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Introductory Seminar on Research CIS5935 Fall 2008

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Introductory Seminar on ResearchCIS5935 Fall 2008

Ted Baker

- Introduction to myself
- My past research
- My current research areas

- Technical talk: on RT MP EDF Scheduling
- The problem
- The new results
- The basis for the analysis
- Why a better result might be possible

- Relative computability
- Relativizations of the P=NP? question (1975-1979)

- N-dim pattern matching (1978)
- extended LR parsing (1981)

- Ada compiler and runtime systems (1979-1998)

- FSU Pthreads & other RT OS projects (1985-1998)

- Stack Resource Protocol (1991)
- Deadline Sporadic Server (1995)

- POSIX, Ada (1987-1999)

- Multiprocessor real-time scheduling (1998-…)
- how to guarantee deadlines for task systems scheduled on multiprocessors?
with M. Cirinei & M. Bertogna (Pisa), N. Fisher & S. Baruah (UNC)

- how to guarantee deadlines for task systems scheduled on multiprocessors?
- Real-time device drivers (2006-…)
- how to support schedulability analysis with an operating system?
- how to get predictable I/O response times?
with A. Wang & Mark Stanovich (FSU)

Will a set of independent sporadic tasks miss any deadlines if scheduled using a global preemptive Earliest-Deadline-First (EDF) policy on a set of identical multiprocessors?

- job = schedulable unit of computation, with
- arrival time
- worst-case execution time (WCET)
- deadline

- task = sequence of jobs
- task system = set of tasks
- independent tasks:
can be scheduled without consideration of interactions, precedence, coordination, etc.

- Ti = minimum inter-arrival time
- Ci = worst-case execution time
- Di = relative deadline

job completes

deadline

job released

next release

scheduling window

- m identical processors (vs. uniform/hetero.)
- shared memory (vs. distributed)
- preemptive (vs. non-preemptive)
- on-line (vs. off-line)
- EDF
- earlier deadline higher priority

- global (vs. partitioned)
- single queue
- tasks can migrate between processors

- Is a given system schedulable by global-EDF?
- How good is global-EDF at finding a schedule?
- How does it compare to optimal?

Global-EDF schedulability for sporadic task systems can be decided by brute-force state-space enumeration (in exponential time) [Baker, OPODIS 2007]

but we don’t have any practical algorithm.

We do have several practical sufficient conditions.

- Varying degrees of complexity and accuracy
- Examples:
- Goossens, Funk, Baruah: density test (2003)
- Baker: analysis of -busy interval (2003)
- Bertogna, Cirinei: iterative slack time estimation (2007)

Sporadic task system is schedulable

on m unit-capacity processors if

where

maximum demand of jobs of i that arrive in and have deadlines within

any interval of length t

maximum fraction of processor demanded by jobs of i that arrive in

and have deadlines within any time interval

single processor analysis uses maximal busy interval,

which has no “carried in” jobs.

Sporadic task system t is global-EDF schedulable on m unit-capacity processors if

where

- There is no optimal on-line global scheduling algorithm for sporadic tasks [Fisher, 2007]
- global EDF is not optimal
- so we can’t compare to an optimal on-line algorithm
- but we can compare it to an optimal clairvoyant scheduler

A scheduling algorithm has a processor speedup factor f ≥ 1 if

for any task system that is feasible on a given multiprocessor platform

the algorithm schedules to meet all deadlines on a platform in which each processor is faster by a factor f.

Any set of independent jobs that can be scheduled to meet all deadlines on m unit-speed processors will meet all deadlines if scheduled using Global EDF on m processors of speed 2 - 1/m.

[Phillips et al., 1997]

But how do we tell whether a sporadic task system is feasible?

If t is feasible on m processors of speed x then it will be correctly identified as global-EDF schedulable on m unit-capacity processors by Theorem 3 if

The processor speedup bound for the global-EDF schedulability test of Theorem 3 is bounded above by

The processor speed-up of

compensates for both

- non-optimality of global EDF
- pessimism of our schedulability test
There is no penalty for allowing post-period deadlines in the analysis (Makes sense, but not borne out by prior analyses, e.g., of partitioned EDF)

- lower bound m on load to miss deadline
- lower bound on length of m-busy window
- downward closure of m-busy window
- upper bound on carried-in work per task
- upper bound on per-task contribution to load, in terms of DBF
- upper bound on DBF, in terms of density
- upper bound on number of tasks with carry-in
- sufficient condition for schedulability
- derivation of speed-up result

problem job arrives

first misseddeadline

other jobs execute

problem job executes

Consider the first “problem job”, that misses its deadline.

What must be true for this to happen?

Details of the First Step

What is a lower bound on the load needed to miss a deadline?

problem job arrives

first missed deadline

previous job

of problem task

problem job ready

The problem job is not ready to execute until the preceding job

of the same task completes.

first missed deadline

problem window

previous job

of problem task

problem job ready

Restrict consideration to the “problem window”

during which the problem job is eligible to execute.

problem window

other tasks execute

problem task executes

The ability of the problem job to complete within the problem window

depends on its own execution time and interference from jobs of other tasks.

problem window

carried-in jobs

deadline > td

- The interfering jobs are of two kinds:
- local jobs: arrive in the window and have deadlines in the window
- carried-in jobs: arrive before the window and have deadlines in the window

other tasks interfere

problem task executes

Interference only occurs when all processors are busy executing

jobs of other tasks.

other tasks interfere

problem task executes

Therefore, we can get a lower bound on the necessary interfering

demand by considering only “blocks” of interference.

other tasks interfere

problem task executes

The total amount of block interference is not affected by

where it occurs within the window.

other tasks interfere

problem task executes

The total demand with deadline td includes the problem

problem job and the interference.

processors busy executing jobs

with deadline problem job

approximation of interference (blocks)

by demand (formless)

average

competing workload

in [ta,td)

processors busy executing other jobs

with deadline problem job

From this, we can find the average workload with deadline td

that is needed to cause a missed deadline.

previous deadline of problem task

problem job arrives

previous job

of problem task

The minimum inter-arrival time and the deadline give us

a lower bound on the length of the problem window.

The WCET of the problem job and the number of processors

allow us to find a lower bound on the average competing workload.

There can be no missed deadline unless there is a

“-busy” problem window.

- [lower bound m on load to miss deadline]
- lower bound on length of m-busy window
- downward closure of m-busy window
- upper bound on carried-in work per task
- upper bound on per-task contribution to load, in terms of DBF
- upper bound on DBF, in terms of density
- upper bound on number of tasks with carry-in
- sufficient condition for schedulability
- derivation of speed-up result

# tasks with carried-in jobs m-1

shows carried-in load max

Observe length of -busy interval ≥ min(Dk,Tk)

covers case Dk>Tk

- Derive speed-up bounds

previous deadline of problem task

problem job arrives

previous job

of problem task

Observe length of -busy interval ≥ min(Dk,Tk)

This covers both case Dk≤TkandDk>Tk

To minimize the contributions of carried-in jobs, we can extend

the problem window downward until the competing load falls below .

maximal -busy interval

maximal -busy interval

at most

carried-in jobs

Observe # tasks with carried-in jobs m-1

Use this to show carried-in load max

- New speed-up bound for global EDF on sporadic tasks with arbitrary deadlines
- Based on bounding number of tasks with carried-in jobs
- Tighter analysis may be possible in future work

- approximation of interference (blocks) by demand (formless)
- bounding i by max
(only considering one value of )

- bounding DBF(i, i +) by (i +)max(t)
- double-counting work of carry-in tasks

bounding DBF(i, i +) by (i +)max(t)

contribution of i

double-counting internal load from tasks with carried-in jobs

carry-in cases

non-carry-in cases

- Is the underlying MP model realistic?
- Can reasonably accurate WCET’s be found for MP systems? (How do we deal with memory and L2 cache interference effects?)
- What is the preemption cost?
- What is the task migration cost?
- What is the best way to implement it?

The End

questions?

maximal -busy interval

at most

carried-in jobs

maximal -busy interval

maximal -busy interval