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