Question 1

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Question 1

• Use time-demand analysis to show whether or not
  the RM scheduler can feasibly schedule the
  following tasks. Show your work.
• T1 (6,3) T2 (9,4) T3 (20,1).

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Question 2

• Consider the following system of fixed-priority
  tasks and write the time-demand functions w3(t)
  of T3 AND w5(t) of T5.
• T1 (10,2) T2 (14,2) T3 (15,3) T4
  (50,1) T5 (24,3)
• Assume a context switch takes 0.1 unit time.
• T3 can self-suspend twice for 1 unit of time
  each,
• T4 contains a nonpreemptable section with
  execution time 0.3, and
• T5 contains a nonpreemptable section with
  execution time 0.5.

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Question 3

• Consider the following tasks given in (?,p,e,D)
  form that are scheduled using the RM algorithm
• T1 (0,2,0.5,4) T2 (0,3,1.3,10) T3
  (0,5,1.0,10)
• For which job(s) of task 3 do you need to
  calculate the worst (i.e. maximum) response time
  to verify schedulability? How did you determine
  this?

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Question 4

• RM algorithm T1 (15,3) T2 (25,2.5) T3
  (35,7)
• If aperiodic tasks are scheduled with a simple
  sporadic server with period 20, what is the
  maximum execution budget?
• If T3 has a nonpreemptable critical section of
  length 5 time units and aperiodic tasks are
  scheduled with a deferrable server with period
  20, what is the maximum execution budget?

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Ch 6 Sample Problems

• 6.9. (3,1) (4,2) (6,1)
• graph time-demand
• schedulable
• graph used to determine schedulability of
  arbitrary priority-driven algorithm?
• 6.11. (5,1) (3,1) (8,1.6) (18,3.5)
• solve for maximum response time of w4(t) by
  solving iteratively.
• 6.15. (3,1) (5,2) (8,3)
• reduce execution time of task 3 to achieve
  schedulability using EDF.
• 6.21. (5,1) (8,2) (14,3) RM algorithm
• first x units of (8,2) nonpreemptable, what is
  the max x for it to remain schedulable?

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Ch 7 Sample Problems

• 7.1. (2.5,1) (4,0.5) (5, 0.75) periodic server
  (2,0.5). RM algorithm
• S1(3,0.75) and S2(7.5,0.6)
• response times of S1 and S2 using polling server
• response times of S1 and S2 using sporadic server
• response times of S1 and S2 using deferrable
  server
• modify periodic server to (1,0.25) keeping
  utilization same)
• response times of S1 and S2 using sporadic server
• response times of S1 and S2 using deferrable
  server
• more interesting problem periodic server (4,1).
• response times improved ??

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Ch 7 Sample Problems

• 7.3. (10,2) (14,3) (21,4) periodic server ps
  8.
• RM algorithm
• if server deferrable, maximum execution time of
  server?
• if server sporadic, maximum execution time of
  server?
• EDF algorithm
• if server total bandwidth, maximum server size?

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Ch 7 Sample Problems

• Determine if each of the following sporadic jobs
  will be accepted given tasks (10,3) (12,3)(20,5)
  scheduled with EDF.
• (2,1,8)
• (3,2,15)
• (7,1,13)
• Determine if each of the following sporadic jobs
  will be accepted given tasks (10,3) (12,3)(20,5)
  scheduled with RM.
• (2,1,8)
• (3,2,15)
• (7,1,13)

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Priority Scheduling

• Assigning Priority
• task-level fixed (RM, DM)
• task-level dynamic, job-level fixed (EDF)
• Schedulability Test
• Schedulable (Breakdown) Utilization
• Time-Demand Analysis
• Assumptions
• Preemptable at any time.
• No self-suspension.
• Independence.

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Non-Preemptability and Self-Suspension

• Priority Inversion task of lower priority
  executing while higher priority task waits.
• Blocking Time time higher priority task waits
  while lower priority task executing.

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Consequences of Blocking

• Job waits (self-suspends) until resource
  available,
• thus it is blocked by another job.
• If you use self-suspension exclusively
• to control access to resources
• BAD THINGS CAN HAPPEN
• Unbounded priority inversion wait is
  potentially infinite.
• Deadlock job A waits for job B, job B waits for
  job A.

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Unbounded Priority Inversion
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Unbounded Priority Inversion
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Deadlock

• Critical sections can be nested, thus jobs can
  hold locks to multiple resources at one time.

J1
J2
J1
J2
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Sharing Resources Control Protocols

• Resource Access Control Protocols
• Nonpreemptive Critical Section (NPCS)
• Basic Priority-Inheritance Protocol
• Basic Priority-Ceiling Protocol
• Stack-Based, Priority-Ceiling (Ceiling-Priority)
  Protocol
• Distinguished by
• Scheduling Rule
• Allocation Rule
• Priority Rule
• Implementation
• Priority Algorithm (fixed or dynamic)
• Simplicity of implementation (a priori
  information)
• Addresses concerns
• Unbounded Priority Inversion
• Deadlock
• Blocking Time

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Nonpreemptive Critical Sections (NPCS)

• Job locks resource and hogs processor.
• Rules of NPCS
• Scheduling Rule
• Ready jobs scheduled on the processor
  preemptively (but nonpreemptively when using a
  resource).
• Allocation Rule
• Jobs granted resource when requested. (Resource
  guaranteed to be free at time of request.)
• Priority Rule
• Priority set to MAX when using resource
  (effectively running nonpreemptively).

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NPCS
Fig 8-7a
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NPCS Good and Bad

• Job locks resource and hogs processor.
• GOOD
• Simple
• No deadlock.
• No unbounded priority inversion
• No prior knowledge about resources.
• Works with fixed and dynamic priorities.
• (especially good for short critical sections with
  high contention)
• BAD
• Tasks blocked even when no contention exists.
• Time-Demand Analysis
• Each task blocked by at most 1 task of lower
  priority
• Block time added to time-demand wi
• bi(rc) ?Tk i lt k ? n max (ck)
• (i.e. max exec time while locking resource)

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Problem with NPCS
Fig 8-7a
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Basic Priority Inheritance Protocol
R resource J job holding resource JB job
requesting resource

• Rules of Basic Priority Inheritance
• Scheduling Rule
• Ready jobs scheduled preemptively at assigned
  priority except as indicated by priority rule.
• Allocation Rule
• if resource free, allocate.
• else, block.
• Priority Rule
• if JB blocked by J, J inherits current priority
  of JB.
• once R released, returns to priority at time of
  acquiring R.

• J gets resource R
• JB requests resource R, but blocked
• J inherits current priority of JB

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Fixing NPCS with Priority Inheritance
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Example of Basic Priority Inheritance Protocol
When job JB blocked by J due to resource R, J
inherits current priority of JB When job J
releases R, priority of J returns to priority at
time of blocking JB
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Listing Resource Access
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Basic Priority Inheritance Protocol and Deadlock
DOES NOT PREVENT DEADLOCK
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Basic Priority-Inheritance Protocol Good and Bad

• When lower priority job blocks, it inherits
  priority of blocked job.
• GOOD
• No unbounded priority inversion
• Simple
• No prior knowledge required
• Works with fixed and dynamic priorities.
• BAD
• Deadlock.
• Blocking of jobs not in resource contention.
• Blocking time could be better. (Fig 8.10)
• Time-Demand Analysis
• Fig. 8-9
• v resources, k lower priority jobs in conflict
• min(v,k)(length of critical section)

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Worst-Case Block Time
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Basic Priority Ceiling Protocol

• Ceiling of Resource Ri ?(Ri) max priority of
  all jobs needing Ri
• Ceiling of System ?(t) max ceiling of all
  resources in use at time t
• Resource allocated only when
• Scheduling
• Ready jobs scheduled preemptively at assigned
  priority except as indicated by priority rule.
• Allocation
• if resource locked, job is blocked.
• if resource free
• if ?(job) gt ? (t) allocate
• else if job holding some Ri s.t. ?(t) ?(Ri)
  allocate
• else block
• Priority Inheritance
• J inheriets current ?(JB)
• When job releases all resources with ?(Ri)
  ?(t),
• job returns to priority at time of acquiring
  resource(s).

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Example of Basic Priority Ceiling Protocol
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Basic Priority Ceiling and Deadlock

• Allocation
• if resource locked, job is blocked.
• if resource free
• if ?(j) gt ? (t) allocate
• else if job holding some Ri s.t. ?(t) ?(Ri)
  allocate
• else block
• At any time t, if ?i(j) gt ?(t) then
• job Ji will not require any resource currently in
  use
• any Jk with ?k gt ?j will not require any resource
  currently in use
• In other words
• no job currently holding a resource can inherit a
  higher priority and preempt Ji

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Basic Priority Ceiling and Deadlock
Preventing Deadlock
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Basic Priority-Ceiling Protocol Good and Bad

• Lower priority job inherits priority of blocked
  job.
• Job may be denied resource even when available.
• GOOD
• No deadlock.
• No unbounded priority inversion.
• Blocking time reduced. (Review Fig. 8-9)
• BAD
• Priorities are fixed.
• Need a priori knowledge of use of resources.
• Time-Demand Analysis
• Blocking Time Described in Section 8.5.4

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Stack-Based, Priority-Ceiling Protocol

• Simpler protocol.
• All tasks can share run-time stack.
• Scheduling
• jobs scheduled preemptively by assigned priority
  except as indicated by priority rule.
• Allocation
• allocate resource whenever requested
• Priority
• ?i max ?(Rk) of all resources held by Ji

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Stack-Based Protocol
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Basic Priority Ceiling vs Stack-Based Protocol
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Stack-Based, Priority-Ceiling Protocol Good and
Bad

• Lower priority job inherits priority of blocked
  job.
• Job may be denied resource even when available.
• GOOD
• Simple.
• Shared run-time stack.
• Reduced Context-Switching
• No deadlock.
• No unbounded priority inversion.
• BAD
• Jobs cannot self-suspend.
• Priorities are fixed.
• Need a priori knowledge of use of resources.
• Time-Demand Analysis
• Blocking Time Described in Section 8.5.4

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Sharing Resources Control Protocols

• Resource Access Control Protocols
• Nonpreemptive Critical Section (NPCS)
• Basic Priority-Inheritance
• Basic Priority-Ceiling Protocol
• Stack-Based, Priority-Ceiling (Ceiling-Priority)
  Protocol
• Distinguished by
• Scheduling Rule
• Allocation Rule
• Priority Rule
• Implementation
• Priority Algorithm (fixed or dynamic)
• Simplicity of implementation (a priori
  information)
• Addresses concerns
• Unbounded Priority Inversion
• Deadlock
• Blocking Time