Michal Paszkiewicz

review: An Introduction to Traffic Flow Theory

Speed limits, as far as I have seen, are mostly a source of annoyance for drivers. I have only recently started learning to drive, so the vast majority of my experiences of road signs are from being a passenger. An overwhelming amount of people that have given me lifts view speed limits as one of the following:

  1. a guideline
  2. a guideline to follow when not in a rush
  3. a guideline to follow when not showing off their fancy car
  4. the speed limit for when there is a police car or speed camera around

This goes to the extent that it is common knowledge that some truck drivers use radios to track police on the roads, while I have personally seen countless cars across Europe flash their lights as a warning that there will be a police car on the other side of the oncoming hill.

What many people don't realise is that many speed limits are set due to calculations that would show that in a perfectly legal case where all drivers are following the law, an accident could still happen provided the speed of the cars exceeds a certain level. This book provides numerous examples of these cases that I hope will stay in my mind forever, stopping me from breaking the laws that will protect me from myself.

The book begins with a quick revision of your standard mechanics course. Linear motion with constant speed, followed by constant acceleration and then varying acceleration. Equations of motion and vehicle trajectories. The first chapter then continues by bringing in the considerations that are essential for traffic modelling, but may not have featured on your mechanics course - the effects of vehicle, driver and driving environment on the motion of a vehicle. You can model a car however you like, but at the end of the day it will be the driver that actually decides how the car moves (provided they are not in an AI car).

The second chapter then dives into car-following models. There are surprisingly many complexities when trying to model just one car following another and this book really makes that clear, while demonstrating various models along with their advantages and disadvantages.

PITT car-following model

Above, I've used one of the simpler car-following models to show how a leader affects following vehicles (or dots, in this case). It is visible that there is a reaction time - the following car will accelerate or decelerate only a moment after its leader has.

Chapters 3-5 are considered Part II of the book and are all about measuring the flow, speed and density of a traffic flow and the capacity of a certain road. It applies a more statistical approach to managing traffic control, including giving directions on figuring out what parts of a route may cause bottlenecks.

Part III of the book is titled "Traffic Operational Analysis Techniques" and it brought with it plenty of brilliant techniques for analysing traffic that I have found quite revolutionary. Shockwave analysis was one specific subject that I found particularly interesting and I particularly gained a lot from seeing the unusual graphs that the author was plotting (they may be perfectly normal for a traffic analyst, but they were definitely unusual to me).

The last part of the book deals with highways, intersections and networks and has given me a good understanding of both driving restrictions and the reasons for the design of various stretches of road.

The book was not as difficult to read as I thought it might be, although I found myself wondering if there could have been a better use of mathematical notation (maybe with more super and subscripts instead of equations with terms like "x(N+1)" which are not entirely clear that they are referring to the x following x(N)). All in all, I have learnt a lot and it was nice to read a book that built upon the knowledge I gained at Uni without requiring quite as much work as I had to put in back then. I would recommend this book to all drivers, to all lovers of applied maths and to anyone that isn't afraid of challenging their minds. This book may stop you speeding, or it might just make you a little brighter.

****

published: Fri May 05 2017

Michal Paszkiewicz's face
Michal Paszkiewicz reads books, solves equations and plays instruments whenever he isn't developing software for Transport For London. All views on this site are the author's views only and do not necessarily represent the views of TfL.