Simply Complexity (21 page)

The complex patterns which arise in traffic systems result from the interactions between the cars – and these interactions between the cars arise from the decisions and actions of their drivers. Drivers tend to make decisions based on the feedback of information that they are receiving, either through their own personal memories of seemingly similar past experiences or from information about what is going on around them. As a result of this feedback, emergent phenomena such as traffic jams can often appear out of thin air without any obvious cause – just like many financial market crashes also have no apparent cause. This is because traffic systems are constantly shifting between ordered and disordered behavior as time evolves, just like all Complex Systems.

We know that traffic jams are painful. But suppose you have already committed yourself to being on a particular road – there isn’t much that you can do, in terms of decision-making, to avoid getting stuck in that jam. Instead, the really important decision-making process actually happened before you took that road: in particular, it was that initial “which route?” question. So let’s start by looking at the common “which route?” dilemmas that we frequently agonize over:

All roads can be thought of as having a certain “comfort limit”
L
, in the same way that a potentially overcrowded bar or financial market will have an intrinsic comfort limit as discussed in
chapters 4
and
6
. If the number of cars is larger than this comfort limit,
the road becomes uncomfortable to be on. There are typically many other people trying to make the same decision about whether to take the same road or not, and we won’t know what the correct decision actually is until it is too late. In other words, we all have to make our decisions and hence take the road or not, and then assess in hindsight whether it was the correct decision based on how many other people decided to do the same thing. So clearly this is the same dilemma as the potentially overcrowded bar or financial market. Therefore everything that we have said so far about these problems – for example, about the emergence of
crowds
and
anticrowds
– will carry over to this road-attendance problem. In
chapters 4
and
6
, choosing between options 1 and 0 represented choosing to attend a particular bar or not, or choosing whether to buy a particular stock or not. Here it represents choosing to take a particular road or not.

This dilemma arises, for example, when there are two routes – say route 1 and route 0 – between work and home. Every night we have to decide whether to take route 1 or route 0. Let’s assume these two routes 1 and 0 are nominally identical. In other words, it would take the same time to get home using either route, in the absence of all other cars. Then clearly we each want to choose the route which is less crowded – in other words, less cars. So if there are say
N
= 101 of us trying to get home and hence playing the same game, then we would feel we had won if we happened to choose the route with 50 or less cars on it. That would imply that 51 cars had taken the other route, and hence we would have managed to choose the less crowded route. In other words, the worst case that we could possibly experience and yet still be winners, would be to have 50 cars on our road including us, and 51 on the other road. Of course there are much better scenarios for us than this – for example, having only 10 cars on our road and 91 on the other is clearly good. But as long as there is a total of 50 or less cars on our road, including us, then there will necessarily be 51 or more on the other one. Hence we will win. Traffic dilemmas 1 and 2 can be made equivalent, by setting the comfort limit
L
of each
route to be just below a half the total number of competing cars. The “just below” bit is important since we want the two routes to be the same, yet we want to eliminate the possibility that both are under-crowded. Suppose that in our example with 101 cars, we made the comfort limit 51 on each route – then in the case that 50 choose one route and 51 the other, neither route would be over-crowded. Hence everyone wins and we won’t get very complex overall behavior. Therefore we should choose a comfort limit of 50.

This second traffic dilemma again represents choosing between two options. In the first traffic dilemma, the choice is to take a particular road or not, and in the language of the bar in
chapter 4
it is to attend the bar (option 1) or not (i.e. go home, which is option 0). Within the context of financial markets, there are many similar situations which are equivalent to a choice between two options: to enter a particular market (option 1) or not (option 0), to buy a particular stock (option 1) or not (option 0) – or supposing that you have already decided to be active in a given stock, to buy it (option 1) or sell it (option 0). Going further, you can see that the entire daily activity of any human being can be strung together into a chain of such binary decisions, giving a “tree” of possible outcomes.

Imagine for example, that you are a trader in a financial market and that you have just driven into work. In the period of time since getting out of bed, you have already taken a bunch of decisions in connection with traffic dilemmas – and yet you are now faced with many more:

Should you enter a particular market A or not? Let’s suppose you decide “yes” (option 1).

Now, given that you have decided to enter market A, and hence have headed down a particular branch of your daily decision tree, should you be active in a particular stock B within that market or not? Let’s suppose you decide “be active” (option 1).

Now, given that you have decided to enter market A, and have decided to be active in a particular stock B, should you buy or sell that stock? Let’s suppose you decide “buy” (option 1).

Now, given that you have decided to enter market A, and have decided to be active in a particular stock B, and have decided to
buy that stock, should you buy large or small amounts? Let’s suppose you decide “large amounts” (option 1).

Now, given that you have decided to enter market A, and have decided to be active in a particular stock B, and have decided to buy that stock, and have decided to buy a large amount, should you then reverse this trade before going home? Let’s suppose you decide “yes” (option 1).

And so it carries on throughout the day until eventually you manage to escape from work and head home – only to face a similar set of traffic decisions on the way home. As you can see, these successive decisions may get compounded as the human being in question struggles along his or her particular chain of daily dilemmas. But while the number of different dilemmas that a given person will face in a day will depend on their individual circumstances, the crucial point is that each of these dilemmas is just a copy of the same old binary decision problem – choosing option 1 or option 0 – and hence the same types of emergent phenomena can be expected at each stage.

Many towns and cities have a road layout which resembles a hub-and-spoke shape. People are therefore often faced with the dilemma of whether to choose a route through the center of the city and risk congestion problems, or to go around the outside and hence risk a longer journey. This dilemma appears to be the same as the two above, since the two possibilities are to go to a potentially crowded place (which in this case means to choose a route through the city center) or not (which in this case means to go around the outside instead). The correct decision will only become apparent after everyone else has made their mind up. However, it is actually a bit more subtle than the previous two traffic dilemmas. In particular, the effective comfort limit
L
of the city-center option will typically depend on how many connections there are between the outside and the center, and how much congestion therefore develops in the center as a result of traffic taking all of these possible spoke roads. It will also depend on whether there is
any monetary charge – such as the congestion charge in London – which will add to the overall cost in terms of time and money.

Thinking back to our discussion in
chapter 5
about networks, we can also see an analogy between the hub-and-spoke road network and the hub networks which we said arise in many other real-world settings – for example, social and communications networks. For these reasons, we will devote the rest of this chapter to trying to understand the Complexity that such hub-and-spoke shapes introduce. We will do this in two ways. First we will assume that the flow of objects on the network is behaving relatively simply – in particular, we assume that there is no detailed decision-making being made and hence the whole problem comes down to assessing the effects of congestion in the center. Then in the last part of the chapter, we will combine the decision-making of the bar problem from
chapter 4
with this hub-and-spoke shape, to see what you might expect to find lurking around a city center near you. We will also open up the problem to a completely different application area – the social and career ladders that we face, and the dilemma of whether to move around within our existing level or to move up.

We hinted above that going through the center of such a hub-and-spoke network might have several forms of cost. First, there is a cost in terms of the time taken to get through the center. In particular, the congestion in the center itself is determined by the number of cars which pass through the center at any one time. This in turn is determined by a combination of the number of roads (i.e. spokes) which connect the outside to the center, and the number of drivers who decide to take each of these roads. Indeed, one can imagine that drivers who are driving round a ring-road are faced with a bar-attendance-like traffic dilemma as they reach each successive intersection with a spoke-road. For this reason, we will first focus just on the effect of the number of spoke roads. Then we will return later in the chapter to consider the additional complications caused by drivers’ decisions. The second cost is a monetary one.

Going through the center may – if we are unlucky – add extra time to our journey
and
cost us real money. Going around the outside may not cost money but, since it is longer in terms of distance, it may end up taking longer if the center is not very congested. The correct decision as to whether to go through the center or around, will therefore depend on how we each balance the importance of time and money. Time is money – but the effective exchange-rate between the two will not only vary between different people, but it may also vary over time for a given person. Interestingly, biological networks such as a fungus (see
chapter 5
) are also faced with such a dilemma when deciding how to transport food from one side of the organism to another. Man-made road designs are obviously planned in advance – but organisms such as fungi (which are incidentally the largest organisms on Earth) have somehow managed to evolve a balance between centralized supply routes and decentralized supply routes all by themselves. On the forest floor where the fungus sits, there are nutrients such as carbon which need to be transported from one side of the organism to another. If these packets of food – like cars on a road – were all passed through one central point in the fungus at the same time, the congestion could be considerable. Yet the organism survives, and even thrives, without a traffic light in sight.

How does a fungus do it? Nobody knows so far. But this has opened up a fascinating research area which is currently being pursued by Mark Fricker, Tim Jarrett and Doug Ashton to determine how the corresponding transport costs in a biological system dictate the type of network structures that are observed. Not only is Mark Fricker’s group well on its way to solving this mystery, they are also gaining valuable insight into possible smart designs for man-made supply networks. Who knows: maybe road planners of the future will simply turn to their friendly neighborhood fungus for new design ideas?

There are many other examples of real-world Complex Systems – both man-made and naturally occurring – where packets of “stuff” (e.g. goods, information, documents, money, datapackets) need to be transported throughout a network structure, and hence the dilemma of choosing centralized versus decentralized routing
arises. And just as with the ring road problem, the shortest route between two points may not actually be the quickest and hence best. In particular, if there happens to be a long waiting-time at some particularly busy central hub, then it might have been quicker to send the packet all the way “around the houses” in order to get from A to B. Specific examples include:

Transport systems
. In addition to cars on roads and datapackets on communications networks, air travellers and airline schedulers have to decide whether to arrange for a stopover at a large international airport or a regional one.

Supply-chains for goods
. A supermarket has to decide whether to have one potentially congested but large central warehouse, or many smaller regional ones.

Information in human organizations
. Members of crime and terrorist networks must presumably decide how much information to pass through some central person, which could become a slow or risky option if the person gets overloaded with information such as in a Godfather scenario – or whether instead to have all information delocalized through crime cells.

Administration and policy-making
. Multinational companies and government institutions have to decide whether to pass all paperwork through some central head-office for rubber-stamping, or have these pieces of paper wander around between regional offices.

Human biology and health
. The growth of a cancer tumor depends on a process called angiogenesis which leads to the creation of nutrient (i.e. oxygen) supply pathways (i.e. blood vessels, like roads) to enable the tumor to continue growing. It is an open question as to the extent to which the tumor balances centralized versus decentralized blood vessel networks. This information could prove crucial in understanding how to restrict the nutrient supply and hence reduce the growth rate of the tumor. Another health-related example of such centralized-decentralized competition, concerns AVMs (Arterio-Venous Malformations) which grow in the brain of many people. These are clumps of abnormal blood vessels which, if the patient is unlucky, may start acting like a new city center through which blood may prefer to flow, instead of taking its normal route through the brain’s elaborate collection
of very small capillaries. Hence AVMs effectively divert all the traffic through them instead of letting it pass through the delocalized network of capillaries. Consequently, much of the brain becomes starved of nutrients. Recent work by the research group of Paul Summers and Yiannis Ventikos at the John Radcliffe Hospital, has led to an improved understanding of when such AVMs might start switching between decentralized (i.e. healthy) and centralized (i.e. unhealthy) blood flow.