[FRIAM] Peloton analog of resource sharing system. Was: can you have 4 operating systems on one buss?

[Hugh Trenchard]

(Phil henshaw) "What kind of information might indicate the approach of 
common resource limits? How would that be different from evidence that other 
users are breaking their agreements? As independent users of natural 
resources tend to have less information about, or interest in, each other's 
particular needs than, say, cyclists in a peloton, how would they begin to 
renegotiate their common habits when circumstances require it?"

Here is a short essay that looks at Phil's questions of resource consumption 
from the perspective of a peloton analog.  It doesn't seek to answer the 
questions, but rather proposes a model in which to analyze them.  It may be 
rather simplistic against the backdrop of sophisticated economic theory, but 
as a very real system, I suggest the dynamics of pelotons may provide 
insight into them.  The scope of my essay may also be overly broad, and in 
that respect, incomplete, but my hope is that there are a few kernels that 
may assist Phil's analysis, or are at the very least, interesting.

Information exchange, resource consumption and sharing in bicycle pelotons: 
a model for analyzing competitive systems

Hugh Trenchard

Bicycle racing is by definition competitive, and involves strategies for the 
cooperative distribution and exploitation of individual and collective 
resources. Individual resources exist in the form of energy available for 
consumption within a rider's body, either in the form of glucose stored in 
rider's livers and muscles, or body fats, and the physiological mechanisms 
which allow riders to expend that energy. Rate of individual resource 
consumption may be reduced by drafting, which occurs when riders are 
positioned in zones of lower air pressure, either directly behind others 
riders', or at angles to the wind direction. Riders in drafting positions 
reduce energy expenditure by as much as 30 - 40% over a rider in front at 
40km/hr, depending on positioning within the peloton (Hagberg and McCole, 
1990).

Reduction of energy expenditure in drafting positions is also a collective, 
or shared resource. It is a collective resource when riders in competitive 
situations either cooperate or exploit this resource to maximally reduce 
their own individual resource expenditure or the expenditure of allies. 
Allies may be team-mates, but are also frequently competitors from different 
teams who cooperate when a peloton has split into groups, thereby 
temporarily becoming allies to achieve specific objectives, before again 
becoming competitors. The relative and continuous balance between 
cooperation and exploitation occurs most notably when a peloton has split 
into groups of two or more, and the objective of group(s) ahead is to remain 
ahead of following groups, while the reverse objective exists for groups 
behind, which is to reintegrate groups ahead. In situations like these, 
free-riders, quite literally, are prevalent, repleat with a number of modes 
of punishment. A more detailed account of that, however, is beyond the scope 
of this discussion.

In the course of their resource consumption, the information cyclists 
receive or generate is largely visual. There is also vocal information, and, 
at the highest levels there is nearly always communication exchanged between 
riders within the peloton and sources outside the peloton (coaches or 
"director sportifs"), via radio contact - an advancement in racing tactics 
that has developed and been allowed in races for roughly 20 years now. 
Generally riders have limited global information due to obstructed viewing 
(i.e. blocked by riders surrounding them) and primarily receive only local 
information about the riders immediately surrounding them. One reason 
(albeit a secondary reason) for advancing or falling back within a peloton 
is to gather information about the positions of competitors. Some of this 
information may be relayed verbally through information links within the 
peloton (other cyclists), or riders acquire the information by visual 
observation, or through radio contact.

The information riders seek is primarily threefold:

1  competitor positioning

2  apparent rider resource consumption

3  course constraints



1. Competitor positioning

This is determined by


a.  local observation of riders in immediate 360 degree visual field, where 
course topography is flat

b.  partial or complete global observations of peloton where elevation and 
course configuration allow visual information to be obtained from higher or 
lateral vantage points (e.g. if a cyclist is near the rear of a descending 
peloton on an open road, the rider has a clear view of cyclists' positions 
ahead);

c.  positional information may also be gleaned by implication, namely if a 
cyclist is at the front, he or she knows all her competitors are behind, and 
will see them if they try to pass. Similarly, but more anxiety causing, if a 
cyclist is at the back, he will know all competitors are ahead of him.

2. Resource consumption

Information about resource consumption is evidenced by competitors' apparent 
discomfort, such as facial contortions, body positions, or by other 
indicators such as failures to take pulls at the front (during cooperative 
situations), struggling to hold minimal distances between wheels, 
deteriorating pedalling form, poor gear ratio selection, or observations 
about fluid intake or food consumption during the race. For example, if a 
rider has lost his water bottle at a critical point, others will have 
exploitative information about his sugar levels.

3. Course constraints

This refers to the physical course and its changes: is there a hill 
approaching, is there an obstacle approaching, is there a bend in the 
course; how strong is the wind, and from what direction is it coming? In 
road racing, courses may be out-and-back or point-to-point, and change 
continuously and, aside from general course information obtained before 
commencing the race, course predictability is relatively low; in road 
circuit races, which may consist of several loops of a course of, say, 1 km 
to 15km or more, the course repeats regularly and so there is a greater 
degree of course predictability, in addition to information obtained before 
hand; a track course is oval, is either 250m or 333m long and is banked, and 
thus is highly regular and allows the greatest degree of predictability and 
available global information.

All of these factors provide clues as to when individual and shared resource 
limits are approaching. These limits arise primarily in the following 
situations:


1.  Shared resources are lost, such as during sufficiently steep hill 
climbs, when speeds fall to a point when drafting advantage is negligible 
(<16km/h (Swain, 1990)) and differentials between cyclists'respective power 
output capacities overwhelm the equalizing effects of any drafting 
advantage;

2.  Shared resources are not-negotiated, such as during a final sprint for 
the finish line, or other situations when speeds are beyond a certain 
threshold between sets of rider causing peloton disintegration**

3.  Shared resources are too dangerous, such as on high-speed descents, 
where collisions with others, obstacles or proceding on trajectories outside 
physical course parameters (e.g. plummetting over a cliff on the outside of 
a hairpin turn!) are avoided by maintaining distances outside of drafting 
range).

Applying the peloton model

A peloton may thus be viewed as a basic resource sharing system which may 
provide clues as to how resources are shared and consumed in other systems, 
especially competitive ones - which arguably most such systems involving 
resource consumption are. I suggest that, in principle, when we investigate 
the question of how to re-negotiate resource sharing, we can first seek to 
understand the nature of these categories of information: competitor 
positioning, apparent resource consumption, and course constraints. These 
factors by themselves are nothing new, but applying a peloton model to other 
systems, at least in any rigourous fashion, is new.

When information about these factors is not available globally, as is most 
often the case, we can examine features exhibited by other systems of 
resource sharing that may be analogous to what occurs in pelotons. For 
example, energy in a peloton is reduced, essentially, by following the paths 
of other riders. Any natural system in which path following serves to reduce 
energy expenditure is analogous to a peloton. As a simple example, when a 
forager tramples a path through snow to a food source, that forager expends 
more energy than all that follow in the established pathway. Forager 
dynamics may be examined against the model of peloton dynamics and its 
pattern thresholds.

In pelotons, thresholds exist where observable collective emergent 
behaviours are exhibited, described by the following phases:

Phase 1 Transitional

As cyclists set off at the beginning of a race, there is a period during 
which the speeds are sufficiently low for cyclists to have no physiological 
necessity to draft one another, as they are all well below individual pain 
thresholds or maximal power output capacity. The phase is characterized by 
roughly random internal peloton movements, or low-pattern formation within 
the peloton.

Phase II Rotational

As speeds increase, a transition occurs whereby resource sharing becomes 
necessary as cyclists approach (but remain below) pain and maximal output 
thresholds, and when the collective drafting resource is exploited. In this 
phase, a balancing occurs between energy expenditure and optimal position 
within the peloton. Because it is a competitive situation, it is better to 
be positioned as close to the front as possible. As this is a continuous 
imperative, rotational movements occur within the peloton, when riders move 
up and down the peloton, or are caught in "eddies" whereby they advance for 
relatively short distances within the peloton, before being shifted backward 
again, and then attempt to move forward again. These movements occur while 
riders attempt to use as little energy as possible to advance. So, where 
there are riders who shift to the outside of the pack (facing the wind by 
doing so), other riders will follow in their draft.
The result is a rotational pattern whereby riders advance up the sides for 
relatively long stretches, while riders drop back within the peloton, and 
while within
the peloton there are smaller-scale rotations, or eddies. The rotational 
patterns which emerge are analogous to the roiling effects of boiling 
liquid, as riders "heat up" by greater energy expenditure in moving forward, 
and cool down by reduced energy expenditure in moving backward through the 
peloton. Incidentally, this pattern is also similar to rotational patterns 
observed in emperor penguin huddles (Ancel, et al., 1997; Stead, 2003).


Phase III Stretching

A third phase transition occurs when the pace shifts up beyond another 
threshold, whereby the speeds are too high for there to be continuous 
rotational movement within the peloton, and the peloton stretches into a 
single line. This phase, while easily observable, is a precurser to a final 
transition where the peloton begins to splinter: individual riders fall off 
the back, or separations occur in the line of riders which following riders 
cannot bridge, resulting in regions of peloton instability and loss of 
cohesion.


Phase IV Disintegration

In this last phase riders fall outside of drafting range, and cooperation 
(or coupling between cyclists) disintegrates as cyclists become either in 
direct competition with the each other. This phase is analogous to the phase 
change between liquid and gas, as cyclists move outside of drafting range, 
thereby de-coupling. In bicycle racing this phase is usually temporary, 
however, as speeds drop quickly, and, through a series of agglomerations, 
the entire peloton either reintegrates or sub-groups form which cooperate 
internally but which are also in direct conflict with each other. In the 
case of sub-groups in conflict, it is the objective of chasing groups to 
reintegrate groups ahead, while it is the objective of groups ahead to stay 
ahead of chasing groups.

Conclusion

Although a peloton is a resource sharing system consisting of human agents 
with competitive human objectives, it is also an energetically dynamic 
system that exhibits self-organized thresholds and emergent patterns.  It is 
reasonable to speculate that when we look at other natural systems in which 
resources are shared and exploited, there are analogous patterns which 
emerge at certain energy consumption thresholds. The physical manifestations 
of such thresholds and emergent patterns may not be easy to identify, but 
here we have a microcosmic model of a competitive, self-organizing system 
which may provide some clues.

____________________________

References


Hagberg, J., McCole, S. The Effect of Drafting and Aerodynamic Equipment on 
Energy Expenditure During Cycling, 1990, Cycling Science, 2, p. 20

Swain, D. Cycling Uphill and Downhill. Sportscience 2(4), 
sportsci.org/jour/9804/dps.html, 1998 (2682 words)

**which threshold I have previously argued on the basis of a coupling model, 
having called it the peloton convergence ratio (PCR). PCR =(Wa-Wb/Wa)/D 
where Wa is the maximum power output (watts) of cyclist A at any given 
moment; Wb is the maximum power output of cyclist B at that moment (assuming 
Wa>Wb), and D is the percent energy savings due to drafting at the velocity 
travelled: Trenchard, H., Mayer-Kress, G. Self-Organized Oscillator Coupling 
and Synchronization in Bicycle Pelotons During Mass-start bicycle racing. 
Book of Abstracts, International Conference on Control and Synchronization 
of Dynamical Systems, Oct 4-7, 2005, Leon, Gto, Mexico. Ratios of =<1 and 
cyclists remain coupled; >1 and cyclists de-couple, when points of 
instability in pelotons occur and peloton disintegration begins.

Ancel, A., Visser, H., Handrick, Y., Masman, D., Le Maho, Y. Energy Saving 
in huddling penguins. Nature, Vol. 385. 23 Jan 1997; Stead, G. An Artificial 
Life Simulation to Investigate the Huddling Behaviour of Emperor Penguins. 
Submitted in partial fulfillment for the degree of MSc in software systems 
technology.