Traffic jams and congestion

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"Michael Bean"
Member
Posts: 22
Joined: Fri Mar 29, 2002 3:39 am

Traffic jams and congestion

Post by "Michael Bean" »

Theres a nice article that could be used for an introduction that appeared in
the Atlantic a couple years ago.

The Physics of Gridlock
http://www.theatlantic.com/issues/2000/12/budiansky.htm

What causes traffic jams? The depressing answer may be nothing at all. As many
of us may have suspected, recent simulations show traffic congestion can arise
completely spontaneously under certain circumstances. Understanding networks of
cars in traffic may help researchers understand how networks in business and the
Internet operate.

Best regards, Michael
_______________________________________
Forio Business Simulations

Michael Bean
mbean@forio.com
www.forio.com
"Jim Hines"
Senior Member
Posts: 88
Joined: Fri Mar 29, 2002 3:39 am

Traffic jams and congestion

Post by "Jim Hines" »

Isnt a traffic Jam basically an inventory oscillator with each driver
trying to maintain an "inventory" of space between himself and the car
in front? Thats what John Sterman told me.

Jim
jhines@mit.edu
Bill Braun
Senior Member
Posts: 73
Joined: Fri Mar 29, 2002 3:39 am

Traffic jams and congestion

Post by Bill Braun »

Jim, how would the inventory model play out at an intersection (assume
fourway, a crossroads) where the spacing must change in an anticipatory
way. For example, in heavy traffic, even though the light is still green, I
wait until the car in front of me clears the intersection before entering
it (temporarily behaving as though the light were red), anticipating that
if the light changes to red before the car in front of me clears the
intersection, Ill be blocking it, leading to gridlock.

Bill Braun
From: Bill Braun <medprac@hlthsys.com>
John Sterman
Senior Member
Posts: 117
Joined: Fri Mar 29, 2002 3:39 am

Traffic jams and congestion

Post by John Sterman »

Jim Hines says that I told him traffic is like an inventory
oscillator, so it must be true!

You can model the velocity control of individual cars as such an
oscillator. The distance between you and the car in front plays the
role of inventory. The distance between the cars accumulates the
difference between the velocity of the car in front and your
velocity. Your velocity is in turn your momentum divided by the mass
of your car. Momentum is a stock that integrates the net force
applied (accelerating force from the drive train less drag and
friction), or equivalently, your velocity integrates the net
acceleration of your car. Through the gas/brake pedals, you control
the change in acceleration (with a delay -- your reaction time plus
the reaction time of the drive train). Thus your momentum is
analogous to the labor force of the firm: it is a stock that
accumulates control actions. You determine acceleration via negative
feedbacks in which you try to control the distance between you and
the car in front, and also attempt to keep your speed at the desired
rate. You have a goal for the distance between you and the next car,
which, as you learned in drivers ed, should be about 2 seconds *
your velocity (except in Boston, where your goal is to maintain less
than one car length so no one can cut in front of you). Note that
the 2 second rule is exactly the same as the basic rule for desired
inventory:

Desired Distance between cars = Desired time between cars * velocity
(meters) = Seconds * meters/second

Desired Inventory = Desired Inventory Coverage * expected shipments
Widgets = days * widgets/day

The structure just described is isomorphic to the basic inventory
control structure, and both are essentially negative feedback systems
with lots of phase lag and some damping. Depending on the gains of
the distance control loop and velocity control loop, along with
parameters such as the mass of your car, the system can be over,
critically, or underdamped. If you are laid back and willing to
tolerate some variation in the distance between you and the car in
front, the gain is low and the system will be overdamped. If you
drive with a lead foot the gain is high and the system will be
underdamped and generate high amplification (do the mental simulation
of what happens when the car in front suddenly slows down by 5 m/sec).

A line of cars on the freeway is thus like a supply chain, and the
dynamics are much like those seen in the beer game, but with many,
many more links in the chain. If a car slows, the driver behind
cannot react instantly, so the distance closes up. That driver must
(temporarily) slow more than the car in front did, to restore the
desired distance. The car behind that must then slow even more, and
so on. There are important nonlinearities here: velocity is (almost
always) nonnegative (you can stop, but you usually dont back up on
the freeway), and the distance between you and the car in front of
you cant be less than zero (attempts to do so result in crushed
metal and much cursing). In off hours, traffic is sparse, and each
car runs at its desired velocity, since the distance between you and
the next car is irrelevant. As rush hour begins and traffic density
builds, the space between cars shrinks. As it does, drivers must
take more aggressive control actions to keep from rear-ending the
driver in front, increasing the gain of the negative loop with the
time delays. As this occurs, the system moves from over to
underdamped (the dominant eigenvalues of the linearized system become
complex conjugates), and then often into a regime of unstable
oscillations, where the eigenvalues of the linearized system cross
into the positive half plane (a Hopf bifurcation for fans of
nonlinear differential equations). At this point the system
generates oscillations in velocity that increase in amplitude until
constrained by the nonlinearities, principally the bounds that
velocity is constrained between zero and the speed limit (in Boston,
between zero and speed limit + 20 mph). The result is stop and go
traffic even on limited access highways with no stoplights. You find
yourself zipping along at 60 for a few seconds, then screeching to a
dead halt, then speeding up again, and so on. The period of the
cycle depends on parameters but is often on the order of 30-90
seconds (though it often seems longer while you sit there stopped).

The most interesting aspect of traffic jams is their spontaneous
character, often occurring on open freeways with no apparent cause
such as an accident. This occurs when the gain of the system is high
enough to move it into the underdamped or locally unstable regime.
In such a situation, even the slightest perturbation can trigger the
amplification leading to a large jam. Perturbations arise from the
heterogeneity of the driver population (drivers have different goals
for speed and distance-to-car-in-front), from lane changes, from
entry/exit ramps, and from driver inattention and variability (e.g.,
taking you eyes off the road to dial the phone -- which you can use
to report the accident that you are about to cause by phoning while
driving).

The model I just described is in the class of car following models,
in which traffic is seen from a microscopic view. There are also
many macroscopic models that abstract from the individual cars to
consider traffic as a fluid and the traffic problem as analogous to
understanding the transition from laminar to turbulent flow.

Formal models of traffic flow have a long and distinguished history,
going back at least to the traffic equation of the late physicist
Bob Herman, in whose honor the "Robert Herman Lifetime Achievement
Award in Transportation Science" is awarded by the INFORMS Section on
Transportation Science & Logistics. A good survey of the history of
traffic models, both macro and microscopic, is Denos C. Gazis (2002)
The origins of traffic theory. Operations Research, 50(1), Jan-Feb,
69-77, available online at

http://www.eng.tau.ac.il/~ami/cd/or50/1 ... 1-0069.pdf.

John Sterman
From: John Sterman <jsterman@MIT.EDU>
"Bruce Skarin"
Junior Member
Posts: 4
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Traffic jams and congestion

Post by "Bruce Skarin" »

I believe that a solely System Dynamics approach would actually be a
fairly poor choice for modeling traffic as opposed to one including an
Agent Based approach. Though an SD model (such as the inventory
oscillator described by John Sterman) might do well at describing how an
individual vehicle (or group of vehicles) moves through traffic, the
goal of discovering the root cause of traffic would be hard to find. In
Johns case why is the system moving from over dampened to under? Is it
all just more cars? You may discover an optimal set of rules for dealing
with traffic (i.e. how far you should follow the car ahead of you), but
I would be very interested in seeing what an Agent Based model reveals
about the root cause.

John Sterman hints at this very important factor with: "Perturbations
arise from the heterogeneity of the driver population (drivers have
different goals for speed and distance-to-car-in-front), from lane
changes, from entry/exit ramps, and from driver inattention and
variability," so why not ask what can be done about it?

A case in point: I have observed at least four different decision rule
sets in drivers today: One is total aggressive individual that is always
speeding, changing lanes, pushing through traffic, riding as close as
possible, and cutting merging traffic off. The second is the moderate
aggressive, tends to remain in his lane, but still speeds and rides the
tail of the car in front of him, refusing to let in merging traffic. The
third is the moderate who stays in a lane and close to the speed limit,
allows for some space in front, and one or two cars to merge at a time.
The fourth is the nice guy who stays at or below the speed limit,
follows from way back, lets anybody over, and never changes lanes in a
hopeless attempt to smooth traffic. Note that there would be variations
for these rules with tractor-trailers since their size and momentum
change how effectively they can follow such rules.

I strongly believe that it is these stark differences in driving rules
that are more to blame for the initial buildup of congestion. If you
have ever seen a simulation of road capacity based on the number of
lanes and a single speed you will know that the potential capacity for
any road is always far higher than what is observed. Of course such
simulations also point out the difficulty in solving such a problem. To
reach these optimal capacities, you would have to get the drivers to act
like the model! That means you would have to convince every driver on
the road to go the exact same speed, leave equal amounts of space in
between cars, and follow finely tuned merging rules in order to smooth
out the flow of cars. Yet it may be possible!

For example I am originally from the West Coast where traffic can also
be a problem, but from my experience I recall it being far less
frustrating than say traffic in Boston. Perhaps I have a distorted
recollection, but it seemed to me that drivers in Seattle tended to
drive more uniformly during rush hours than those in Boston, resulting
in a more steady flow of cars. I believe that further improvements could
be made to nearly eliminate traffic if drivers were provided better
information (such as varying speed limits and following distances) and
if such information was followed carefully. Perhaps thats too
optimistic, but really, what direction do we want to be going?

-Bruce
From: "Bruce Skarin" <
bruceskarin@hotmail.com>
Bob Powell
Junior Member
Posts: 3
Joined: Fri Mar 29, 2002 3:39 am

Traffic jams and congestion

Post by Bob Powell »

Wilfredo Ruiz Oliveras wrote:
<<Does anybody have a model. a reference, or a suggestion on real life
traffic jams and congestion ... it should reflect real world attempts to
improve the traffic problem without decreasing the general well being of
the community. >>

Responses have addressed the dynamics of what happens as traffic volume
increases. Another question is. "Why do our roadways become so overburdened
that traffic volume increases to the point where we have the oscillatory
behavior characteristic of traffic congestion?"

I dont have a simulation model, but I do believe systems thinking has
helped me understand the structures that result in nationwide
infrastructure backlogs ... overburdened roads being a significant
component. As this is a nationwide problem, it led me to a top-level
national policy as causing it, which means local efforts alone will be
ineffective. This is a really difficult problem to solve ... as Forrester
wrote: "There is no utopia in social systems." In other words, its a
"Gilda Radnor world" ... "Theres always something!"

In summary:
Regions compete for jobs by lowering taxes and reducing regulations to
attract companies ("escalation"). This encourages development that
overloads existing infrastructure ("tragedy of the commons"). Because taxes
from sales and wages cover short-term costs, but do not cover long-term
infrastructure costs for roads and schools, more new development is
encouraged to "increase the tax base." This new growth further increases
the long-term infrastructure backlog and results in calls for even more
growth ("addiction"). Further, attractive regions attract until they become
no more attractive than any other place ("the attractiveness principle"),
often due to increasing traffic congestion. The increasing traffic
congestion results in calls for more road building, which leads to even
more growth (Stermans road building "fix that fails" in Business Dynamics,
Ch. 5).

Regions compete for jobs because the Federal Reserve only allows so many
jobs to be created: when unemployment drops too low (below whats
considered to be NAIRU), the Federal Reserve raises interest rates to
"cool" the economy. An exacerbating factor is that we poorly count
unemployment ... not counting those who "dont meet the test," are
discouraged, have temporary or part-time jobs looking for more or better
work, illegal aliens, etc. Because there are considerably more people than
jobs, the added value of any one person or region approaches zero (game
theory), which depresses wages and taxes (as described above) ... taxes
might be seen as the "regional wages" available to maintain quality of life
... when those "wages" are insufficient, we get stuck in traffic. I found
it interesting that wages at the bottom dropping to zero (in the absence of
a minimum wage) and people getting stuck in traffic are both results of Fed
policy.

A causal loop diagram that addresses this, and much more, is in the paper,
The Tangle of Growth. Click on the link at my website to go to the page
from which the Table of Contents, Preface, Summary and Introduction can be
downloaded.

Bob Powell
From: Bob Powell <scuba@usa.net>
Continuous Improvement Associates
Colorado Springs, CO Ph. 719 599-0977
http://www.exponentialimprovement.com/
"Davies, Paul"
Newbie
Posts: 1
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Traffic jams and congestion

Post by "Davies, Paul" »

The M25 motorway (freeway) runs an approximate circle of radius 20 miles
around London. It has an enormous traffic flow, and in principle reaches the
limiting conditions described by John Sterman for about 14 hours in each 24.
However, about 5 years ago a system of overhead gantries was introduced at 1
mile intervals, notifying drivers of the change in speed limit from 70mph
(the National limit in UK) down to whatever is deemed appropriate to calm
the local traffic. The higher the traffic flow, the lower the speed limit is
set. It is also set progressively lower in advance of a known accident. This
all has the effect of reducing the distance between cars (as per JSs model)
and also reducing the damping component of reaction times, making the system
more tolerant to heavy-footed drivers. It is also enforced by cameras on the
gantries and heavy fines for breaking the (locally set) speed limits.
Against the intuition of 95% of the driving population, it works, and
despite the increase in traffic density the system flows more freely than 6
years ago (although since they increased the motorway from 6 to 8 lanes at
the same time, the cause-and-effect isnt so clear).

My question is this. I heard a rumour that somebody used an SD model to
predict the behaviour as part of the justification to the planners and
financiers, but Ive never seen a reference to the model. Anybody got one?

Paul Davies
Technical Manager
Thales Sensors
Leicester
UK
+44 (0)116 259 4174
paul.davies@uk.thalesgroup.com
Yaman Barlas
Member
Posts: 44
Joined: Fri Mar 29, 2002 3:39 am

Traffic jams and congestion

Post by Yaman Barlas »

This is a delayed reply to the "traffic congestion" query and a couple of
related notes.
A couple of students in our group did a nice modeling project of the
dynamics of bottlenecks/gridlocks caused by *feedback effects* at
intersections. (I believe Bill Braun referrred to this phenomenan).

The abstract:

Traffic Deadlock Caused By Two Intersections

Ömer Akkentli,
Mert Nuhoðlu, Bogaziçi University Industrial Engineering Department,
Istanbul
Contact Person:
Mert Nuhoglu
E-mail address:
mert.nuhoglu@isnet.net.tr

The usual simulation models of the traffic flow are based on spatial
automata modeling, queuing theory or other modeling technique that doesnÕt
consider or focus on the feedback dynamics. In this work, we discovered an
important feedback structure in the traffic flow, which generates a
threshold value that causes deadlock in the traffic flow.
The map of the roads modelled in this work is shown in Appendix A. There is
a two-way main artillery, which is fed by two intersecting roads in reverse
directions. Thus the system contains two intersections. At the times when
the traffic flow is congested, one of the main artilleries may become full.
Then the cars coming from the intersecting road that feeds this artillery
stop up in the junction. By doing so, these cars cause the other main
artillery, which is in the reverse direction, to be blocked. Therefore the
tail of the jam in this artillery becomes longer and the cars entering in
the artillery stop up in the outflow junction of the first artillery. Since
the other road is also blocked, the outflow of this road becomes blocked and
none can move anywhere.

The full paper can be downlowaded at:
http://www.ie.boun.edu.tr/sesdyn
esources/traffic.htm

Mert Nuhoglu is -I believe- planning to extend this type of modeling toward
more real-life scale, professional versions. (His email above).
Yaman barlas
From: yaman barlas <ybarlas@boun.edu.tr>

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Yaman Barlas, Ph.D.
Professor, Industrial Engineering Dept.
Bogazici University,
34342 Bebek, Istanbul, TURKEY
Fax. +90-212-265 1800. Tel. +90-212-358 1540; ext.2073
http://www.ie.boun.edu.tr/~barlas
SESDYN Group: http://www.ie.boun.edu.tr/labs/sesdyn/
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