Traversable Markov Chain State Transition Prediction
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Solution Overview
Problem
Computer systems face challenges in accurately predicting failures due to the limitations of non-traversable Markov chains, which do not consider state transition history, leading to potential system crashes and disruptions in larger networks.
Innovation Solution
The implementation of a traversable Markov chain that uses state transition identifiers, specifically prime numbers, to trace and combine state transition histories, allowing for more accurate predictions of future system states and enabling proactive remedial actions.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a non-traversable Markov chain is used to model system states, then the model structure is simple, but the prediction accuracy deteriorates because state transition history is not considered
Solution Approach 1:
The patent segments the Markov chain into traversable components by introducing state transition identifiers (prime numbers) that allow tracking of specific transition paths. This segmentation enables the system to distinguish between different histories leading to the same state, improving prediction accuracy while maintaining manageable model structure through modular path tracking.
Solution Approach 2:
The patent introduces state transition identifiers (prime numbers) as intermediary elements between states and transitions. These identifiers act as mediators that encode transition history without requiring complex state representations, allowing the system to track path information while keeping the overall model structure relatively simple.
2Measurement precision
If state transition history is tracked using traversable Markov chains, then prediction accuracy improves, but device complexity increases due to additional tracking mechanisms
Solution Approach 1:
The patent changes the parameter representation by using prime numbers as state transition identifiers instead of complex path encoding. This parameter transformation allows efficient tracking of transition histories through multiplicative combination of primes, improving prediction accuracy while minimizing the complexity increase through mathematical elegance.
Solution Approach 2:
The patent creates a composite tracking mechanism by combining prime number identifiers with Markov chain states. This composite approach encodes transition history information within the state representation itself, allowing multiple histories to be distinguished through prime factorization without requiring separate tracking structures.
3Reliability
If proactive remedial actions are implemented based on accurate predictions, then system reliability improves, but response time requirements increase the operational complexity
Solution Approach 1:
The patent implements preliminary action by using prediction models to identify at-risk states before failures occur. The system proactively triggers remedial actions based on predicted transition probabilities, improving reliability by preventing failures before they happen rather than reacting after they occur.
Solution Approach 2:
The patent establishes feedback loops where system state predictions continuously inform operational decisions. The prediction model receives real-time state data, processes it through the traversable Markov chain, and outputs probability assessments that feed back into operational control, creating a closed-loop system that adapts to changing conditions.
Data Source
AI summary
A process includes accessing data representing a directed graph model state for a computer system. The directed graph includes a plurality of transitions among the model states, and the directed graph includes, for each transition, a transition identifier that is associated with the transition and a probability that is associated with the transition. The process includes characterizing a history of the computer system to reach a current state of the computer system. The current state corresponds to a given model state and the history corresponds to first transitions. Characterizing the history includes, based on the data, identifying first transition identifiers associated with the first transition, and applying a first arithmetic operator to the first transition identifier to provide a history identifier, which corresponds to the history. The process includes, based on the history identifier, determining a likelihood that the computer system will transition from the current state to a given future state; and based on the likelihood, initiating a responsive action in anticipation of the computer system transitioning to the given future state.