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Theoretical Control Model for QoS Adaptations in Resource Management

This work presents a sophisticated Task Control Model utilizing digital control theory to formalize application adaptations to resource and Quality of Service (QoS) variations. The model analyzes equilibrium, stability, and fairness by representing each application as an ensemble of tasks within a dynamic Task Flow Model. It accounts for real-world scenarios where complete task state information is not observable. The design involves a Target Task, an Adaptation Task for control algorithms, and an Observation Task to monitor states, ensuring responsive and stable resource allocations without surpassing fair share limits.

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Theoretical Control Model for QoS Adaptations in Resource Management

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  1. Control Theoretical Model for QoS Adaptations • Goal: develop a Task Control Model to formally model applications that adapt to resource/QoS variations • Use digital control theory • Analyze equilibrium, stability and fairness • Model realistic cases where complete task state information are not observable • Map to an adaptive control system - Target System to be controlled takes actions to process input - input is determined by a Controller - controller monitors states or output of target system and compares them to desired values (the reference)

  2. Task Flow Model • Consider each application as an ensemble of functional components (tasks) • A task performs certain actions to deliver a result to other tasks or end-user • Task Flow Graph is a directed acyclic graph showing dependencies among tasks • A task can be uniquely characterized by its input quality, output quality and utilized resources (needed to perform actions)

  3. Task Control Model • Models a single task in the Task Flow Graph • This is the Target Task to be controlled • In addition, - Adaptation Task performs the adaptive control algorithm - Observation Task observes states of the Target Task and feeds them back to Adaptation Task

  4. Task Control Model (cont’d) • Adaptation Task modifies a set of controllable parameters, i.e. possible to affect their values, which in turn can affect states of Target Task and thus its output quality • Task States characterize the internal dynamics in the Target Task. The most important states are its parameters related to its resources • Observation Task observes task states if they are observable. If not, estimates or predicts the current states

  5. Control Equations • Task is said to be at equilibrium/stable when its state does not change • Assume Target Task can be characterized accurately by discrete-time equations

  6. Example • Resource requests for temporal or spatial resources • Request rate of a task throttled by Adaptation Task, so that it does not exceed its fair share • Assume to observe the total number of outstanding resource requests made by all tasks at time k • Under PID control, find stability conditions, equilibrium states, and evaluate responsiveness configurability • Show stability, equilibrium and configurability are preserved when Observation Task can only observe the number of outstanding requests made by the task itself

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