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QoSbased Management of Multiple Shared Resources in Dynamic RealTime Systems

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We may only allocate a fraction of resources to the soft real-time tasks ... real-time tasks then one or more tasks have. to run at a lower utility, thus ... – PowerPoint PPT presentation

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Title: QoSbased Management of Multiple Shared Resources in Dynamic RealTime Systems


1
QoS-based Management of Multiple Shared
Resources in Dynamic Real-Time Systems
  • Klaus Ecker, Frank Drews
  • School of EECS, Ohio University, Athens, OH
  • ecker, drews_at_ohio.edu

2
Overview of the Talk
  • Introduction
  • Feedback-control based resource management
    architecture
  • Heuristics for allocating multiple resources to
    soft real-time tasks
  • Results
  • Simulation results
  • Outlook and future work

3
Introduction
  • Problem of adaptive resource management with soft
    real-time tasks
  • sharing multiple resources
  • having discrete QoS (Quality of Service) settings
    that correspond to varying resource usage and
    varying user benefit (utility)
  • having minimum QoS requirements
  • being deployed in a mixed critical system
  • integrated into a feedback-control based resource
    management architecture

4
Real-time Design and Development
  • Traditional design
  • often pessimistic ...
  • use worst-case execution times of tasks
    guaranteeing provably correct timeliness e.g.,
    rate monotonic analysis
  • infrequent critical instants,
  • inaccurate resource profiles, etc.
  • ... may lead to poor performance

5
Soft Real-Time Tasks Allow Alternative Approaches
  • System resource usage is controlled by modifying
    QoS parameters
  • Objective maximize overall system benefit
  • E.g., multimedia applications
  • quality of service depends on the amount of
    resources for the individual tasks
  • Our system model is similar to Q-RAM
  • Q-RAM ? MCMDKP (Multiple Choice Multidimensional
    Knapsack Problem)
  • Static Optimization Problem
  • No notion of run-time variations

6
Additional requirements
  • We associate 2 profiles with each task
  • Resource profile maps QoS to resources
  • Utility profile maps resources to system
    benefit
  • Resource availability may change over time
  • Resource profiles are inherently inaccurate
  • We may only allocate a fraction of resources to
    the soft real-time tasks
  • ? Requires run-time resource reallocations
  • A good static resource management algorithm may
    result in instability in the presence of run-time
    variations in resource availabilities
  • ? Resource reallocations based on feedback
    control

7
Motivation / Background
  • Mixed critical task systems
  • Soft real-time tasks may be periodic, aperiodic,
    or event-driven periodic
  • We may want to allocate a share of available
    resources to soft real-time tasks
  • may change over time
  • Resource profiles may be inaccurate

8
Feedback-control Architecture
  • set point (100-desired slack)
  • measured resource availability (feedback)
  • Error

QoS RM Controller
Resource allocation algorithm
QoS settings
9
Basic Controller Operation
  • Controller is event-driven. It is driven by the
    following events
  • End of a task period
  • Task arrival
  • Task termination
  • The controller computes the error and
    calls the QoS resource allocation algorithm
  • This algorithm determines new QoS settings for
    all tasks

10
Controller Requirements
  • Basic QoS controller requirements
  • Robustness with respect to modeling errors, i.e.,
    inaccurate resource profiles
  • Stability with respect to dynamic changes in the
    resource availability
  • The system should not exhibit a cyclic behavior
  • Errors should not accumulate
  • Low time complexity
  • Upper and lower bounds on the optimal solution
    can be used to characterize the QoS control
    performance

11
Observations
  • We generally expect the controller to minimize
    the control error
  • Observation 1
  • If the tasks QoS settings are discrete and
    concave, minimizing is not sufficient for
    maximizing the overall system benefit

12
Notation
  • The model The model different
    resource types each of them available in
    several units
  • The non- soft r.-t. tasks require some share of
    the available resources, which may vary over time
  • Unused resources at current time units of
  • The soft r.-t. tasks
  • compete for these,
  • their performance depends on the amount of
    allocated resources.
  • Performance of a task …
  • depends on the type and number of assigned
    resources

13
Objective
  • Objective The resource units are to be
    distributed (allocated) among the soft r.-t.
    tasks such that QoS is maximized
  • Assumption
  • Utility (Performance) of a task is
    discrete and concave
  • Concave utility functions are widely used in this
    area
  • Examples of utility measures
  • Inverse of processing time the more resources a
    task has, the shorter the processing time, and
    the higher the benefit.
  • Precision of computation more resources lead to
    better computational results.

14
  • The total utility of an allocation is
    defined as
  • Optimization Problem (formally)
  • Given minimal resource constraints
    ,
  • find resource values for each
    such that
  • is maximum,
  • subject to for

MCMDKP ? Multiple Choice Multidimensional
Knapsack Problem
15
Algorithmic Approaches
  • Algorithms
  • apply
    Kuhn-Tucker theorem adaptation to discrete
    functions
  • Rajkumar et al., 1997 The discrete problem is
    NP-complete in the case of one resource type
  • Judd et al., 2005 Feedback-control framework
    Algorithm with bounds on optimal solution and
    prove for control stability
  • It can be solved in polynomial time in case of
    unit step functions

Single resource type
16
  • In case of concave functions the discrete
    problem is NP complete, even in case of unit step
    utility functions
  • Proof Reduction from the Maximum Packing Integer
    Programming Problem

Case of m ? 2 resource types
17
  • Chen Lee et al., 1999 a linear programming
    algorithm for unit resource allocation steps and
    non-concave functions
  • Complexity
  • pseudo-polynomial time and space complexity
  • not appropriate for on-line resource management
    with large

Case of m ? 2 resource types
18
Multidimensional Kuhn-Tucker Algorithm
  • Applies to the resource directions
    in some chosen order, say .
  • Properties of MDKT
  • time complexity is linear in the number of tasks,
    n
  • not optimal in general

19
  • Alternative heuristics Steepest_Ascent
  • allocates the excess resources unit by unit such
    that,
  • at each step, the total utility is increased
    by the
  • maximum possible amount.
  • Properties of STAS
  • time complexity is linear in the number of tasks
    n
  • not optimal in general

20
Estimating Lower and Upper Bounds
  • Special "uniform" utility functions
  • ai, bi ... utility increase by adding one
    resource unit
  •  

MDKT is optimal for uniform utility functions
21
  • General utility functions Non-trivial lower
    and upper bounds on can easily be found
  • Replace each by
  • uniform functions and
  • that are close to the original functions
  • Then

22
  • Simulations for the case of resource
    types
  • Utility function were generated in two
    different ways
  • Directly using random numbers from the interval
    0,100
  • By evaluating the function
  • Where the parameters were chosen arbitrarily
    between 0 and 200.

23
Sample Utility Function
24
Results
  • The lower and upper bounds for are
    approx 10 apart.
  • Experimental studies also show that
    performed on average on order or magnitude better
    than
  • We performed simulations with fixed task numbers
  • between 2 and 35, and resource units between 2
    and
  • 100.
  • In each case we performed 10000 tests.

25
  • Performance of MDKT and STAS against
  • the optimum, for varying task numbers
  • between 5 and 35
  • In average, the utility of the MDKT-solutions is
    less than 0.3 below the optimum

26
  • The next simulation compares MDKT and STAS for 5
    tasks and varying numbers of resource units
  • There are up to 15 units of each resource
    available
  • More resource units lead to better performance of
    MDKT.
  • Again there is no significant deviation of STAS
    from the optimum.

27
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28
Dynamic Changes of Resource Availability
  • If resource units are withdrawn from soft
  • real-time tasks then one or more tasks have
  • to run at a lower utility, thus resulting in a
  • smaller total system utility.
  • If available resource units increase the
  • tasks should take advantage in order to
  • increase their contribution to the total
  • system utility.

29
General Strategy
  • If one of the resource limits is reduced by one
    unit, reduce the assignment of this resource for
    a task that has minimum loss of utility.
  • If one of the resource limits is increased by one
    unit, then assign the additional unit to a task
    that offers maximum utility gain.
  • Simulation studies show that the system behaves
    stable.

30
Conclusions
  • Extending the work of QRAM, we have presented
    heuristics to optimize utility with respect to
    QoS settings.
  • The heuristics are efficient and stable control
    algorithms
  • optimize task QoS settings within known margins,
  • do not accumulate errors over time

31
Future Work
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