Quality of Service Based Scheduling

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Quality of Service Based Scheduling

• Maximizing Utility Using Available Resources

Naimisaranya Busek Tom Schoellhammer
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What is Quality of Service?

• QoS is maximization of the usefulness of a
  resource constrained system based on usefulness
  to the user.
• QoS must
• Meet min.resource requirements for all tasks
• Perform admission control
• Use any free system resources to increase the
  usefulness of current tasks

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Why QoS?

• Many applications have resource requirements that
  must be met for the application to be useful to
  the user.
• Networking
• Streaming media (min. bandwidth)
• Real time interaction and response (max. delay)
• Distributed Systems
• Timeliness, security, reliable data transfer
  (error correction, encryption)

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Scheduling for QoS

• A task has min. resource requirements
• Memory, Devices, CPU Time, Data Integrity etc.
• The scheduler must verify that a tasks minimum
  requirements can be met.
• If tasks can deliver variable levels of quality
  the scheduler must allocate extra resources to
  maximize system usefulness.
• The scheduler ensures QoS requirements are met.

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QoS Scheduling Assumptions

• A task has quantifiable properties
• Minimum resource requirements
• Change in quality if allocated additional
  resources
• A maximum amount of resources the task can use
• A task can operate anywhere in this range with
  varying return
• Limited system resources will often not allow the
  allocation of the maximum resources to all tasks

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Defining a Tasks UsefulnessThe Utility
Functions

• The assumption of QoS is that a metric can be
  defined that represents the usefulness of the
  task to the user.
• This metric is the application utility function.
• The applications utility is dependent on the
  resources allocated to it.
• The total system utility is the weighted sum over
  all application utility functions.
• Maximizing the system utility will provide the
  best return for resources expended.

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Maximizing the System Utility Function

• A utility function has dependence one or more QoS
  dimensions
• Example Data Transfer
• Timeliness
• Cryptography
• Data quality
• Reliable delivery
• Each application utility function can be varied
  along each of these dimensions until the system
  maximum is found.

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A Quick Reality Check

• Work that has been done
• Finding optimal solutions for
• One QoS Dimension and One Resource
• Multiple Indep. QoS Dimensions and One Resource
• Solutions (not optimal)
• One QoS Dimensions and Two Resources (1 dep.)
• Proof that optimizing U with a single resource
  with and dependency in the QoS dimensions is
  NP-Hard
• Finding approximation algorithms for more general
  case

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Nothin but the math Maam

• Let ti be the ith task, where i is from 1 to n.
• Let the system have m resources R1,,Rm
• Let Ri Ri,1,,Ri,m be the resources allocated
  to ti from each resource.
• App. Utility Function is ti then defined as Ui
  Ui(Ri)
• Each task ti has a relative weight wi.
• Assuming independence of tasks the total system
  utility is U(R1,,Rn) SumOf(wiUi(Ri)) over i
  from 1 to n.
• Maximizing U is the goal of QoS scheduling.

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QoS-based Resource Allocation Model (Q-RAM)

• Imposes stricter assumptions
• All applications are independent
• All utility functions are monotonically
  increasing
• Applications compete for a single resource
• Results
• A solution is optimal if for all i either Ri 0
  or for any i,j (including i j) Ri gt 0, Rj gt 0
  and Ui(Ri) Uj(Rj).
• Assumes
• Ui(Ri) and Ui(Ri) exist and Ui(Ri) ? 0.

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Ui(Ri) ? Uj(Rj) ? Max Utility?
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Ui(Ri) Uj(Rj) ? Max Utility!
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Utility Maximization Example

• Example Embedded Sensor Node
• Reactivity to environment
• Power saving (sleep, clock slow down, etc)
• Local computation
• Communication
• Assumptions
• Utility functions for power savings Up and
  responsiveness Ur
• Single resource CPU time

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Utility Maximization Example cont.

• System utility Us wrUr wpUp
• Choose wr wp 1
• Allocate minimum resources to all tasks
• Distribute resources to maximize U
• Let Responsiveness be Task 1
• Let Power Saving be Task 2

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Utility Maximization Example cont.

• System Utility UTask1(x) UTask2(1-x)

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Utility Maximization Example cont.
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Utility Maximization Example cont.
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Dealing With More Complex Problems

• Finding the optimal resource allocation for
  dependent and discrete QoS dimensions is NP-Hard
  (reduces to the backpack problem)
• Approximate solutions
• Can generate an approximate Utility Curve by
  finding the convex hull of the actual utility
  curve.
• Use the convex hull as Q-RAM Utility Curve.

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Approximating with convex hull
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Implementations

• Linux / RK
• Real-time extension to Linux
• Provides timely, guaranteed and enforced access
  to system resources
• Amaranth Project
• Real-Time Deadlines
• Dependability
• Cryptographic Security
• Application Performance

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Future Work (not ours)

• Performance of embedded systems in the presence
  of stochastic processes
• Improved metrics to measure system performance
• Multiple Resource, Multiple QoS Dimensions
• Distributed QoS

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Questions and References

• Chen Lee, John Lehoczky, Raj Rajkumar and Dan
  Siewiorek "On Quality of Service Optimization
  with Discrete QoS Options" In Proceedings of the
  IEEE Real-time Technology and Applications
  Symposium June 1999
• Raj Rajkumar, Chen Lee, John Lehoczky and Dan
  Siewiorek "Practical Solutions for QoS-based
  Resource Allocation Problems" In Proceedings of
  the IEEE Real-Time Systems Symposium December
  1998
• Raj Rajkumar, Chen Lee, John Lehoczky and Dan
  Siewiorek "A Resource Allocation Model for QoS
  Management" In Proceedings of the IEEE Real-Time
  Systems Symposium December 1997
• K.T. Kornegay, G. Qu, M. Potkonjak, "Quality of
  Service and System Design", IEEE Workshop on VLSI
  99, pp. 112-117, Orlando, FL, April 1999.
• Amaranth Probabilistically Guaranteed Quality of
  Service for Distributed Computing Systems
• http//www-2.cs.cmu.edu/afs/cs/project/ices-amaran
  th/www/
• Linux/RK
• http//www-2.cs.cmu.edu/rajkumar/linux-rk.html