Large Complex Systems

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Large Complex Systems

• Yi Pan
• Jun Suzuki
• Jun Lu
• Keita Fujii
• Weilin Zeng
• Yan Huang

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Large Complex Systems

• Definition of a complex system
• A large complex system should
• Be large in scale (thousands of entities)
• Have relationship among entities
• System transition between equilibrium points
• Control and order come from emergencies rather
  than predetermined
• Internet as a complex system
• Large scale entities
• Thousands of routers, millions of users
• Relationship among entities forms a network
• Entities are connected through media
• The behavior of the media is regulated by
  protocols
• System equilibrium point changes over time
  (network dynamics)
• Control protocols are designed for HOT purpose
• Highly optimized tolerance approach is widely
  accepted in protocol design
• Unexpected events are inevitable and will force
  the network becomes an ordered structure out of
  the chaos

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Large Complex Systems

• Observation of Internet as a complex system
• Hierarchical complex system
• Layered protocol design makes the Internet as a
  hierarchical complex system
• Transport layer protocols see the transmission
  rate as the utility function and be priced by
  network layer control protocols (routing,
  queuing, packet dropping in routers)
• Network layer protocols take the acquisition of
  low latency paths as the utility function and be
  priced by link layer protocols which regulate the
  behavior of links
• Domain-based administration makes the Internet as
  a hierarchical complex system
• User utility functions compete within a domain
  which is a market
• The inter-domain traffic is aggregated and an
  aggregated utility functions for different
  domains compete with each other makes an economy

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Large Complex Systems

• Observation of Internet as a complex system
• Heterogeneous complex system
• Large number of different protocols run in the
  Internet
• For the protocols at the same layer, different
  protocols force different behaviors of the
  control entities
• It invalidates one assumption in the economic
  system, which is every customer has the same
  knowledge about the market
• But several typical classes of protocols address
  for the majority, which implies a limited number
  of different levels of knowledge about the
  market exists
• Order from emergency
• Observed self-similar features in Internet
  traffic is rooted in a number of emergencies
• The human behavior which is unpredictable
• The HOT protocols which can not handle low
  probability emergencies properly, etc.
• The self-similar structure comes out of chaos
  because of those reasons

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Large Complex Systems

• Research questions
• Model the Internet as a complex system is not
  hard, to get analytic results is hard
• We dont know with a incomplete math model, what
  we can prove
• Network dynamics is important since
• As a complex system, the system transitions among
  equilibrium points
• The equilibrium point in Internet changes over
  time and locations

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Large Complex Systems

• Network dynamics
• Questions
• What is the definition of a equilibrium point in
  Internet?
• I assume the equilibrium point should be similar
  to economic system in which the equilibrium point
  is the best match of demand and supply in a
  market
• In Internet, the equilibrium point is the best
  match of demand and supply of information/data in
  the network subject to some constraints
• What is the dynamics of demand of
  information/data in the Internet over time and
  locations?
• Is there any structural behavior in the dynamics
  of the demand?
• Will different computational model changes the
  dynamics of the demand greatly?
• Will the emerging mobile wireless technique
  change the dynamics of the information demand
  greatly?
• What is the dynamics of constraints in the
  Internet?
• Dynamics of constraints include topology change,
  resource utilization change, node failure, etc.
• Different constraints may be regulated by
  different protocols which may provide different
  patterns of dynamics
• Combining the above two questions, the
  equilibrium point of Internet changes
  dynamically. What is the dynamics of the changing
  equilibrium point?
• The imagination is the changing of equilibrium
  point follows a self-similar multi-fractal
  structure
• Can we make a better prediction of the network
  dynamics based on the answer to the above
  questions? Can the prediction help us design the
  control protocols?

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Large Complex Systems

• Topics?
• The patterns of network dynamics can not be
  achieved all at one time
• The discovery of new types of network dynamics
  may prefer one protocol for convergence to
  equilibrium than the other
• Wireless and mobile computing could be one type
  of changes in Internet that brings in new types
  of network dynamics that cause old protocols
  behave badly
• Identify the particular reason for the bad
  behavior is difficult
• Extensive work has to be done before the
  self-similar feature of the traffic dynamics is
  discovered in Internet that causes bad behavior
  of old protocols for long time
• A systematic and analytical approach to
  investigate the bad behavior of the utility
  function derived for a protocol could reveal the
  reason. The range of domain D that the utility
  function doesnt work well is the range that new
  network dynamics often goes into
• New variables for the utility function is hard to
  discover.
• The discover of new network dynamics can be
  directed if the utility function has a fixed set
  of variables

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Large Complex Systems

• Given the large complex system, to allow the
  system converges to the equilibrium point is
  difficult
• Decentralized control is preferred
• Evolutionary algorithm is preferred (bio-net?
  Economic model?)
• A protocol which allows better prediction/knowledg
  e of the network dynamics behave better and other
  entities evolve their control to that protocol
• May use the knowledge of network dynamics learned
• Not all network dynamics can be learned in a
  complex system, evolution is necessary in that
  case
• During the evolution, bad protocols should be
  replaced
• Replacement of bad protocols should have an
  accelerating speed
• It is analogous to dumb customers in the
  market. If everyone is dumb, dumb customers
  can survive the less the dumb customer is, the
  faster they dye
• Interaction between a better protocol and a bad
  protocol is important issue
• Coexistence of good and bad control protocols
  is the same as the coexistence of smart and dumb
  customers in a market
• Good control protocols may be over greedy with
  coexistence with bad control protocols. This is
  the major issue in TCP protocol evolution.
• To avoid a single or small portion of good
  control protocols making great harm to large
  number of still existing bad control protocols
  seem to be one important issue (is it still true
  if we ignore economic factors?)
• When the number of good control protocols
  grows, the impact of the good control protocols
  on bad protocols should grow in the same domain
  (market) to allow accelerated replacement of
  bad protocols

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Large Complex Systems

• Given the large complex system, to allow the
  system converges to the equilibrium point is
  difficult (contd)
• Quick convergence is preferred
• Given that the equilibrium point is also dynamic,
  how to decide the convergence step size in a
  control function? Several proposed ways
• Adaptive step size with respect to the difference
  to the equilibrium point
• Noise free optimal step size toward the current
  equilibrium point
• Step size free approach? (Professor Kevin Tsai
  mentioned some research on that)
• Question on the acquisition of equilibrium point
  the equilibrium point is not always globally
  available to the control function which regulates
  the convergence steps.
• How to achieve good convergence step estimation
  base only on local estimation of the equilibrium
  point in the network?