Feasibility analysis in preemptive uniprocessors

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Feasibility analysis in preemptive uniprocessors

• Mok friends. Resource partition for real-time
  systems (RTAS 2001)

2
All about models..
3
All about models..

• tradeoff between
• expressiveness versus
• tractability of analysis
• analysis questions for real-time systems
• feasibility
• run-time scheduling
• Well talk about
• uniprocessors
• preemptive
• dynamic priority (mostly)
• gt
• run-time scheduling is not an issue

4
Sporadic task models -- the framework

• Jobs basic units of work
• arrival time
• execution requirement
• deadline
• Tasks or processes
• finite (a priori known) number
• generate the jobs
• code within an infinite loop
• different tasks are assumed independent
• (in particular, no relationship between arrival
  times of diff tasks jobs)

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Sporadic task models ? a short history (I)

• Liu Layland model (mid- to late- 60s)
• Ti (ei, pi)
• feasibility analysis in linear time
• 3-parameter (Mok) model (late 70s to early 80s)
• Ti (ei, di, pi)
• feasibility analysis
• identify worst-case (synch ASAP) and simulate
  EDF
• exponential time (simulate to lcm)
• if utilization ? c for some predefined constant c
  lt 1, then simulate to
• c/(1-c) ? max pi - di
• gt pseudopolynomial time

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Sporadic task models ? a short history (II)

• MultiFrame model (early 90s -- Mok Chen)
• vector of execution requirements T (e1, e2,
  e3,...eN, p)
• identifying the worst-case
• the demand bound function (dbf) abstraction
• feasibility analysis
• assuming utilization is bounded by clt1, still
  pseudopolynomial time
• Relationship between the models

L L
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Sporadic task models ? a short history (III)

• Generalized MultiFrame model (mid 90s)
• vectors of everything T ( e1, e2,...eN, d1,
  d2,...dN, p1, p2,...pN )
• all vectors must be of the same size!
• feasibility analysis
• compute dbf
• verify that SUM dbf(Ti, t) ? t for all t? 0
• assuming utilization is bounded by clt1, still
  pseudopolynomial time
• computing dbf(T,t) is more interesting

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Two directions forward...

• further generalize the task model...
• recurring branching task model
• recurring real-time task model
• generalize the machine model
• the Mok friends paper well be looking at
• do not require the processor to offer constant
  execution rate
• application a hierchical scheduling framework

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Generalizing the task model

• LL T(e,p)

Mok T(e,d,p)
MF T(e,p)
GMF T(e,d, p)
The obvious extension non-straight-line graphs
(trees)
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Conditional real-time code (I)
T1 Every 100 time units

• Not clear which branch is worse...
• if T2 (5,5) the then branch
• if T2 (8,10), the else branch

• if (C) then (1,1)
• else (3,10)
• endif

• The recurring branching tasks model
• A task is represented by
• a (rooted) tree, and
• a period

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Conditional real-time code (II)

• The trouble with trees dont allow for

if (C1) then (1,1) else
(3,10) endif . . if (C2) then (1,1) else
(5,20) endif . .
The obvious next generalization a directed
acyclic graph
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A detour back to this...
Priorities S(static) F
(fixed) D (dynamic)
Migration N R Y
We have utilization bounds (upper and lower)
Next goal looking for domination and
incomparability relationships between classes in
this table