Different perspectives on road traffic

This post aims to introduce different ways in which road traffic can be modeled. I will focus on outlining the conceptional differences between  what I call choice-based and action-based models of traffic and look at two particularly interesting papers in detail.

Most publications do primarily focus on the "choose-a-route" problem, meaning that road traffic and congestion as a macroscopic emergence of the system are primarily influenced by the route choices of individuals. This assumes that it is mainly the density of traffic (i.e. the  ratio of the number of travelers on  over the capacity of a particular route) that gives rise to congestions and traffic jams. In other words, once you chose a particular road, there is not much left to be done in terms of decision-making (i.e. driving behavior) in order to avoid getting stuck in a jam. This appears sensible, as it serves the intuition that every individual driver is intrinsically dependent on the behavior of other drivers and that his influence on the overall system should be very limited.

Yet, it is also interesting to observe how, given a certain density-level, different driving styles can yield very different outcomes in terms of efficiency of the traffic system. Kai Nagel has done some interesting work on life-times of simulated traffic jams that might become particular relevant when we try to draw conclusions about the business cycles, i.e. which policies might be most effective when trying to get the economy out of a recession, say.

For now, I want to introduce two papers. The first paper "Individual Apaption in a path-based simulation of the freeway network of Northrhine-Westfalia" by Kai Nagel aims to examine how individuals learn and adapt their route-choices, based on the past performance of their respective choices and how the system evolves accordingly. The second paper "How Individuals take turns: Emergence of alternating cooperation in a congestion game and the prisoner's dilemma" by Dirk Helbing, Martin Schoenhof, Hans-Ulrich Stark and Janusz A. Holyst  takes a game-theoretical approach to observe how people's choices in a two and higher dimensional set-up might or might not yield socially efficient equilibria. Both papers give a nice intuition about how we might want to model  the choose-a-route problems associated with road traffic.

Here is the basic set-up of the choice-based models. All roads can be thought of as having a certain comfort limit L. If the number of cars on the road exceeds this comfort limit L, the road gets uncomfortable to be on, i.e. jam or at the very least traffic delays occur. Drivers choose particular routes, essentially trying to outguess everyone else. The essential bit is that they won't know that the correct decision, i.e. the route that minimizes the travel time from A to B, is until it is too late.

Nagel's paper introduces a similar set-up. Using the freeway network of the German Land Northrhine-Westfalia, a simulation is built, where there are many travelers with different origin-destination pairs. Each traveler has a choice between 10 different paths (or routes) that connect his origin with his destination. In the course of the simulation, each driver tries every single route and from then on on a daily basis choses the route that has performed best in the past (i.e. the route that minimized the time to get from A to B). The simulation runs 6000 iterations where each iteration consists of a preparation phase, where each traveler chooses his path for the day according to past performances, and a traffic microsimulation phase, where the daily traffic dynamics are simulated and macroscopic phenomena like jams are recorded.

The results of these simulations are somehow surprising. Nagel finds that the network performance decreases as drivers optimize their individual route and settle down on a route which is most convenient for themselves. In other words as individuals learn and adapt strategies that optimize their own performance, the aggregate system performs worse. This is partly due to the fact that jams are "equilibrated" , meaning that fastest ways around congested areas tend to vanish over time.

Dirk Helbing et al take a different approach and yet, they draw somehow similar conclusions.

Helbing et al conducted experiments where the test persons were instructed to choose between route 1 which corresponded to a freeway and route 2 that represented a side road. Participants were told that if more than half of the participants would choose route 1, everyone would receive 0 points. If on the other hand   half would choose route 1, they would receive the maximum average of 100 points, but 1-choosers would profit at the cost of 2-choosers.  This paper introduces the route-choice game as a "multi-stage symmetrical N-person single commodity congestion game". What exactly does  this mean?

Multi-stage: The game is played several times.
"Symmetrical": Refers to the fact that the payoffs associated with a certain strategy do only depend on the other strategies that are played and not on who plays them.
"single commodity ": the single available commodity is space on the road
"congestion game": The payoff for each player depends on the resource that he choses and the number of players choosing the same resource.

Previous research on congestion games has shown that there always exists a Wardrop equilibrium. This is characterized by the property that no driver can decrease her travel time by choosing a different route and that travel times on all used routes is roughly the same. Yet, the Wardrop equilibrium does not generally reach the system optimum, i.e. minimize the overall travel time. According to Braess paradox additional streets might even increase the overall travel time. Note that this can be seen to correspond to Nagel's findings.

Nevertheless Helbing et al find that oscillatory cooperation (the notion of taking turns in order to maximize the system outcome) "can still emerge in route choice games with more than 2 players after a long period (rarely within 300 iterations)". They also find though that "emergent cooperation is unlikely to appear in real traffic systems" under the current conditions. The paper suggests that an automated route guidance system where drivers get individual and on average fair route choice recommendations based on the current traffic situation might help to reach the system optimum.

So looking at two papers that model road traffic from complexity science's point of view, we learn that the system might actually become less efficient as travelers adapt strategies that optimize their individual performance . Game theory tells us that the introduction of more space might actually further worsen the system's performance. All this might have very interesting consequences for our study of aggregate economic behavior. The next step is to look at models that try to measure how the behavior of individuals once they chose a particular road might affect the efficiency of the overall traffic system. Bringing both perspectives together will hopefully give us an idea of the key factors that yield traffic inefficiencies, which in turn will help us when comparing it to other systems that exhibit complex behavior as well, such as the behavior of ants and birds.

Road traffic as a reference model for aggregate economic behavior

Can we assume road traffic to represent a reference model for aggregate economic behavior? I will not focus  very much on justifying that road traffic exhibits complex behavior as well. I will instead focus on justifying the step of introducing it as a reference model. In order to establish this step, I will be looking at incentives and structures that might be similar in both systems.

Dirk Helbing argued in his paper "Modeling and Optimization of Production Processes: Lessons from Traffic Dynamics" (2003) that we can draw parallels between road traffic and production processes. Helbing does particularly mention "the presence of moving entities (persons or objects) which interact in a non-linear way" and  the presence of a  "competition for  limited resources" (such as capacity, time or space) in order to justify this approximation. I want to argue that we can extend this approximation by saying that we can assume road traffic to represent a reference model for the whole economy, of course bearing in mind the simplifications that have to be made in order to justify this step.

Optimization is a key incentive that is present in both systems. Consumers, firms and governments aim to optimize their respective key parameters, i.e. their utility, profits or social welfare. In order to do so, they try to gain competitive advantages by making use of past experiences. Participants in road traffic usually aim to optimize the time it takes them to get from A to B (which can be seen as trying to minimize the cost of getting from A to B). This may involve picking a particular time of the day for the journey, but assuming that most working parts of the population do not have the freedom to make this choice, this optimization process is mainly about picking the right route. Neil Johnson puts it that way: Road traffic can be seen "as a collection of decision-making objects repeatedly competing...to find the least crowded route from A to B" (Johnson, Simply Complexity). Hence it seems as if the incentive-structures are similar in both systems.

To further see this imagine the situation of an individual firm in the economy when it has to decide about whether or not to enter a particular market. This is similar to an individual driver's decision of whether or not to enter a particular road. In a similar manner consumers have to decide how much to consume and how much to save for future consumption. In the economy individuals are constantly faced with "Choose -a-route" problems, the difference is simply that in the case of road traffic the number of problems narrows down to one. All these decisions seem to have to do with an optimal allocation of the resources that are available to individual agents.

Also the character of possible interventions in the system is of similar nature. Central banks try to influence the economy through monetary policy (such as interest rates), governments try to stimulate or slow activity down through fiscal policy and regulation. In the same manner, road planners try to optimize traffic flow through speed limits, lights and the general traffic structure.


How do the emerging macroscopic phenomena compare? In the aggregate economy they are visible in form of sudden starts and stops in economic activity. In road traffic we can observe the sudden appearance and disappearance of traffic jam. Traffic jam  as such is a inherent inefficiency of road traffic (just like stops of economic activity or recessions) and a lot of the following will look at different ways in which complexity science models traffic jam and thereby explains the occurrence of these inefficiencies. Here it might be important to note that this UROP is particularly interested in inefficiencies that arise within the system, meaning that arise without external influence. It is especially the appearance and disappearance of traffic jam out or sudden starts and stops that does not have an external cause (such as construction sites, accidents or a change in monetary policy) that is of particular interest. 


So the main parallels that seem to justify the introduction of road traffic as reference model for the aggregate economic behavior seem to be the following:

• The inherent incentive structure: Optimization as a key component of both systems

• The nature of the problems that agents face: "Choose-a-route"
  

• The nature and means of interventions that institutions try to make are similar.

• Emergent phenomena are of similar nature and can arise within the system without any external influence

At this point it might be important to note that this approximation is of course limited.  It does not seem to be clear how added value, a key component of economic activity, could arise within road traffic. I do not really have an answer for that. 


Even though there might be more points that will make the approximation less powerful, I still believe that it is sufficient for the purposes of this project. I am aiming to introduce various ways in which road traffic can be modeled and extract some key factors that these models lists for the appearance of traffic jam. I will then look at a different complex system, the behavior of ants, birds or a fungus, and see what we can learn from their behavior  about inefficiencies in road traffic and in the aggregate economy.

The Economy as a Complex System

This post will use the criteria that I have outlined earlier in order to establish how we can view the economy  as a complex system.

• The system contains a collection of many interacting objects, whose behavior is affected by memory or „feedback“ (the objects include some capacity for adaption and learning)

This does certainly apply. The interacting objects are  roughly speaking consumers, firms and governments. Each of these market participants  makes decisions according to  a certain set of decisive parameters and history shows that agents adjust or complement these decision rules, according to their experience.

• 
  The system is open, meaning that the system can be influenced by its environment

This also goes without much saying. What is going on in the economy is surely not solely caused by events that happen within the economy. Wars, natural influences and  also political frameworks are examples for ways in which the environment can influence the system.

• 
  The system evolves in a highly non-trivial way and is generally far from equilibrium, meaning that in principle anything could happen and provided that we observe the system long enough, it probably will.

It is at this point where economist's might at least scratch their heads. Intuitively, it seems to make sense to suggest that the economy is generally far from a stable equilibrium, based on our experience with short-term fluctuations and sudden starts and stops. There exist concepts of a natural level of output and employment or ceteris paribus long-run steady states in macroeconomics, which suggest that in the long run there might exist something like an equilibrium. But if we focus on the short-run (especially for our purposes, the study of business cycles, this seems appropriate) it seems to be fair to say that the economy generally seems to be far from equilibrium.

• 
  The emergent phenomena are not brought about by some central controller

If this wasn't true, then Economics would be an entirely useless subject (some might argue that it is, yet this is not  the point of this discussion). It seems to be sensible to suggest that no regulatory institution like for example central banks, the FSA or governments have the power to ultimately cause the emergent macroscopic behavior that the economy exhibits. Our hope as policy makers is to be able to partially influence this behavior and it is exactly the point of this project to determine ways in which we might be able to do so more effectively. But it certainly does hold that there would be a central controller with ultimate decisive power.

• 
  The system exhibits a mix of ordered and disordered behavior

This criterion seems to be a tricky one and requires the most thinking. Chaos is formally defined as the behavior of a non-linear, dynamic system, which is highly-sensitive to initial conditions. Lorenz's "butterfly-effect" is the most common example of this phenomenon.  The term chaos is due to everyday experience quite misleading, in fact mathematical chaos does not celebrate utter disorder but a new kind of order. This can be phrased as "self-organization", the spontaneous emergence of order out of seeming chaos (note that the little applications in the active essay try to make exactly that point). In the context of social systems such as the economy this is called "spontaneous order", a concept that has been widely elaborated by Friedrich Hayek (who calls it "extended order"in his book The fatal Conceit). Hayek argues that the spontaneous order (resource allocation) that emerges out of the free interaction of self-interested individuals in a competitive market is superior to any other possible allocation. Similar to the way  in which the temperature (another example of an emergent macroscopic behavior) is subject to change, this allocation is not stable. As we observe the  economy over time, we will constantly observe new spontaneous orders. This is why we might be able to say that the economy exhibits a mix of ordered and disordered behavior. Looking at this simulation (http://llk.media.mit.edu/projects/emergence/on-the-edge.html) might clarify this point (even though this system eventually reaches a steady state at some point).

So summing it up it seems as if we can justify the description of the economy as a complex system. The next posts will introduce the reference models and will look at how we can use the fact that all the economy and  the reference models exhibit complex behavior to learn more about hot and cold flushes in business cycles.

Complexity? Comlexity!

What is complexity all about, and why exactly is it that it might help us to get a little bit closer to understanding why the observed hot and cold flushes come about? Some think of Complexity Science to be the science of all sciences. I want to explain why I share this view by briefly introducing Complexity and the phenomenon  of emergence and hinting at some of the most fascinating aspects of this relatively young discipline. 

Complexity science is concerned with the study of phenomena which emerge in a system that consists of a collection of interacting objects.  Mostly, these phenomena are not explainable by simply looking at the behaviour of individual objects. What makes complexity so exciting is that we can observe complex, higher order structures emerging from the interaction of objects that are equipped with fairly simple decision rules. Some of the most popular examples of complex systems include the financial markets, our immune system, ecological systems or even the world of quantum physics. In fact, the range of systems that could potentially be subject to study appears endless.   

The following  set of necessary properties that a complex system should exhibit is proposed by Neil Johnson (Neil Johnson, Simply Complexity). This will be useful for the purposes of this project when trying to identify how both the economy and the introduced reference models fit these criteria.

1. The system contains a collection of many interacting objects, whose behavior is affected by memory or „feedback“ (the objects include some capacity for adaption and learning)
2. The system is open, meaning that the system can be influenced by its environment
3. The system evolves in a highly non-trivial way and is generally far from equilibrium, meaning that in principle anything could happen and provided that we observe the system long enough, it probably will
4. The emergent phenomena are not brought about by some central controller.
5. The system exhibits a mix of ordered and disordered behaviour.

Looking at this set, it seems fairly intuitive to restrict study to systems “where we have useful descriptions in terms of rules and laws” (Holland, Emergence), at least for the purposes of this project.

The goal of complexity science is to model, describe and possibly predict the behavior of such systems.  Here it  might  be interesting to note that we might not need to fully understand the constituent objects of a system in order to describe how the aggregate behaves, as simple bits interacting in a simple way might lead to a rich variety of higher order structures and outcomes. This is why complexity science might be so relevant. A lot of academic research has been focused on understanding every aspect of a particular problem. But it seems likely that no level of understanding of individual objects will help us to explain certain phenomena (for example understanding individual brain cells might not help to explain the occurrence of Alzheimer).  


What I find particularly exciting is that a lot of the research suggests that partially understanding one system from say Physics might actually help us to increase our understanding of another system from a totally unrelated discipline, say economics. It is this inter-disciplinarity that this project will also make use of. All the work that is done at the Santa Fe Institute is a prime example of the possible relevance of this approach. 

The next step will to be to look at the aggregate economy from a Complexity point of view. I will apply the above set of criteria in order to justify the claim that the economy can be seen as a complex system. I am then hoping to be able to justify that both road traffic and  the behavior of  ants are complex systems  that can be seen to exhibit parallel or contrasting behavior to the observed hot and cold flushes in business cycles. The challenge will be to show that both models can be seen as reference models for the economy. This will involve a formulation of the possible dangers and limitations of such an approximation. Building on that, I will look at the occurrence of inefficient phenomena in both reference systems and hopefully will be able to draw some conclusions about the subject of interest.

(If complexity science is a fairly new subject  to you, then looking at Mitchel Resnick's active essay "Exploring Emergence" (a link is provided at the sidebar) might be an entertaining and nice way to familiarize yourself with the subject matter. Also check out the homepage of the Santa Fe institute, if you are interested in the whole range of possible applications of the study of emergence)

Hot and Cold Flushes in Business Cycles?

All modern industrial economies experience significant swings in economic activity. The now standard definition of business cycles was provided by Arthur Burns and Wesley Mitchell in "Measuring Business Cycles", where a cycle consists of a time of expansion with increased general economic activity, followed by a time of recession.

Deviation from long-term growth in the US GDP

Here it is important to note that the term cycle seems to be somewhat misleading. In fact, looking at the data one gets the impression that there are hardly any patterns that would allow us to account for regularity in both timing and duration of upswings and downswings.  The figure to the right shows a business cycle for the US economy from 1955 to 2005. Recessions in the figure are negative deviations from trend. Clearly, both recessions and expansions vary significantly in both duration and intensity.

This UROP will focus on the varying magnitude and on the volatility of this curve. Starts and stops to economic activity do seem to come about very sudden and do seem to vary in their impact. We  can see  hot and cold flushes, represented by the many turning points of the curve. Some of them do eventually turn the economy around (the points of largest deviation in a particular period), but most of them seem to disappear more or less immediately after they have occurred.

This UROP will take a complexity point of view on this occurrence of hot and cold flushes  and observe what this can teach us about the way in which we could interpret and improve our handling of such events. I want to discuss how we can view the economy as a complex system and how the introduction of road traffic and the behavior of ants and birds as reference models can help us to improve our understanding of aggregate economic behavior.