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ComplexModels.com
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ComplexModels.com is Joe Weinman's simulation web site intended for a small number of models addressing
structure, dynamics, and financial analysis of utility and cloud computing, random graphs, power law preferential attachment graphs,
and other simple models that may illustrate complex, emergent characteristics or behavior. Joe Weinman works for AT&T. The views expressed herein are his own and do not necessarily reflect the views of AT&T.
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Value of Utility Resources in the Cloud
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model illustrates the relationship between various demand curves,
capacity strategies addressing those types of demand singly or in combination,
and the economics of tradeoffs. Is it better to use solely static capacity engineered to peak demand?
Or to use less static capacity and accept penalties associated with inability to meet peak requirements (e.g., loss of
revenue associated with unserved customers)? Or use purely utility resources to meet all demand? Or to use a hybrid approach?
The answer is: it depends, and this model shows the relationships between the different factors that would lead to an optimal selection.
Go directly to the simulation model or first review how it works.
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Value of Resource Pooling and Load Sharing Across a Grid
| This model illustrates the benefits of pooling resources, which may be geographically dispersed.
Aligning each demand source individually with a partitioned set of resources means that each set of resources
must be engineered to meet the peak demand associated with that resource. Pooling resources and meeting demand via
any available resource has the benefit that the capacity required is not the sum of the peak demand, but the peak of the sum of the demands,
which is provably no larger, and is typically smaller. Consequently, pooling resources and distributing load across them is usually a good idea (subject to ancillary costs
not addressed in this model. A special case of this is geographic dispersion across time zones, where some demand types, e.g., 9 to 5 weekday work, can
lead to dramatic savings through a "follow the sun" approach.
Go directly to the simulation model or first review how it works.
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Value of Dispersion in Latency Reduction
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This model illustrates the benefits of dispersion for latency
reduction, as well as the diminishing returns of additional node builds,
leading to a "sweet spot" number of nodes. This model is relevant in scenarios as diverse as locating coffee shops, fast food restaurants, distributed
interactive computing environments, and content delivery architectures. Dispersion can have additional benefits, e.g., enhanced business continuity, as well as costs, e.g., operations and real estate, but these are not modeled here.
Go directly to the simulation model or first review how it works.
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Value of Aggregation in Variability Smoothing and Peak Reduction
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This model illustrates the two main benefits of aggregating demand:
reduction in peak capacity requirements as well as increase in utilization. The increase in utilization comes about in two ways.
One is that the same demand is served by a smaller-sized pro forma capacity, but the second is that aggregation of random variables preserves
absolute variance, but reduces relative variance. The so-called "coefficient of variation" is a measure of variability relative to the mean, and this is
reduced as more and more random variables are summed.
In a cloud or utility environment, this is one of the drivers of service provider economics.
Go directly to the simulation model or first review how it works.
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Central Limit Theorem and Combinatorics
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This model also illustrates the benefits of aggregating demand:
reduction in peak capacity requirements as well as increase in utilization. Strictly speaking, the peak does not change across all possible combinations, but the mass near the peak does, therefore reducing the cost of unserved demand. The
distribution of the sum increasingly is normal, in accordance with the Central Limit Theorem.
This model shows the effect by determining the distribution of sums of dice that are randomly rolled, and seeing how summing more and more dice results in a tighter (reduced coefficient of variation) distribution.
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Network Evolution via Preferential Attachment
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Mathematical modeling and empirical analysis of Internet connectivity by Professor and author Albert-Laszlo Barabasi has demonstrated
that network evolution by "preferential attachment" leads to so-called power-law, aristocratic, or scale-free node degree distributions. In other words, the "rich" nodes get "richer" as new entrants
to the network preferentially decide to attach to them. This simulation shows the difference between preferential attachment and random attachment, up to just over 1000 nodes, and
enables viewing of the resulting network from both a node degree distribution perspective as well as an actual graph.
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Yard-Sale Simulation: The Rich Get Richer
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In "Group Theory in the Bedroom", Brian Hayes reviews so-called "Yard-Sale Simulations," or asset exchange models, where pairwise traders operate in a market
on a zero-sum basis to randomly win or lose trades. For very small "bets" and short time periods, an initially equal distribution of wealth will evolve to a normal distribution, as wins and losses
tend to cancel each other out. However, for larger bets and/or longer periods of time, the market evolves to concentrate wealth increasingly, eventually resulting in a "winner-take-all" results. This is because once
a trader goes broke, no matter how unlikely that is, they cannot reenter the market. Interestingly, even when wealth is initially equal across all traders, it can rapidly evolve to a power-law or exponential distribution.
Go directly to the simulation model or first review how it works.
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Investor Risk
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This is a simplified version of the Yard-Sale simulation. Investors either win or lose on each trial, with the amount of the gain or loss dependent on the investment rules. Due to Brownian effects, eventually investors can go broke, at which point they exit the
system. This results in increasing concentration of wealth. Different rules lead to different distributions: an equal distribution of wealth evolves to a normal distribution shifts to what appears to be a power-law or exponential distribution.
Go directly to the simulation model or first review how it works.
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Brownian Motion and Drunkard's Walks
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This illustrates the random processes at work behind such phenomena as Brownian motion. Ten particles begin the simulation in the same location, but then move, each trial, based on a rule. Some variations are one-dimensional, others are two-dimensional.
The one-dimensional rule is similar to a simplified version of investor risk model, which is a simplified version of the asset exchange model (yard-sale simulation). The only difference is that any particle (i.e., investor), can go deeply into debt, so remains in the simulation. Consequently,
rags to riches is not unlikely.
Go directly to the simulation model or first review how it works.
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JoeWeinman.com has a variety of resources,
including a paper entitled "The Evolution of Networked Computing Utilities" that addresses some of the insights gained running earlier versions of the utility and grid simulations.
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