The last post tried to relate the discussion in road traffic and other traffic networks to the current debate in macroeconomics. It has found that the emphasize on the local origins or systematic traffic congestion is matched by the shift of economists' attention from looking at aggregate shocks to considering idiosyncratic sectoral shocks when trying to explain the volatility and sudden starts and stops of the business cycle.
I have argued that some insights that the discussion of road traffic inefficiencies yielded might both support and maybe even enhance the standpoint that academics like Acemoglu or Gabaix take. Local digestions, i.e. idiosyncratic sectoral shocks, are inherent to the system road traffic, due to our imperfect anticipation of other drivers' behaviour. Likewise, most papers that try to argue that sectoral shocks might lead to aggregate fluctuations assume that these idiosyncratic shocks come about with equal probability in every sector. What I want to argue is that these sectoral shocks do only spread through the input-putput supply network if other sectors are not able to substitute away from the sector that experienced the shock (ie change routes as they see a congestion coming up) or if firms that are sufficiently close connected to the sector act sufficiently unccoperative. In other words, countries where sectors are heavily dependent on smooth supply schedules from closely connected sectors should experience higher levels of fluctuations in the business cycle, ie higher GDP volatility.
In order to support this, it might be interesting to see whether one can find some empirical evidence for the argument that the flexibility of a sector's production function across all sectors (ie how volatile the economy as a whole is to sectoral supply shocks) and intersectoral cooperation are related to GDP volatility.
In order to do so, one will need measures that allow to compare this asymmetry in input-output networks and intersectoral ooperation across countries.
The previous post already hinted at the importance of the notion of network centrality when trying to assess a sector's potential ability to substitute away from certain inputs. In their paper "Vertex centralities in Input-Output Networks reveal the Structure of Modern Economies" (2011) Florian Bloechl, Fabian Theis, Fernando Vega-Redondo and Eric Fisher suggest two possible ways of measuring vertex centralities in input-output networks. I will only focus on Random Walk Centrality, as this seems to be the more relevant measure for the purposes of this project.
Based on Freeman's closeness centrality, which is defined as the inverse of the mean geodesic distance from all nodes to a particular one, the authors define random walk centrality to be a generalization of this measure that allows its application to input-output tables.
The idiosyncratic shocks are assumed to be supply shocks that cloesely connected sectors experience. These supply shocks flow through the network of intermediate inputs. The pattern of this flow is modelled as a random walk. A high random walk centrality of a sector therefore corresponds to the idea that a sector is sensitive to supply conditions anywhere in the economy, ie that he is volatile to idiosyncratic shocks in many other sectors in the economy.
The authors provide codes to obtain the sectoral random walk centralities for a given input-output network. Data on these networks is provded by the OECD and the results are comparable across countries. I would like to argue that the simple mean across a country's sectoral random walk centralities might provide a decent measure for the asymmetry in a country's input output network. The higher the average random walk centrality of a given network, the more sensitive an economy is to idiosyncratic sectoral shocks.
The OECD input-output tables are most reliably available for the year 2000. I therefore suggest to consider the standard deviation from trend for a given country from 1995 to 2005 as a measure of a country's GDP volatility. I obtained this data using the OECD quarterly national accounts and using the standard procedure to obtain the standard deviation from trend (ie the applying the hp-filter on the logged variables and taking the standard deviation of the cycle).
I yet have some issues finding an appropriate measure that allows to quantify levels of intersectoral cooperation across country's. The World Bank's corruption index might be an option, yet does not fully capture the concept of intersectoral cooperation. It might be possible that the hypothesis needs to be modified in order to allow for an empirical test of the predictions.
For now, I have carried out a simple OLS on the model:
volatility=constant+a*asymmetry+error
The first results are promising , yet far from being ready to be published as more data will need to be obtained in order to allow for a more sophisticated model.
A Complexity view on Business Cycles
Saturday, February 18, 2012
Saturday, February 4, 2012
Some first results
This post will try to analyse how the previous findings could enhance the most recent discussion on the origin of the occurrence of sudden starts and stops in aggregate economic activity. In order to do so it will establish an understanding of where research seems to be standing at the moment by looking at some more recent papers. It will conclude that complexity science supports the current direction of research and might actually be able to provide an alternative point of view on the current standing of research in business cycles.
The analysis of this project so far has highlighted the role that individual incentive-structures and local occurrences of congestion seem to play when trying to disentangle the reasons for systematic inefficiencies in road traffic. Consequently, when trying to apply our results to the research question, our analysis will focus on the role of shocks at the micro level and how these could potentially spread to become systematic, i.e. to cause aggregate fluctuations. Yet, most of the research that macroeconomics has devoted to the business cycle focuses on the role of aggregate shocks to output (such as changes in monetary or economic policy, wars, natural disasters) and argues that idosyncratic shocks to individual firms and sectors average out in the aggregate, due to a diversification effect. But more recently scholars like Gabaix (2009) or Acemoglu (2011) have argued that such idiosyncratic shocks to individual firms or sectors might in fact be responsible for most aggregate fluctuations.
In their paper "The Network Origins of Aggregate Fluctuations" Acemoglu et al (2011) argue that "local" microeconomic shocks may lead to aggregate fluctuations due to inter-sectoral input-output linkages.
Acemoglu et al model the aggregate economy as an inter-sectoral network where different sectors interact through input-output linkages. They present a static variant of the model that Long and Posner first presented in their 1983 paper "Real Business Cycles". In this economy households supply labor and choose their input output bundles, maximizing their Cobb-Douglas utility function. There are n numbers of goods, where each is being produced by a sector and can either be consumed or used as an input for production by other sectors. The subsequent inter-sectoral input-output relations form the inter-sectoral network of this economy.
The authors now prove mathematically that given the presence of such input-output linkages, the diversification argument that has been brought forward to dismiss the role of micro shocks in aggregate fluctuations may not hold. If the roles that sectors play as direct or indirect suppliers to others are significantly asymmetric, then "sizable aggregate fluctuations may originate from microeconomic shocks".
These findings correspond to the results of Xavier Gabaix's paper "The Granular Origins of Aggregate Fluctuations" (2009). Gabaix argues that if the distribution of firm size is fat-tailed, then the diversification argument breaks down. A fat-tailed distribution of firm size and a significant asymmetry in the roles of sectors as output suppliers might here be interpreted to be mirror-images of the same phenomenon.
So current research seems to be moving away from focusing on the role of aggregate shocks (note that these are mostly exogenous) to underlining and further examining the importance of shocks to individual firms or sectors. I find this very pleasing as this tendency is in line with the sentiment of this project for the entire discussion on road traffic was exclusively centered around endogenous causes for the occurrence of inefficiency and highlighted the role of "shocks" that happened at the link level.
It will now be interesting to see how, based on the model that Acemoglu et al and Gabaix use, one could apply some of our previous results to the occurrence of hot and cold flushes in business cycles and relate them to the current standing of macroeconomic research.
Compare the inter-sectoral network to the model of road traffic where road traffic is represented as a network of junctions and links. The following interpretation of possibly existing parallels between both models might seem reasonable. A particular route might represent a particular sector of the economy. The cars on this route at any given point in time could represent firms that operate in this sector. Firms that engage in the production of several products in different sectors can be represented by cars that pass through different roads. The input-output linkages between sectors in the inter-sectoral network model could possibly be compared to the junctions that connect different roads and routes. All of the above is of course simplistic, yet I feel that given an awareness for the simplicity of this approach, it might provide a ground on which we can potentially transfer some of our results.
In line with Acemoglu et al, our former considerations yield the observation that systematic congestions, i.e. aggregate fluctuations across the wider network, can be rooted in congestions, i.e. shocks on the micro level. The mechanisms through which these local shocks might spread seem to be quite well understood in both systems. In road traffic the velocity fluctuations can create backward spreading waves of increasing fluctuations which then break down the free flow of traffic. These fluctuations can spread over the junction to the system level and cause aggregate breakdowns in wider areas. In the economy a idiosyncratic shock leads to low output levels in the relevant sectors, which in turn leads to low input levels in first-order connected sectors, which in turn affects second-order connected sectors etc. Acemoglu et al call this a cascade effect, an effect that will become more relevant as shocks hit sectors with more linkages.
Before proceeding, note how all of this already yields important results for our initial research question. It shows how, even if the general trend is positive, a idiosyncratic shock, i.e. a local congestion, can cause a negative aggregate response. It therefore already hints at some explanations for the sudden occurrence of starts and stops in business cycles.
So far we could interpret our results to support the findings in the literature. But how can they add something to the discussion? The literature so far has been able to identify a mechanism through which shocks that hit individual central sectors in the network may give rise to aggregate fluctuations. But it has so far been unable to determine whether or not the network-centrality of a sector is a sufficient or a necessary condition for the occurrence of aggregate fluctuations. Can our analysis add something to that discussion?
Note that by definition the network-centrality of a sector in the inter-sectoral economic model is crucially determined by the number of firms that operate in this sector, the number of firms that use the respective good as an input and by the number of goods that firms in this sector use as production inputs. Transferring this into our road traffic model, the centrality of a route is affected by both the number of firms that pass through it and the number of junctions that it crosses. But remember, complexity research on road traffic has given rise to the conclusion that a certain level of vehicle density is a necessary, yet it is not a sufficient condition for the occurrence of traffic congestion on systematic level. Complexity science hence seems to suggest that a sufficient network centrality alone is not enough to trigger aggregate fluctuations when a sector experiences a shock.
What else did matter? In road traffic, the initial shocks themselves are brought about by drivers' imperfect anticipation of the actions of other drivers. But whether or not they spread to cause breakdowns of thefree traffic flow at the aggregate level did heavily depend upon the incentives and actions that drivers displayed at the junction level. Uncooperative behavior at the junction and/or failures to change the route in order to avoid the congested links were key factors that would allow local inefficiencies to spread to the system level. How can we use this result in order to enrich the existing discussion?
Complexity science seems to suggest that given the fulfillment of certain requirements, shocks to an individual sector can cause aggregate fluctuations. This holds if the sector is sufficiently connected in the inter-sectoral network (in line with the existing research) and if either closely connected sectors cannot or fail to substitute away from the input that the sector in trouble produces (i.e drivers fail to alternate their route at junctions) or firms that operate in closely connected sectors display excessively uncooperative behavior (i.e. drivers fail to cooperate at junctions).
A next step will be to empirically test the results that these results, i.e. to test whether the failure or incapability to substitute away from goods that are produced by sectors that experience shocks and/or uncooperative behavior of firms in closely connected sectors can provide further necessary conditions under which the diversification argument might not hold. In order to do so it will be key to provide real world data that either back or support the above results.
The analysis of this project so far has highlighted the role that individual incentive-structures and local occurrences of congestion seem to play when trying to disentangle the reasons for systematic inefficiencies in road traffic. Consequently, when trying to apply our results to the research question, our analysis will focus on the role of shocks at the micro level and how these could potentially spread to become systematic, i.e. to cause aggregate fluctuations. Yet, most of the research that macroeconomics has devoted to the business cycle focuses on the role of aggregate shocks to output (such as changes in monetary or economic policy, wars, natural disasters) and argues that idosyncratic shocks to individual firms and sectors average out in the aggregate, due to a diversification effect. But more recently scholars like Gabaix (2009) or Acemoglu (2011) have argued that such idiosyncratic shocks to individual firms or sectors might in fact be responsible for most aggregate fluctuations.
In their paper "The Network Origins of Aggregate Fluctuations" Acemoglu et al (2011) argue that "local" microeconomic shocks may lead to aggregate fluctuations due to inter-sectoral input-output linkages.
Acemoglu et al model the aggregate economy as an inter-sectoral network where different sectors interact through input-output linkages. They present a static variant of the model that Long and Posner first presented in their 1983 paper "Real Business Cycles". In this economy households supply labor and choose their input output bundles, maximizing their Cobb-Douglas utility function. There are n numbers of goods, where each is being produced by a sector and can either be consumed or used as an input for production by other sectors. The subsequent inter-sectoral input-output relations form the inter-sectoral network of this economy.
The authors now prove mathematically that given the presence of such input-output linkages, the diversification argument that has been brought forward to dismiss the role of micro shocks in aggregate fluctuations may not hold. If the roles that sectors play as direct or indirect suppliers to others are significantly asymmetric, then "sizable aggregate fluctuations may originate from microeconomic shocks".
These findings correspond to the results of Xavier Gabaix's paper "The Granular Origins of Aggregate Fluctuations" (2009). Gabaix argues that if the distribution of firm size is fat-tailed, then the diversification argument breaks down. A fat-tailed distribution of firm size and a significant asymmetry in the roles of sectors as output suppliers might here be interpreted to be mirror-images of the same phenomenon.
So current research seems to be moving away from focusing on the role of aggregate shocks (note that these are mostly exogenous) to underlining and further examining the importance of shocks to individual firms or sectors. I find this very pleasing as this tendency is in line with the sentiment of this project for the entire discussion on road traffic was exclusively centered around endogenous causes for the occurrence of inefficiency and highlighted the role of "shocks" that happened at the link level.
It will now be interesting to see how, based on the model that Acemoglu et al and Gabaix use, one could apply some of our previous results to the occurrence of hot and cold flushes in business cycles and relate them to the current standing of macroeconomic research.
Compare the inter-sectoral network to the model of road traffic where road traffic is represented as a network of junctions and links. The following interpretation of possibly existing parallels between both models might seem reasonable. A particular route might represent a particular sector of the economy. The cars on this route at any given point in time could represent firms that operate in this sector. Firms that engage in the production of several products in different sectors can be represented by cars that pass through different roads. The input-output linkages between sectors in the inter-sectoral network model could possibly be compared to the junctions that connect different roads and routes. All of the above is of course simplistic, yet I feel that given an awareness for the simplicity of this approach, it might provide a ground on which we can potentially transfer some of our results.
In line with Acemoglu et al, our former considerations yield the observation that systematic congestions, i.e. aggregate fluctuations across the wider network, can be rooted in congestions, i.e. shocks on the micro level. The mechanisms through which these local shocks might spread seem to be quite well understood in both systems. In road traffic the velocity fluctuations can create backward spreading waves of increasing fluctuations which then break down the free flow of traffic. These fluctuations can spread over the junction to the system level and cause aggregate breakdowns in wider areas. In the economy a idiosyncratic shock leads to low output levels in the relevant sectors, which in turn leads to low input levels in first-order connected sectors, which in turn affects second-order connected sectors etc. Acemoglu et al call this a cascade effect, an effect that will become more relevant as shocks hit sectors with more linkages.
Before proceeding, note how all of this already yields important results for our initial research question. It shows how, even if the general trend is positive, a idiosyncratic shock, i.e. a local congestion, can cause a negative aggregate response. It therefore already hints at some explanations for the sudden occurrence of starts and stops in business cycles.
So far we could interpret our results to support the findings in the literature. But how can they add something to the discussion? The literature so far has been able to identify a mechanism through which shocks that hit individual central sectors in the network may give rise to aggregate fluctuations. But it has so far been unable to determine whether or not the network-centrality of a sector is a sufficient or a necessary condition for the occurrence of aggregate fluctuations. Can our analysis add something to that discussion?
Note that by definition the network-centrality of a sector in the inter-sectoral economic model is crucially determined by the number of firms that operate in this sector, the number of firms that use the respective good as an input and by the number of goods that firms in this sector use as production inputs. Transferring this into our road traffic model, the centrality of a route is affected by both the number of firms that pass through it and the number of junctions that it crosses. But remember, complexity research on road traffic has given rise to the conclusion that a certain level of vehicle density is a necessary, yet it is not a sufficient condition for the occurrence of traffic congestion on systematic level. Complexity science hence seems to suggest that a sufficient network centrality alone is not enough to trigger aggregate fluctuations when a sector experiences a shock.
What else did matter? In road traffic, the initial shocks themselves are brought about by drivers' imperfect anticipation of the actions of other drivers. But whether or not they spread to cause breakdowns of thefree traffic flow at the aggregate level did heavily depend upon the incentives and actions that drivers displayed at the junction level. Uncooperative behavior at the junction and/or failures to change the route in order to avoid the congested links were key factors that would allow local inefficiencies to spread to the system level. How can we use this result in order to enrich the existing discussion?
Complexity science seems to suggest that given the fulfillment of certain requirements, shocks to an individual sector can cause aggregate fluctuations. This holds if the sector is sufficiently connected in the inter-sectoral network (in line with the existing research) and if either closely connected sectors cannot or fail to substitute away from the input that the sector in trouble produces (i.e drivers fail to alternate their route at junctions) or firms that operate in closely connected sectors display excessively uncooperative behavior (i.e. drivers fail to cooperate at junctions).
A next step will be to empirically test the results that these results, i.e. to test whether the failure or incapability to substitute away from goods that are produced by sectors that experience shocks and/or uncooperative behavior of firms in closely connected sectors can provide further necessary conditions under which the diversification argument might not hold. In order to do so it will be key to provide real world data that either back or support the above results.
Saturday, January 21, 2012
A wrap up on road traffic and a perspective on ants and birds
The aim of this post is to comprehensively summarize the key factors complexity science seems to identify when looking at road traffic inefficiencies. I will then be discussing how looking at alternative systems of collective motion, such as the behavior of ants and birds, might help us to further enhance our understanding of these inefficiencies. This post will also hint at possible ways in which one might want to apply these findings to the research question.
Having looked at both, choice and action-based approaches to road traffic, the following findings appear to be most relevant.
1) Over time, we might observe a decrease in system efficiency as individual agents optimize their behavior according to their respective key parameters
2) External efforts to reduce these inefficiencies, i.e. through the provision supplementary roads, might actually further increase the inefficiency of the system
3) Not the density of the vehicles on a particular stretch of a road, but the interaction between these vehicles represents the origin of endogenous breakdowns of the free flow of traffic (through backward spreading velocity fluctuations)
4) The spread of a congestion from a local level to the system level crucially depends on the level of cooperation that drivers choose at the junction level.
Looking at these factors, one might already be able to think of ways of how to apply those results to the research question. For now though, I would like to look at a group of other systems that exhibit both complex and traffic behavior as well. Contrasting the efficiency and the inherent incentive structure of both systems will hopefully further enhance our understanding by gaining yet another perspective on the conclusions so far.
Ants and birds are famous for exhibiting sophisticated forms of collective motion. Colonies of the New World army ant Eciton burchelli for example consist of up to a half million members. The ants form traffic systems made up by up to 200,000 virtually blind individuals that transport up to 30,000 items in one run (Franks et al, 1991) and display minimal congestions. Likewise birds, the interaction of ants hence can give rise to self-organized structures that seem to be vastly superior to road traffic in terms of efficiency. These structures display a swarm intelligence that vastly exceeds the intelligence of every individual member and that hence is beneficial to every participant. In fact, scholars were capable of simulating the behavior of ants without having to assume that the ants possess any form of memory at all (e.g. Millonas: Swarms, Phase Transitions, and Collective Intelligence").
For the purposes of this project it will be sufficient to look at the simplest forms of models that aim to simulate the collective behavior of ants and birds and at the assumptions with regards to the behavioral incentive-structures that they make. Craig Reynolds introduced an agent-based model for the aggregate motion of flocks, herds or swarms in his paper "Flocks, Herds and Schools: A Distributed Behavioral Model (1987)" that simulated birds as independent individual actors that navigate according to their local perceptions of the environment and a set of of behavioral patterns. The behaviors that lead to the simulated collective motion are as following:
1) Decision-makers seek to avoid collisions with other agents (Collision avoidance)
2) Decision-makers attempt to match their speed with other nearby agents (Velocity matching)
3) Decision-makers want to stay as close as possible to nearby agents (Flock centering)
Given a certain density of interacting agents, these behavioral patterns are sufficient to bring about realistic forms of swarming behavior and hence the transition from chaotic to ordered behavior. The graphical results of Reynold's simulations can be seen on the following page: http://www.red3d.com/cwr/boids/ . These principles also represent the cornerstones of other, more sophisticated self-propelled particle models that aim to simulate the complex behavior displayed by New World ants or birds.
How can this analysis help us to further enhance our understanding of factors that might contribute to the occurrence of endogenous congestions in road traffic? Comparing the behavioral patterns and conditions that allow for the occurrence of the respective macro-structures, one finds that it seems to be the flock centering behavior that makes the crucial difference.
Both collision avoidance and velocity matching are to an extent inherent to the behavioral structure of drivers on the road and have in fact been identified to cause the fluctuations in velocity that can potentially cause the breakdown of the free traffic flow. Flock centering on the other hand reflects the inherently different incentive-structures on the microscopic level of individual agents between both systems. Whilst an ant or a bird greatly benefits from staying close to other flockmates, a driver on the road when faced with a choice between two routes of equal length will always pick the less crowded one. For ants and birds , a sufficiently high density of interacting agents is necessary for collective motion to occur in the first place, whilst the density of vehicles on the road is a necessary condition for the endogenous occurrence of traffic jam.
Cooperation and mutual interests on the individuals' level hence seem to crucially affect the efficiency of a system. This can be seen to further underline and support the implied conclusion of our previous analysis that incentive-structures might to an extent turn out to be more important than macro factors, such as the number of available roads for the efficiency of road traffic. The introduction of a second class of reference models therefore allows us to further strengthen the results of our analysis.
The next post will make use of the results obtained so far by applying these results to the observation of sudden starts and stops in business cycles. In order to so it will, based on the previous discussion on how road traffic could represent a reference model for aggregate economic, behavior carefully construct analogies between road traffic and the economy that will help to reveal the relevance of this findings for the research question. The goal has to be to comprehensively formulate a hypothesis that can then be tested against the available empirical evidence.
Having looked at both, choice and action-based approaches to road traffic, the following findings appear to be most relevant.
1) Over time, we might observe a decrease in system efficiency as individual agents optimize their behavior according to their respective key parameters
2) External efforts to reduce these inefficiencies, i.e. through the provision supplementary roads, might actually further increase the inefficiency of the system
3) Not the density of the vehicles on a particular stretch of a road, but the interaction between these vehicles represents the origin of endogenous breakdowns of the free flow of traffic (through backward spreading velocity fluctuations)
4) The spread of a congestion from a local level to the system level crucially depends on the level of cooperation that drivers choose at the junction level.
Looking at these factors, one might already be able to think of ways of how to apply those results to the research question. For now though, I would like to look at a group of other systems that exhibit both complex and traffic behavior as well. Contrasting the efficiency and the inherent incentive structure of both systems will hopefully further enhance our understanding by gaining yet another perspective on the conclusions so far.
Ants and birds are famous for exhibiting sophisticated forms of collective motion. Colonies of the New World army ant Eciton burchelli for example consist of up to a half million members. The ants form traffic systems made up by up to 200,000 virtually blind individuals that transport up to 30,000 items in one run (Franks et al, 1991) and display minimal congestions. Likewise birds, the interaction of ants hence can give rise to self-organized structures that seem to be vastly superior to road traffic in terms of efficiency. These structures display a swarm intelligence that vastly exceeds the intelligence of every individual member and that hence is beneficial to every participant. In fact, scholars were capable of simulating the behavior of ants without having to assume that the ants possess any form of memory at all (e.g. Millonas: Swarms, Phase Transitions, and Collective Intelligence").
For the purposes of this project it will be sufficient to look at the simplest forms of models that aim to simulate the collective behavior of ants and birds and at the assumptions with regards to the behavioral incentive-structures that they make. Craig Reynolds introduced an agent-based model for the aggregate motion of flocks, herds or swarms in his paper "Flocks, Herds and Schools: A Distributed Behavioral Model (1987)" that simulated birds as independent individual actors that navigate according to their local perceptions of the environment and a set of of behavioral patterns. The behaviors that lead to the simulated collective motion are as following:
1) Decision-makers seek to avoid collisions with other agents (Collision avoidance)
2) Decision-makers attempt to match their speed with other nearby agents (Velocity matching)
3) Decision-makers want to stay as close as possible to nearby agents (Flock centering)
Given a certain density of interacting agents, these behavioral patterns are sufficient to bring about realistic forms of swarming behavior and hence the transition from chaotic to ordered behavior. The graphical results of Reynold's simulations can be seen on the following page: http://www.red3d.com/cwr/boids/ . These principles also represent the cornerstones of other, more sophisticated self-propelled particle models that aim to simulate the complex behavior displayed by New World ants or birds.
How can this analysis help us to further enhance our understanding of factors that might contribute to the occurrence of endogenous congestions in road traffic? Comparing the behavioral patterns and conditions that allow for the occurrence of the respective macro-structures, one finds that it seems to be the flock centering behavior that makes the crucial difference.
Both collision avoidance and velocity matching are to an extent inherent to the behavioral structure of drivers on the road and have in fact been identified to cause the fluctuations in velocity that can potentially cause the breakdown of the free traffic flow. Flock centering on the other hand reflects the inherently different incentive-structures on the microscopic level of individual agents between both systems. Whilst an ant or a bird greatly benefits from staying close to other flockmates, a driver on the road when faced with a choice between two routes of equal length will always pick the less crowded one. For ants and birds , a sufficiently high density of interacting agents is necessary for collective motion to occur in the first place, whilst the density of vehicles on the road is a necessary condition for the endogenous occurrence of traffic jam.
Cooperation and mutual interests on the individuals' level hence seem to crucially affect the efficiency of a system. This can be seen to further underline and support the implied conclusion of our previous analysis that incentive-structures might to an extent turn out to be more important than macro factors, such as the number of available roads for the efficiency of road traffic. The introduction of a second class of reference models therefore allows us to further strengthen the results of our analysis.
The next post will make use of the results obtained so far by applying these results to the observation of sudden starts and stops in business cycles. In order to so it will, based on the previous discussion on how road traffic could represent a reference model for aggregate economic, behavior carefully construct analogies between road traffic and the economy that will help to reveal the relevance of this findings for the research question. The goal has to be to comprehensively formulate a hypothesis that can then be tested against the available empirical evidence.
Wednesday, January 11, 2012
Further lessons about road traffic
The last post introduced two fundamental approaches to road traffic modeling. It mainly focused on the choice-based approach, meaning that it discussed papers that studied the way in which people choose a particular route and how this affects the performance of the system as a whole. This post is to focus on the action-based approach which is centered around the question how driving behavior affects the efficiency of road traffic.
Sugiyama et al. argue that factors that are related to the density of cars on the road, such as route-choices or bottlenecks, are "only a trigger and not the essential origin of a traffic jam" (Sugiyama et al: "Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam", 2002). Clearly, this fits well into our interpretation of action-based approaches to road traffic.
Sugiyama et al argue that the development of traffic flow, given that the average vehicle density surpasses a certain critical point, is crucially dependent on the interaction of vehicles. They back up this claim both theoretically and experimentally. In their paper, road traffic is modeled "as a non-equilibrium physical system consisting of moving particles with asymmetric interaction of exclusive effect".
Their model is based on the experience that there are always fluctuations in the movement of vehicles as vehicles adjust their speed when they see other drivers in order to avoid collisions . If the vehicle density is sufficiently small, these fluctuations can disappear and the free flow of traffic is ensured. If on the other hand the vehicle density is beyond a certain critical value, the fluctuations can potentially grow steadily and eventually cause a breakdown of the free flow that manifests itself in the formation of a jam. Hence once a critical vehicle density is surpassed, the system mathematically exhibits two solutions. A free flow solution where all vehicles move at roughly the same velocity and a jam flow solution where vehicles are stuck in a cluster. These solutions are essentially not stable over time and the system will alternate between both in irregular patterns.
The authors conducted an experiment on a circular road in order to verify these theoretical results. As predicted, traffic jam did occur once a certain density level was reached and the velocities of the cars were controlled by drivers (as opposed to automatic velocity control). The following video that captures the experiment illustrates, how traffic jam emerges as a result of steadily growing fluctuations in velocity. These in turn are caused by individual agents' reactions to other agents.
Building on this result Manley and Cheng develop a model that describes the development of congestion as an emergent property of road traffic that is rooted in the microcosm of the behavior of individual drivers and try to identify circumstances under which a local congestion might lead to a network congestion. (Manley, Cheng: "Understanding Road Congestion as an Emergent Property of Traffic Networks", 2008).
In order to do so, they distinguish three different levels, namely the link, junction and network level. The link level refers to roads that are relatively unaffected by junctions or intersections (like the circular road in Yugisama's experiment). Here, congestion may start through the mechanism that Yugisama et al have described, i.e. increasing fluctuations that cause delays which in turn spread backwards. But as soon as congestion reaches Junction level, this relative linearity fades as individuals make choices that may or may not contribute to the spread of the congestion to network level. Such choices include whether or not to cooperate or to change the route at the junction. These choices will determine whether or not a congestion at link (i.e. local) level will spread to affect a wider area of road network, i.e. whether or not a congestion will spread over many junctions and links to affect the macro network.
Using the Blackwall Tunnel in London as a case study, the authors find that it is especially illegal or uncooperative behavior that contributed to the spread of a congestion from the local to the network level. In other words it is especially the selfishness of individual drivers that could lead to temporary or even permanent delay.
Summarising what we have learned from these two papers, one can say that action-based approaches to road traffic provide us with another perspective on the emergence of inefficiencies in traffic flows. We went from developing an idea of the emergence of traffic jam on the individual level to trying to understand, how local congestions spreads to become a network congestion. It gave us an idea of how we could see traffic jam to be more dependent on the interaction and choices of drivers whilst on the road than on the actual vehicle density. Both discussed papers might prove themselves to be highly relevant for the purposes of this project as they provide a framework of discussing why some local congestions, caused by asymmetric actions and the resulting fluctuations, do actually lead to a congestion on network level, whilst others do not. Relating this to business cycles, this might be helpful in explaining how the sudden starts and stops of economic activity come about and why some of them do actually reverse the business cycle, whilst others do not.
The next post will bring together the results of this and the previous post. It appears to be essential to comprehensively identify factors that contribute to and affect the performance of the system road traffic in order to proceed with our analysis. The next post will also study, how the behavior of ants and birds does essentially differ from the behavior of road drivers and how this contributes to the efficiency of the respective system.
Sugiyama et al. argue that factors that are related to the density of cars on the road, such as route-choices or bottlenecks, are "only a trigger and not the essential origin of a traffic jam" (Sugiyama et al: "Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam", 2002). Clearly, this fits well into our interpretation of action-based approaches to road traffic.
Sugiyama et al argue that the development of traffic flow, given that the average vehicle density surpasses a certain critical point, is crucially dependent on the interaction of vehicles. They back up this claim both theoretically and experimentally. In their paper, road traffic is modeled "as a non-equilibrium physical system consisting of moving particles with asymmetric interaction of exclusive effect".
Their model is based on the experience that there are always fluctuations in the movement of vehicles as vehicles adjust their speed when they see other drivers in order to avoid collisions . If the vehicle density is sufficiently small, these fluctuations can disappear and the free flow of traffic is ensured. If on the other hand the vehicle density is beyond a certain critical value, the fluctuations can potentially grow steadily and eventually cause a breakdown of the free flow that manifests itself in the formation of a jam. Hence once a critical vehicle density is surpassed, the system mathematically exhibits two solutions. A free flow solution where all vehicles move at roughly the same velocity and a jam flow solution where vehicles are stuck in a cluster. These solutions are essentially not stable over time and the system will alternate between both in irregular patterns.
The authors conducted an experiment on a circular road in order to verify these theoretical results. As predicted, traffic jam did occur once a certain density level was reached and the velocities of the cars were controlled by drivers (as opposed to automatic velocity control). The following video that captures the experiment illustrates, how traffic jam emerges as a result of steadily growing fluctuations in velocity. These in turn are caused by individual agents' reactions to other agents.
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In order to do so, they distinguish three different levels, namely the link, junction and network level. The link level refers to roads that are relatively unaffected by junctions or intersections (like the circular road in Yugisama's experiment). Here, congestion may start through the mechanism that Yugisama et al have described, i.e. increasing fluctuations that cause delays which in turn spread backwards. But as soon as congestion reaches Junction level, this relative linearity fades as individuals make choices that may or may not contribute to the spread of the congestion to network level. Such choices include whether or not to cooperate or to change the route at the junction. These choices will determine whether or not a congestion at link (i.e. local) level will spread to affect a wider area of road network, i.e. whether or not a congestion will spread over many junctions and links to affect the macro network.
Using the Blackwall Tunnel in London as a case study, the authors find that it is especially illegal or uncooperative behavior that contributed to the spread of a congestion from the local to the network level. In other words it is especially the selfishness of individual drivers that could lead to temporary or even permanent delay.
Summarising what we have learned from these two papers, one can say that action-based approaches to road traffic provide us with another perspective on the emergence of inefficiencies in traffic flows. We went from developing an idea of the emergence of traffic jam on the individual level to trying to understand, how local congestions spreads to become a network congestion. It gave us an idea of how we could see traffic jam to be more dependent on the interaction and choices of drivers whilst on the road than on the actual vehicle density. Both discussed papers might prove themselves to be highly relevant for the purposes of this project as they provide a framework of discussing why some local congestions, caused by asymmetric actions and the resulting fluctuations, do actually lead to a congestion on network level, whilst others do not. Relating this to business cycles, this might be helpful in explaining how the sudden starts and stops of economic activity come about and why some of them do actually reverse the business cycle, whilst others do not.
The next post will bring together the results of this and the previous post. It appears to be essential to comprehensively identify factors that contribute to and affect the performance of the system road traffic in order to proceed with our analysis. The next post will also study, how the behavior of ants and birds does essentially differ from the behavior of road drivers and how this contributes to the efficiency of the respective system.
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