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AutoPilot 2001

AutoPilot 2001

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AutoPilot 2001

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  1. AutoPilot 2001 Jerrold F. Stach, Ph.D. Eun Kyo Park, Ph.D. School of Interdisciplinary Computing and Engineering University of Missouri – Kansas City

  2. Perception by Fuzzy Membership Function Multi-attribute Decision Making for Agent Mobility

  3. 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

  4. 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.

  5. Perception In Subjective Time • Congestion • Acceptancewith Goodness of Fit • Acceptance with Certainty • Difference • Reliability/Mortality Perception

  6. Reasoning • Next Migration • Next Computation • Death (Subjective Time) Reasoning -indicates intermediate progress - indicates future work

  7. 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

  8. 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

  9. 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

  10. 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 weight*Time Correspondent value • Create a Time Vector of the attributes

  11. Linear and Scalar attributes cont. • Compute the mass of the time vector as a multi-body system:

  12. 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

  13. 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)

  14. 2001 Research Goals • Develop a set of relevant perception functions producing Percepts by Fuzzy Membership Functions | 0≤ai ≤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

  15. 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 membershipis not intended to convey a likelihood or probability that u has some particular attribute.

  16. 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.

  17. The Notion of Perception • An Agent’s 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.

  18. Example - Perceiving Congestion Perception Unsafe Region The vertical line can be moved to the left according to the agent’s 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

  19. Example - Perceiving Congestion Perception Unsafe Region The vertical line can be moved to the left according to the agent’s 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

  20. Example - Perceiving Congestion Perception Unsafe Region The vertical line can be moved to the left according to the agent’s 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

  21. Theoretical Basis Characterizing the World

  22. 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 < name > • Node Queue Length Lq • Agent Service Rate μ • Agent Arrival Rate λ • AService Place can inquire to the Trader Place <?World> and receive response < {[SP1, Lq,μ,λ],s1,s2,...,sk}, ..., {[SPn, Lq,μ,λ ],s1,s2,...,sm} >

  23. 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.

  24. Agent Sensory Functions • An Agent can enquire to the Service Place <?D,Service_Place_Name>with response <Service_Place_Name,h>where d is in hops. • An Agent can enquire to the situated Service Place <?Environment> with response <Lq,μ,λ> for current local information • An Agent can Inquire to the Service Place <?service_name> and receive reply < [SP1, Lq,μ,λ] ... [SPn, Lq,μ,λ] > where SPn is a Service_Place_Name.

  25. Argument for Exponential Streams In The Agent Population • At any observation SP staten can only transition to staten+1 (birth) or staten-1 (death), independent of arrival rate or time. This is the memoryless property of an exponential stream. • Exponential distribution is thelimiting 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.

  26. Service Place Population Characterization • let l be arrivals per unit of time and m be services per unit of time.

  27. 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

  28. Service Place Effectiveness

  29. Service Place Effectiveness continued

  30. Theoretical Basis The Notion of Fuzzy Sets and Membership

  31. 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.