of Frederikssundsvej towards Copenhagen, observed over a period of about three months (only weekdays). Where the minimum travel time, the free flow travel time, is around 10 minutes, the maximum varies up to about 40 minutes in the morning peak
Fosgerau, M., Hjorth, K., Brems, C., & Fukuda, D. (2008, December). Travel time variability: Definition and valuation.
Given a road segment, space is discretized (\(dx\)). We have:
This is a mathematical abstraction inspired by fluid mechanics.
We assume in \(dx\) space we have homogeneous conditions for density and speed.
\(dv = \frac{dq}{d \rho}\)
Järv, Olle, et al. "Dynamic cities: Location-based accessibility modelling as a function of time." Applied geography 95 (2018): 101-110.
Data availability: Many countries do not have comprehensive data systems, and even where data is available, it may be incomplete or outdated.
Vehicle diversity: Passenger cars to heavy-duty trucks and buses, each with different emission profiles. Moreover, Vehicle age, maintenance, and fuel quality plays role.
Driving behavior: Speed, acceleration, and idling time.
Dynamic traffic conditions: Dynamic emission models are a bigger challenge.
The journey times in all routes actually used are equal and less than those that would be experienced by a single vehicle on any unused route.
John Glen Wardrop
(1922–1989)
This network has two nodes having two paths as links. Let us suppose a case where travel time is not a function of flow as shown in other words, it is constant.
If the demand from node 1 to node 2 is 12, what is the flow on each link?
Answer: \(x_1=12\) and \(x_2=0\).
100 cars are traveling from A to D. What is the user equilibrium?
Answer: Equilibrium will occur when 50 drivers travel via ABD and 50 via ACD. Every driver now has a total travel time of 3.5.
Reference: Wikipedia
100 cars are traveling from A to D. What is the user equilibrium?
Equilibrium will occur when 25 drivers travel via ABD, 50 via ABCD, and 25 via ACD. Every driver now has a total travel time of 3.75.
If the 100 cars agreed that 50 travel via ABD and the other 50 through ACD, then travel time for any single car would actually be 3.5, which is less than 3.75.
Reference: Wikipedia
Dietrich Braess (1968): Adding one or more roads to a road network can slow down overall traffic flow through it
Video link.
2009, New York
2003, Seoul
In practice, experimented in several cities:
Seoul, New York, Stuttgart, Paris, Rouen, London
Travelers differ in
Wardrop's first principle:
The journey times in all routes actually used are equal and less than those that would be experienced by a single vehicle on any unused route.
Zhu, S., & Levinson, D. (2015). Do people use the shortest path? An empirical test of Wardrop’s first principle. PloS one, 10(8), e0134322.
3 weeks, random vehicles equipped with GPS devices, Minneapolis, St. Paul metropolitan area.