CS523 Operating Systems

1
CS523Operating Systems

• Fred Kuhns
• Applied Research Laboratory
• Computer Science
• Washington University

2
Simplifying Precedence Constraints

• To accommodate precedence and timing constraints
  derive a set of effective release times and
  deadlines
• Effective release time no predecessors then
  equal to its release time. If predecessors then
  maximum of its own and predecessor release times.
• Effective deadline No successor, then original
  deadline. Otherwise minimum of its deadline the
  effective deadlines of its successors.

3
Modeling System

• Modeling the system for an average response time
  calculation
• Assume
• Poisson arrival rate
• FIFO dispatch discipline
• No items dropped from queue
• General independent server times
• Single server, single queue

Tq Tw Ts Tw ?TsA / (1 - ?) A 1/21
(?Ts/Ts)2
? arrival rate
Departure
Dispatching Service
Server
w items in Q Tw Time waiting
Ts Service Time ? utilization ?Ts
q number of items in system, Tq total time in
system
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Average Response Time
...
B1
B2
B3
B5
B4

• View as one large sample space comprised of the
  individual Task sample spaces (used to calculate
  average and second moments, EBi and EBi2).
• Individual events scale by 1/(1-U)
• eAi Bi/(1-U)

5
Average Response Time

• Average queuing time inversely proportional to
  the square of the aperiodic bandwidth (1-U).
• Can improve average response of some jobs by
  using priority queues.

6
Scheduling Sporadic Jobs

• Sporadic jobs
• represent as S(d,e) d deadline, e execution
  time
• have hard deadlines,
• minimum interrelease times and maximum execution
  time are not known in advance
• maximum execution time is known on release
• jobs are preemptable
• Apply an acceptance test at run time
• When job is released, determine if there is a
  feasible schedule that includes this sporadic job
• If no feasible schedule, then reject job and
  notify application of rejection

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Performing an Acceptance Test

• S(d,e) released at time t in frame x-1
• for example an interrupt is received in frame
  x-1.
• The deadline d is in frame (y1) gt
• S must complete in frame y
• Current total slack time available between frames
  x and y (inclusive) Qc(x, y)
• S is rejected if
• e gt Qc(x, y),OR
• some previously accepted jobs will not meet
  deadline
• Order waiting jobs using EDF

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Earliest Deadline First (EDF)

• EDF priority driven scheduling algorithm with
  dynamic task (fixed job) priority assignment.
• earlier the deadline, higher the priority
• priorities are assigned on job realease
• Jobs placed in run queue by priority
• Assumptions
• Tasks are preemptable and independent
• Tasks have arbitrary release times, arbitrary
  deadlines
• Single Processor
• Optimal EDF can produce a feasible schedule o a
  set of Jobs J if and only if J has a feasible
  schedule.

9
Latest Release Time (LRT)

• Goes "backwards" in time Treats release times as
  deadlines and deadlines as release times.
• job with latest release time has highest priority
• May leave processor idle when jobs are ready, so
  not a priority-driven algorithm.
• Optimal LRT can produce feasible schedule for a
  set of jobs J if and only if feasible schedules
  for J exist.

10
Least Slack Time First (LST)

• LST or Maximum Laxity First (MLF)
• Dispatch job with minimum slack time smaller
  slack time, higher priority.
• Optimal Can produce feasible schedules for J if
  and only if feasible schedules for J exist.
• Requires knowledge of execution times, while EDF
  does not. Consequently may underutilize
  processor when using maximum (worst-case)
  analysis.

11
Performing and Acceptance Test

• Beginning of each frame perform acceptance test
  on any waiting sporadic tasks
• Two steps
• Determine if sporadic task can complete execution
  using available slack time (subtract any slack
  time used by accepted tasks with deadlines before
  d)
• Determine if any already accepted sporadic tasks
  with deadlines after d will be affected

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Implementation Calculating Slack Time

• Calculating the available slack time
• S was released within previous frame, (x - 1)
• S has deadline in frame (y 1) so must complete
  execution no later than frame y
• Acceptance test performed at start of frame x
• calculated between frame x and frame immediately
  preceding deadline, frame y
• if deadline is in frame x then S can not be
  scheduled
• Suffices to know original slack time between all
  frame pairs within one major cycle, Q(x, y) for
  x, y in H.
• Assume x is in major cycle j and y is in major
  cycle k
• Q(x,y) Q(x,F) Q(1,y) (k - 1) - jQ(1,F) k
  gt j
• Q(x, y) is known if k j, y gt x.
• Q(x, x) is known, slack in current frame

13
Accepting S Step 1

• If sporadic jobs are already in system then the
  available slack time is given by
• Qc(x, y) Q(x, y) - Sumdk?d (ek - e'k)
• slack plus remaining execution time of higher
  priority tasks.
• e'k time job k has already executed
• The sum is over all jobs with deadline dk ? d.
• If S is accepted
• Slack before new sporadic job's deadline
• Qs Qc(x, y) - e
• if job accepted store this value with job
• reject if Qs ? 0,

14
Accepting S Step 2

• Check all jobs with deadlines after d to verify
  they will not miss their deadlines.
• d deadline of new sporadic task
• e execution time of new sporadic task
• Let Sl be the set of already accepted sporadic
  tasks with deadlines after d.
• Let Ql be the calculated slack for sporadic task
  Sl
• Accept if Step one is valid and te following
  condition is valid
• Ql - e ? 0 for all sporadic jobs with dl gt d.

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Summary Acceptance Test

• Scheduler must store the following
• Precomputed slack table, Q(x, y), x ,y 1, 2,
  ..., F
• Completed execution time of accepted sporadic
  jobs, e'k
• Current slack (Qs) of every sporadic job
• Optimality of Cyclic EDF (on-line algorithm)
• it is optimal compared to other schemes that
  perform an acceptance test at beginning of frames
• Not optimal compared to algorithms performing
  acceptance tests at arbitrary times.
• However, this may impact the periodic tasks which
  may be interrupted an arbitrary number of times
  in order to perform acceptance tests for released
  sporadic jobs.

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Practical Considerations

• Frame Overruns
• Abort job, schedule recovery job
• Execute unfinished portion as aperiodic job
• Continue executing job
• Mode changes system reconfiguration. Assume
  periodic jobs are independent
• Hard-deadline
• Soft-deadline
• Other Workloads

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Assessing Clock-Driven Scheduling

• Advantages
• Simplicity account for dependencies and resource
  contention. No need for synchronization
  mechanisms.
• Timing constraints verified or enforced at frame
  boundaries while minimizing overhead due to
  context switches and IPC mechanisms. Simple
  scheduling algorithm to minimize overhead.
• Minimal impact of asynchronous system processing
  (interrupts for example)
• often verification is simple

18
Assessing Clock-Driven Scheduling

• Disadvantages
• inflexible
• Model and implementation may be too simple and
  restrictive
• Difficult to add new components or change
  existing system parameters
• Release times must be fixed
• Must know all periodic parameters in advance
• operation modes must be explicitly enumerated and
  scheduled