Phantom Traffic Jams andAutonomous Vehicles

Benjamin Seibold

Associate Professor of Mathematics

April 21, 2016

CST Board of Visitors Meeting

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 1 / 16

Phantom Traffic Jams and Jamitons What Are They?

The driver ahead of you brakes, so you brake, which causes braking behindyou. But there is no discernable cause. . .

Phantom Traffic Jam

Initially uniform traffic flow of vehicles becomes inhomogeneous, in theabsence of obstacles.

Jamiton

Traveling wave in traffic flow [c.f. soliton = nonlinear wave in physics]

Vehicles run into a sharp front, break heavily, then slowly speed up.

Hot-spot for accidents; increased fuel consumption.

Research Goals

Understand causes and dynamics of phantom traffic jams.

Use this knowledge to devise technology to prevent/dissolve them.

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 2 / 16

Phantom Traffic Jams and Jamitons Where To Go Jamiton-Spotting?

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 3 / 16

Phantom Traffic Jams and Jamitons Jamitons in Observations

Observation: Jamitons on Long Road (video: [D. Helbing])

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 4 / 16

Phantom Traffic Jams and Jamitons Jamitons in Experiments

Experiment: Jamitons on Circular Road [Sugiyama et al.: New J. of Physics 2008]

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 5 / 16

Phantom Traffic Jams and Jamitons Jamitons in Traffic Models

Traffic Models

Microscopic: N Vehicles on Road

Position of j-th vehicle: xj

Velocity of j-th vehicle: vj

Acceleration of j-th vehicle: aj

Physical Principles

Velocity is rate of change ofposition: vj = xj

Acceleration is rate of changeof velocity: aj = vj = xj

“Follow the Leader” Model

Accelerate/decelerate towardsvelocity of vehicle ahead of you:

aj =vj+1 − vj

xj+1 − xj

“Optimal Velocity” Model

Accelerate/decelerate towards anoptimal velocity that depends onyour distance to the vehicle ahead:

aj = V (xj+1 − xj ) − vj

use computersto simulate −→

Combined Model

aj = αvj+1 − vj

xj+1 − xj+ β (V (xj+1 − xj ) − vj )

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 6 / 16

Phantom Traffic Jams and Jamitons Jamitons in Traffic Models

Microscopic Traffic Models

Simulation: phantom jams and jamitons

Macroscopic Traffic Modelsρt + (ρu)x = 0

(u+h)t +u(u+h)x = 1τ

(U−u)

Describe traffic via fluid dynamics.

−→ up-scale simulations to largemetro areas

−→ incomplete data and privacy

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 7 / 16

Phantom Traffic Jams and Jamitons Instability

Key Point: Instability

In real traffic there are constant perturbations: road bumps, enginehick-ups, driver inattention, etc.

These effects are too small to produce large-scale phenomena (suchas traffic waves) alone.

Phantom traffic jams are arise when uniform traffic flow is unstable.

Stable traffic flow: small perturbations of uniform flow decay.

Instability: small perturbations of uniform flow amplify, and eventuallygrow into large traffic waves (“jamitons”).

Traffic models reveal: there is a critical threshold density ρc

(depending on driver behavior):Below ρc, uniform flow is stable; above ρc, unstable.

Crucial Practical Insight

Phantom jams can result from collective driving behavior;no bad drivers needed for them to arise.

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 8 / 16

Jamitons . . . are analogs of detonation waves

Jamitons are mathematical analogs of detonation waves

Self-Sustained Detonation Wave

Vehicle acceleration plays role of chemical reactions.

Vehicles run into a sharp increase in density (“shock” = braking zone).Attached to shock is a “reaction zone” that ends at a sonic point.Sonic point is event horizon: once passed, a vehicle cannot affect jamiton.

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 9 / 16

Jamitons Relation to Other Phenomena

Traffic wave

Founders of Detonation Theory

Detonation wave

A shock supported by atrailing exothermic reaction

Detonations

combustion

certain explosions

Black hole

sonic point = event horizon

Roll waves

Hydraulic jump

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 10 / 16

Jamitons Jamitons in Numerical Computations

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 11 / 16

Jamitons Jamitons in Numerical Computations

Infinite road; lead jamiton gives birth to a chain of “jamitinos”.

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 12 / 16

Future Traffic Control via Autonomous Vehicles

CollaboratorsBenedetto Piccoli (Rutgers Math)

Jonathan Sprinkle (U of Arizona ElecEng)

Daniel Work (UIUC Civil Eng)

Support

NSF CNS–1446690

CPS: Synergy: Control of vehiculartraffic flow via low density AVs

traffic science: understand traffic flow via models, analysis, and computation

traffic engineering: develop future traffic control to prevent/dissolve trafficwaves (make whole flow safer and more fuel efficient)

traditional highway traffic controls: ramp metering, variable speed limits(neither can break up traffic waves)

use autonomous vehicles (AVs); low cost: in10–15 years, AVs will be on our roads anyways

human factor in a cyber-physical system:humans interact with AVs; fundamental needto better understand human driving behavior

Univ. of Arizona AV

CollaboratorsRodolfo Ruben Rosales (MIT Math)

Aslan Kasimov (KAUST)

Morris Flynn (Alberta MechEng)

Support

NSF DMS–1007899

Phantom traffic jams, continuummodeling, and detonation wave theory

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 13 / 16

Future Traffic Control Simulation and Experiments with Autonomous Vehicles

Experimental measurements of human driving

Simulation: uncontrolled vs. AV-controlled traffic flow

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 14 / 16

Broader Impact of Traffic Flow Research

Media Education

New course (Spring 2016):

CST 2100: Topics in Science andTechnology: Modeling and Simulationin Science and Technology

Without formal programming background,students engage in agent-based modelingand simulation: swarming ants and birds,population dynamics, traffic flow and humancrowds, bacterial motion, stock marketmodels, etc.

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 15 / 16

Atherosclerotic Plaque Growth . . . has mathematically similar features to traffic waves

Atherosclerotic Plaque GrowthModeling and simulation of long-term (30 years) growth:

LDL & LDLox: dc ∆c − kccM = 0 in Ω(t)macrophages: dM ∆M − kMcM = 0 in Ω(t)foam cells: Ft +∇ · (~vF ) = (kc +kM )cM in Ω(t)growth field: ∇ · ~v = (kc +kM )cM in Ω(t)domain motion: Ω = ~v

Key Messages

Research: Ripples observed on plaques can beexplained via an instability of the model equations.

Tiny imperfections grow into wave structures thatfundamentally affect the properties of the structure(e.g. risk of rupture) — same as in traffic waves.

Applied and Computational Mathematics: model-and equation-driven research; advance mutualinsight in seemingly disconnected fields.

Result: ripples can be explained viainstability of equations.

Collaborators

Kurosh Darvish (Temple MechEng)

Pak-Wing Fok (U Delaware)

Sunnie Joshi (Temple University)

Support

NSF DMS–1318641

A computational framework for athero-

sclerotic plaque growth simulations

Benjamin Seibold (Temple University) Phantom Traffic Jams and AVs 04/21/2016, CST Board 16 / 16