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Control Theoretical Model for QoS Adaptations

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

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Control Theoretical Model for QoS Adaptations

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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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