AutoPilot 2001

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AutoPilot 2001

• Jerrold F. Stach, Ph.D.
• Eun Kyo Park, Ph.D.
• School of Interdisciplinary Computing and
  Engineering
• University of Missouri Kansas City

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Perception by Fuzzy Membership Function

• Multi-attribute Decision Making for Agent Mobility

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AutoPilot Framework

• Years 1,2 concentrated on the theoretical basis
  of mobility and construction of baseline
  simulator.
• Network load leveling was demonstrated as a
  second order effect of individual agent mobility
  decisions.
• Year 3 concentrated on quantification of
  perception using characteristic functions and
  subjective time.

Meta data
Behavior
Reasoning
Perception
Sensing
Autonomous, Rational Agent
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Sensory Functions
Trader Place and Local Service Place Inquiries
Population Density

• Current Time
• Distance in Hops
• Queue Length
• Arrival Rate
• Service Rate

Distance
Objective Time
Sensing
Service Planner at SP provides instantaneous local
measures. Trader Place provides measures of
remote SPs since last update.
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Perception In Subjective Time

• Congestion
• Acceptance with Goodness of Fit
• Acceptance with Certainty
• Difference
• Reliability/Mortality

Perception
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Reasoning

• Next Migration
• Next Computation
• Death (Subjective Time)

Reasoning
- indicates intermediate progress
- indicates future work
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Behavior

• Non-Deterministic Choice
• stay or go
• next location
• next computation
• self replicate
• genetic mutate
• (signature splice)
• Request Transport

Behavior
- indicates intermediate progress
- indicates future work
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Meta Data

• Life History (experiences)
• Algebraic Signature (Genotype)
• Phenotype
• Intermediate Data e.g. progress toward goal,
  beliefs etc.
• Join locations

Meta data
- indicates intermediate progress
- indicates future work
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2000 Results

• Single attribute functions were given for
• Distance
• (Objective time based on hops and payload)
• Cost of Service
• Accuracy (quality) of Service
• Mobility was solved using a graph theoretic
  solution which is optimal but has exponential
  running time
• Service Places were weighted in a task graph
  using a multi-attribute normalization

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Mapping of Subjective Time to Scalar Time for
Linear Attributes such as Cost and Accuracy was
Given

• Compute the Origin and Limit of Scalar Time
  Bounds of current network diameter
• For each attribute
• compute the slope of the attribute scale
• obtain the time correspondent
• compute the mass of the attribute using its
  weightTime Correspondent value
• Create a Time Vector of the attributes

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Linear and Scalar attributes cont.

• Compute the mass of the time vector as a
  multi-body system

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2000 Observations

• Many environmental (sensed) attributes do not
  scale linearly
• congestion
• quality
• reliability
• acceptance
• AutoPilots must be able to reason over attributes
  with various CDFs in subjective time

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2001 Observation

• Many non-linear, environmental attributes exhibit
  characteristic CDFs over a universe of discourse
• congestion (exponential)
• strength of yes/no (parabola)
• magnitude of difference (logarithmic)
• reliability/mortality (bath tub)

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2001 Research Goals

• Develop a set of relevant perception functions
  producing Percepts by Fuzzy Membership Functions
  0ai 1 for Service Place and Service
  attributes Develop a method to interpret the
  Percepts for individual attributes
• Prove the multi-mass function developed in 2000
  is pareto-optimal
• Prototype and validate the Percepts

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The notion of membership

• For a fuzzy set A?0,1, A is called
• the membership function and A(u) for u ? U is
  called the degree of membership of u in the fuzzy
  set.
• The degree of membership is not intended to
  convey a likelihood or probability that u has
  some particular attribute.

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2001 Research Tasks

• Design ways to get reasonable membership
  functions
• Functions should have good correspondence to the
  subjective notions they represent
• Functions should be based in theory, i.e. a
  characteristic function over the universe values
  of the attribute.

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The Notion of Perception

• An Agents life is finite in the system
• An Agent carries a Phenotype and Genotype (task
  signature) yielding an expectation of the
  duration of work
• An Agent must therefore sense its own mortality
  with regard to achieving its goal, i.e. reason in
  subjective time.

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Example - Perceiving Congestion
Unsafe Region

• Perception

The vertical line can be moved to the left
according to the agents subjective model of
time. Congested nodes need not be considered in
the mobility decision.
Safe Region
Waiting Time as a Function of Service Place
Utilization
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Example - Perceiving Congestion
Unsafe Region

• Perception

The vertical line can be moved to the left
according to the agents subjective model of
time. Congested nodes need not be considered in
the mobility decision.
Safe Region
Waiting Time as a Function of Service Place
Utilization
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Example - Perceiving Congestion
Unsafe Region

• Perception

The vertical line can be moved to the left
according to the agents subjective model of
time. Congested nodes need not be considered in
the mobility decision.
Safe Region
Waiting Time as a Function of Service Place
Utilization
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Theoretical Basis

• Characterizing the World

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Trader Place is a Sensor with Memory

• At each update interval the following is reported
  from each Service Place to its Trader Place
• Service Place Name lt name gt
• Node Queue Length Lq
• Agent Service Rate µ
• Agent Arrival Rate ?
• A Service Place can inquire to the Trader Place
  lt?Worldgt and receive response lt SP1,
  Lq,µ,?,s1,s2,...,sk, ..., SPn, Lq,µ,?
  ,s1,s2,...,sm gt

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Observation

• Trader Place update intervals are relatively long
  compared to agent arrival rates and service rates
• Each Trader Place Update is a snapshot of one
  state of the Universe at a near past instant of
  measurement
• Trader Advertisements are recent history, not
  current state.

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Agent Sensory Functions

• An Agent can enquire to the Service Place
  lt?D,Service_Place_Namegt with response
  ltService_Place_Name,hgt where d is in hops.
• An Agent can enquire to the situated Service
  Place lt?Environmentgt with response ltLq,µ,?gt for
  current local information
• An Agent can Inquire to the Service Place
  lt?service_namegt and receive reply lt SP1, Lq,µ,?
  ... SPn, Lq,µ,? gt where SPn is a
  Service_Place_Name.

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Argument for Exponential Streams In The Agent
Population

• At any observation SP staten can only transition
  to staten1 (birth) or staten-1 (death),
  independent of arrival rate or time. This is the
  memoryless property of an exponential stream.
• Exponential distribution is the limiting
  distribution of the normalized statistic of
  random samples drawn from continuous populations
• Exponential distribution provides the least
  information where information content has
  entropy. It is the most random law and is a
  conservative approach to modeling the agent
  population as a dynamic entity as we move to an
  A-Life model of the AutoPilot agency.

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Service Place Population Characterization

• let l be arrivals per unit of time and m be
  services per unit of time.

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Service Place State Characterization

• Let pn be the percentage of time in steady state
  the system is in state n.

Assuming the probabilities sum to 1 over the
states then
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Service Place Effectiveness
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Service Place Effectiveness continued
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Theoretical Basis

• The Notion of Fuzzy Sets and Membership

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The notion of a fuzzy set

• A crisp set is defined

A fuzzy subset of a set U is a function
On the Powerset P(U) of all subsets of U are the
familiar functions of union, intersection and
complement.