Overload Scheduling in Real-Time Systems

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Dr. Pedro Mejia Alvarez Curso de Sistemas de Tiempo Real

Overload Scheduling in Real-Time Systems

Dr. Pedro Mejía Alvarez Sección de Computación.CINVESTAV-IPN, México

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Outline

• Motivation• Related Work• Methodology• The INCA Server Algorithm• The Approximate Algorithm• Analysis of the INCA Server• Simulation Results

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Motivation

Many systems are provisioned incorrectly Correctly provisioned systems have:

Changes in the environment, Many arrivals of asynchronous events or Faults of peripheral devices.

Overloads occur when safety is at stake need efficient algorithm

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Related Work

• Best effort scheduling algorithm (Locke and Jensen):

• The RED (Robust Earliest Deadline) algorithm (Buttazzo):

• Imprecise Computations

• Skip Model

• The (m,k) Model

• The Elastic Task Model

• The Incremental Server Model.

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Best effort scheduling algorithm

• Rejection policy for overloaded systems based on removing tasks

with the minimum value density (introduced time valued functions).

(a)

t

U

d

(b)

t

U

d

(c)

t

U

d

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• aperiodic tasks in overloaded systems. Combines criticality-based

scheduling and deadline tolerance. Remove the task with least

value on overload.

The RED (Robust Earliest Deadline) algorithm

Planning Ready queue

Reject queue

task

Reclaimingpolicy

Rejection policy

Scheduling policyRUN

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Imprecise Computation Model

Each Task is composed by a mandatory and an optional part.

Mi: mandatory part of task i

Oi: optional part of task i

Mi precceds in execution to a OiOi could not execute or it may execute partiallyThe deadline of Mi must be guaranteed.The deadline of Oi could be missed if necesarry.Execution of Oi refines the result obtained by MiThe goal in the scheduling of imprecise tasks is to execute the most possible number of optional parts such that:•No deadline of mandatory parts is missed•The error is minimized. Error is greater when more optional parts are not executed

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Example of Execution of Imprecise Tasks

Task T M O P U 1 30 5 5 3 0.333 2 40 5 5 2 0.250 3 50 10 2 1 0.240

0.823

Task 3 misses the deadline ofIf optional part on its first Job At time: t = 50

0 20 40 60 80 100 120 140 160

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The Skip Model

•Some Jobs can be skipped, ocassionally•On-line guarantee

•A job is either executed within its deadline or it is rejected.

•Each Task is characterized by (Ci,Ti,Di,Si)

•Si is the minimum number of Jobs that must be executed between two consecutive skips

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The Skip Model (Example)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

C1 = 1, T1 = 3; C2 = 2, T2 = 4, Si = 2

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The Elastic Tasks Model

•The idea is to control the processor load by tuning the task periods•Task utilization are variable with given elastic coefficients•A periodic task is characterized by: (Cu, Ti0, Timin, Timax, Ei)•The actual period Ti Є [Timin,Timax]

Ri Timin Ti0 Timax

Ei

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Problems with Related Work

• Criteria for rejection = discard the lesser-valued tasks.

• The time valued functions:

• difficult to obtain

• performance may be degraded if the system designers

are not familiar with these functions.

• How far from optimal is the performance of the algorithms?

• Discarding “less critical” tasks during overload requires:

• exploration of a large search space (combination of

tasks) to discard solution not practical.

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Incremental Server for Scheduling Overloads

Goal: Selecting Optional Parts to schedule in real-time systems under overloads.

Problem: Selection while maximizing system value requires the exploration of a large number of combinations.

Approach: Adjust the system workload by executing a sequence of approximate algorithms in incremental steps.

• At every phase, load is adjusted and solution is refined.

• Property: The most critical tasks in the systems are always scheduled and the total value is maximized.

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M1 M3

M4

M5

M6

M2

O1 O2

O3

O6

O5

O4

Mandatory Parts Optional Parts

OVERLOADED SYSTEM

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M1 M3

M4

M5

M6

M2

O1 O2

O3

O6

O5

O4


OVERLOADED SYSTEM

•Optimal Solution•High Complexity

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M1 M3

M4

M5

M6

M2


OVERLOADED SYSTEM

•Low Cost•Poor Solution

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O1 O2

O3O6O4

•Solution is Refined•Complexity Increases

INCREMENTAL EXECUTION OF ASEQUENCE OF APPROXIMATE ALGORITHMS

O1

O2 O4

[...AP(0)][....................AP(1)] .............. [..........AP(k)]

Solutions

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INCREMENTAL EXECUTION OF ASEQUENCE OF APPROXIMATE ALGORITHMS

AP(0)][...............AP(1)][.......................................AP(k)]

U

Slack

0

1

• AP(1) runs on the Slack Time recovered by AP(0)

Overload

Time

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Task Model

• Imprecise periodic tasks: 0/1 constraints

• The arrival of each task is aperiodic (ri instances per task).

• Overload is caused by optional parts.

• Overloads only due to new task arrivals (comp times are fixed)

• Optional parts may be discarded under overloaded conditions.

• Each task has an associated criticality value vi.

• Earliest Deadline First (EDF) dispatching.

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Methodology Proposed

1. Define the search space and the objective functions,

2. Define the conditions for the feasibility of a solution,

3. Find a feasible element within the search space that

satisfies an optimality criteria.

4. Execute the Approximate Algorithms in an incremental

fashion, during system idle times.

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Search Space

Set Search Space

S4 {1,1,1,1}

S3 {1,1,1,0} {1,1,0,1} {1,0,1,1} {0,1,1,1}

S2 {1,1,0,0} {1,0,1,0} {1,0,0,1} {0,1,1,0} {0,1,0,1} {0,0,1,1}

S1 {1,0,0,0} {0,1,0,0} {0,0,1,0} {0,0,0,1}

S0 {0,0,0,0}

• Each element in S denotes either a Feasible or Non-Feasible Solution• Xi = 1, optional part i is chosen for execution.

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Objective Functions and Feasibility test

• Objective Functions:

• Utilization: (s) = mi/Ti + xj (pj/Tj)

• Criticality Value: (s) = xi (vi/Ti)

• Feasibility Test (utilization based)

true if (s) <= 1UBT(s) =

false otherwise{

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The Optimization Problems

Maximize Utilization Maximize the Value

maximize (s) maximize (s)

Subject to UBT(s) Subject to UBT(s)

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Formulation for Maximizing Utilization

Problem: If an arriving task I causes an overload:

1. Decide whether to accept the new task.

2. Determine the time for the scheduling of the new task.

3. Determine the optional parts to shed.

4. Maximize the usage of the resources at a low cost.

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Incremental Scheduling Server

• Adjust the workload in response to transient overload requests.

• Executes a sequence of Approximate Algorithms

AP(0), ..., AP(n) during idle time.

• At each level k, AP(k) determines which optional parts to shed

to satisfy optimality criteria

• AP(k) obtains a solution closer to optimal than AP(k-1) but with

longer execution time.

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Metodology for Handling Overload

1. Activating the Incremental Server

2. Execution of AP(0): Overload Removal

3. Scheduling the New Task.

4. Execution of AP(1),..., AP(n)

5. Stopping the execution of the Server

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Triggers for activating the INCA Server:

1. A new task arrives and causes an overload: UBT Test

2. A task leaves the system.

• While waiting for new tasks, the INCA server do not cause

overhead in the system.

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Execution of AP(0) yields Overload Removal:

“shed the less critical optional parts”

•AP(0) is a greedy algorithm O(n) finds a sub-optimal solution.

•If overload persists after AP(0) the new task is rejected.

•Optional Tasks are temporarily suspended, not discarded.

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Scheduling the New Task occurs only at the end of the

longest period of all preempted tasks.

• The resulting utilization can not be immediately subtracted.

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Incremental Execution of AP(1), ..., AP(n)

• AP(1) runs on the slack time recovered by AP(0).

• Similarly, slack from AP(1) is used to run AP(2), ... And so on...

• INCA server will execute as many AP(k)’s as possible

• AP(i) solution better than AP(i-1)

• AP(i) runtime longer than AP(i-1)

• Results from AP(i) may increase the utilization, reducing the

amount of available slack.

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Triggers for stopping the execution of the INCA Server

• There is no slack in the schedule to execute AP(k) stop server

• AP(k) gives a solution no better than AP(k-1) stop server

• After AP(n) is executed stop server

• Another task arrives in the system stop and re-start server

• A Task leaves the system stop and re-start server

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Incremental Scheduling Server INCA Server:

input: Set of tasks, including the newly arrived task

1: Execute AP(0);

2: if the system is still overloaded then exit;

3: Compute the start time of the new task;

4: Schedule the new task at its start time;

5: k=1;

6: while (there is slack in the schedule) do

7: Execute AP(k) (during slack time)

8: if the result (utilization) from AP(k) is better than AP(k-1)

9: then Adjust the workload (remove optional parts)

10: else exit;

11: k = k+ 1;

12: end;

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Each Approximate Algorithm

• Greedy algorithm to select optional parts for execution.

• AP(k) considers all possible (feasible) subsets in the

search space with al least k optional parts.

• Characteristics:

• The time complexity of AP(k) is: O(nk+1)

• The worst-case performance ratio is: k/(k+1)

• For a small value of k, AP(k) give a solution “close to

optimal”.

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Performance of the Approximate Algorithm

Maximize Utilization k 0-0.01% 1-5% 5-10% 10-15% 15-20%

0 617 251 119 13 0

1 662 336 2 0 0

2 951 49 0 0 0

3 999 1 0 0 0

4 1000 0 0 0 0

Maximize Criticality k 0-0.01% 1-5% 5-10% 10-15% 15-20%

0 631 131 62 50 0

1 829 35 54 51 0

2 911 15 25 25 0

3 1000 0 0 0 0

4 1000 0 0 0 0

Number of Solutions

within x percent near

optimal

• 1000 Simulations

• 10 tasks

• U = 120%

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Analysis of the INCA Server

Results.

1. Using INCA gives better results than using NON-INCA,

when the objective is to maximize (s) (utilization).

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Simulation Experiments: setup

1. Measure the quality of results over a set of dynamic tasks.

2. Measure and compare the performance among several stages

of our different optimality criteria

• 100 independent simulations (first 5 stages of AP(k))

• 5,000 tasks (life time of each task: 400-600 instances)

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Performance Evaluation: Metrics

Criticality Ratio = CV(I)

Total Criticality

Utilization Ratio = CU(I)

Total Utilization

CU(I) = i ri * pi ri = number of instances of task i

CV(I) = i ri * vi

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Simulation Results

Utilization Ratio for up to 5 stages

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Simulation Results

Criticality Ratio for up to 5 stages

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Conclusion on the INCA Server

• Only few stages of the INCA server are necessary for

achieving near-optimal results.

• INCA Algorithm is easy to implement.

• Performance metrics (utilization and criticality) are easy

to obtain for system designers.

Overload Scheduling in Real-Time Systems

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