Mobility Modelling

Lecture 3 - General Mobility Modelling Metrics

20 Feb 2023

Mozhgan Pourmoradnasseri, Ph.D.

MOBILITY ELEMENTS

Supply; Road Network

Demand; Traffic Flow

Regulations; Signaling

MOBILITY ELEMENTS; Supply

  • Transportation infrastructure and services that enable mobility in cities.
  • Transportation infrastructure can influence land use and density.

MOBILITY ELEMENTS; demand

  • Travel behavior and choices of people who are moving within a city.
  • It is influenced by demographics and socioeconomic factors. 
  • More demand can influence infrastructure investments. 

MOBILITY ELEMENTS; regulations

  • Policies, regulations, and laws that govern transportation and mobility in cities.
  • Can impact both the supply and demand for transportation services by affecting the design and operation of transportation infrastructure.

For efficient management and informed decision making, cities need to know ...

Transportation network

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, ...

ELEMENTS OF DEMEND

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.

Some metrics to access the preformance

  • Modal Share
  • Travel Time
  • Congestion
  • Accessibility
  • Safety
  • Emmissions
  • Costs

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.

  • Measures the percentage of trips taken by each mode of transportation in a city. It can be measured for walking, biking, driving, or taking public transit.
  • Important for understanding how people travel in a city and can help identify areas with a high demand for certain modes of transportation.
  • Helps to guide transportation planning and policy decisions.

Modal share

Link

Link

  • The time it takes to travel from one place to another.
  • Important indicator of the efficiency of urban mobility.
  • A well-designed and connected network of roads, public transport, and other modes can help reduce travel time.
  • Very complex to estimate accurately and in dynamic setting.

travel time

EXAMPLE

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)

AVERAGES DON’T TELL THE FULL STORY

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

TRAVEL TIME

Systematic Delay Actors:

  • the general (average) demand level
  • the physical road characteristics, i.e. the general capacity level
  • the speed-flow relationship

Higher demand \(\rightarrow\) Higher traffic density \(\rightarrow\) Higher travel time \(\rightarrow\)  Higher variability 

TRAVEL TIME IS IMPORTANT
Reliability is more important :)

This is not an ad.

Understanding travel time is essential for reliable route choices and traffic management and control.

  • Increasing traffic demand and limited road capacities, resulting in congestion.
  • Congestion not only increases travel times, but travel times also become more variable and unpredictable as congestion increases.
  • Changes in travel times are routinely handled in economic evaluations of transport policy through the application of values of time.

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. 

TRAVEL TIME VARIABILITY

Variability Actors:

  • Demand variation through the day
  • Traffic control signals
  • Unforeseen incident
  • Weather conditions
  • Random perturbations to traffic flow

 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.

CASE STUDY; COPENHAGEN

  • A significant problem in many cities worldwide, leading to lost time, increased air pollution, and reduced quality of life.
  • The average time a driver spent in traffic congestion worldwide in 2020 was 74 hours.
  • Environmental empacts.
  • Reducing traffic congestion through measures such as road pricing, carpooling, or investment in public transport can improve urban mobility.

Traffic congestion

How to measure and underestand congestion 

MACROSCOPIC TRAFFIC FLOW

Given a road segment, space is discretized (\(dx\)). We have:

  • density \(\rho(x,t)\): number of vehicles per length unit (veh/km)
  • traffic flow \(q(x,t)\): number of vehicles per time unit (veh/h)
  • mean speed \(v(x,t)\) in km/h

 

This is a mathematical abstraction inspired by fluid mechanics.

We assume in \(dx\) space we have homogeneous conditions for density and speed.

\(dv = \frac{dq}{d \rho}\)

  • Ease and convenience with which people can reach destinations, such as workplaces, schools, healthcare facilities, shops, and other amenities.
  • Have a significant impact on the quality of life for residents, the economic vitality of the city, and the sustainability of the urban environment.
  • Accessibility can be measured in a number of ways, including travel time, distance, and cost. 

Accessibility

Järv, Olle, et al. "Dynamic cities: Location-based accessibility modelling as a function of time." Applied geography 95 (2018): 101-110.
https://github.com/AccessibilityRG/DYNAMO
  • Safety indicators can include the number of accidents, injuries and fatalities on the road, and collision types.
  • Policies and strategies that can help to improve transportation safety
    • Infrastructure improvements
    • Speed management
    • Vehicle safety standards
    • Law enforcement and penalties
    • Public transportation safety
    • Driver education and training

Safety

  • Air pollution
  • Greenhouse gas emissions
  • Noise pollution

Environmental impact

  1. Data availability: Many countries do not have comprehensive data systems, and even where data is available, it may be incomplete or outdated.

  2. Vehicle diversity: Passenger cars to heavy-duty trucks and buses, each with different emission profiles. Moreover, Vehicle age, maintenance, and fuel quality plays role.

  3. Driving behavior: Speed, acceleration, and idling time.

  4. Dynamic traffic conditions: Dynamic emission models are a bigger challenge.

Challenges

WARDROP'S FIRST PRINCIPLE OF ROUTE CHOICE, AKA "USER EQUILIBRIUM"

 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)

EXAMPLE

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 \(x_2=0\). 

EXAMPLE

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

EXAMPLE

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

INDUCED DEMAND BY BRAESS'S PARADOX

DO PEOPLE USE THE SHORTEST PATH?

Travelers differ in

  • attributes (value of time (VOT), willingness to pay, time budgets, etc.)
  • behavioral preferences (e.g., willingness to take risks, willingness to switch routes with potential savings),
  • experience, and knowledge about travel, all of which could lead to significant heterogeneity in route choice behavior. 

 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.

  • The results show that about two-thirds of the subjects do not use the shortest travel time path.
  • No subjects followed the shortest distance path unless it also coincided with the shortest travel time path.
  • Travelers clearly have other preferences when making their route choices. Therefore, a better understanding of people’s route preferences could also inform the development of choice set generation algorithms.

Case study