Chapter 13: Scheduling

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Chapter 13 Scheduling
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Background

• There are many ways to schedule a set of tasks
  (processes) on a processor
• The output from the program should be identical
  for all such schedules, but the timing behavior
  may differ considerably
• A scheduling scheme provides two features
• An algorithm for ordering the use of system
  resources (in particular the CPU)
• A means of predicting the worst-case behavior of
  the system when the scheduling algorithm is
  applied

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Process model

• The application consists of a fixed set of
  processes (N)
• All processes are periodic, with known periods
  (T)
• The processes are completely independent of each
  other
• All systems overheads, context-switching times
  and so on are ignored
• All processes have deadlines (D) equal to their
  periods
• All processes have fixed and known worst-case
  execution times (C)
• The processor utilization (U) of each process is
  defined as UC/T

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The cyclic executive approach

• We lay out a fixed major cycle
• The major cycle consists of a number of minor
  cycles each of fixed duration
• No actual processes exist at run-time
• Shared data do not need to be protected since
  concurrent data accesses are not possible
• All process periods must be multiples of the
  minor cycle

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The cyclic executive approach - example

• Process A, period T 25, computation time C 10
• Process B, period T 25, computation time C 8
• Process C, period T 50, computation time C 5
• Process D, period T 50, computation time C 4
• Process E, period T 100, computation time C 2

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The cyclic executive approach - example

• Loop
• Wait_for_interrupt
• Procedure_for_A
• Procedure_for_BProcedure_for_C
• Wait_for_interruptProcedure_for_AProcedure_for_
  BProcedure_for_DProcedure_for_E

• Wait_for_interrupt
• Procedure_for_A
• Procedure_for_BProcedure_for_C
• Wait_for_interruptProcedure_for_AProcedure_for_
  BProcedure_for_D
• End loop

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Process based scheduling approaches

• Fixed-Priority SchedulingEach process has a
  fixed static priority which is computed before
  the system is started.
• Earliest Deadline FirstProcesses are executed in
  the order determined by their absolute deadlines.
  The priorities are thus dynamic.
• Value-Based SchedulingThis strategy is used in
  overloaded systems, where one need to adapt the
  priorities depending on the load.

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Preemption and non-preemption

• Preemptive scheduling means that the runable
  (non-blocked) process with highest priority will
  always execute.
• Non-preemption means that a running process will
  continue to execute until it has completed it
  becomes blocked.
• Some systems allow a low-priority process to
  continue to execute for a bounded time (not
  necessarily to completion). These schemes are
  known as deferred pre-emption or cooperative
  dispatching.
• Most real-time systems use preemptive scheduling

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Rate monotonic priority assignment

• The behavior of a set of processes (tasks) using
  fixed priority preemptive scheduling is decided
  by the way we assign priorities to processes.
• The rate monotonic priority assignment scheme
  assigns priorities based on process periods (or
  deadlines) processes with short periods get
  high priority.
• The rate monotonic priority assignment scheme is
  optimal in the sense that if some task misses its
  deadline using this scheme then there is no other
  priority assignment scheme such that all tasks
  meet all of their deadlines.

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Utilization-based schedulability tests

• Consider a set of N processes.
• If the the total utilization (Sum(Ui i 1..N))
  is less than or equal to N(21/N - 1) then the
  process set is always schedulable using fixed
  priority assignment and rate monotonic priority
  assignment, i.e. all processes will always al
  their deadlines in all periods.
• For large N, the bound asymptotically approaches
  69.3, i.e. all process sets with a utilization
  less than 69.3 will always meets all deadlines
  using fixed priority scheduling and rate
  monotonic priority assignment.

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Critical instance

• The worst-case scenario (critical instance)
  occurs when all processes are released at the
  same time

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Example, Sum(U) 0.82
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Example, Sum(U) 0.775
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Example, Sum(U) 1.0
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Schedulability overview
Utilization
Unschedulable
1
Sometimes schedulable
Always schedulable
Number of processes
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Utilization-based schedulability test for
Earliest-Deadline-First

• Consider a set of N processes.
• If the the total utilization (Sum(Ui i 1..N))
  is less than or equal to 1 then the process set
  is always schedulable using earliest-deadline-firs
  t (EDF).
• N.B. EDF is a scheduling algorithm that uses
  dynamic priorities.

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Example, Sum(U) 0.82
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Fixed Priority vs. Earliest-Deadline-First

• EDF can schedule more process sets
• FPS is easier to implement
• It is easier to include processes with no
  deadlines in FPS
• It is possible to include other priority aspects
  in FPS
• The behavior of FPS is more predictable during
  overload situations

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Response time analysis for FPS

• We will now look at an exact schedulability test
• A process i is schedulable if Ri lt Ti, where Ri
  is the worst-case response time for process i
• Ri Ci Ii, where Ii is the interference from
  processes with higher priority
• The interference from a high-priority process j
  on process i is CjCeiling(Ri/Tj).
• Ri Ci Sum(CjCeiling(Ri/Tj), process j has
  higher priority than process i).
• This can be solved numerically

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Example
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Sporadic and aperiodic processes

• For sporadic and aperiodic processes we interpret
  T as the minimum inter-arrival interval.
• For sporadic tasks we usually have a deadline D
  that is shorter than the minimum inter- arrival
  time.

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Hard and soft processes

• Many systems consist of a mix of hard and soft
  processes.
• Rule 1 all processes should be schedulable
  using average execution times and average
  inter-arrival rates.
• Rule 2 all hard processes should be schedulable
  using worst-case execution times and arrival rates

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D lt T

• In this case we use deadline monotonic
  scheduling, i.e. processes are given priorities
  based on their deadlines.
• It is the same as rate monotonic scheduling when
  T D.
• Deadline monotonic scheduling is optimal.

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Priority inversion

• When processes interact we may get priority
  inversion
• Priority inversion means that a high priority
  process is waiting for a low priority process to
  complete a certain part of its execution

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Priority inversion example with two shared
resources Q and V
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Priority inheritance

• The effects of priority inversion can be limited
  by a technique called priority inheritance
• Process priorities are no longer static
• If a process A is suspended waiting for a process
  B to undertake some computation, the n the
  priority of B becomes the maximum priority of A
  and B while A is blocked waiting for B.
• With this scheme the priority of a process is the
  maximum of its own priority and the priority of
  the processes depending on it.

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Priority ceiling protocols

• The standard priority inheritance protocol gives
  a bound on the number of blocks a high-priority
  process can encounter, but the blocking effect
  can still be intolerably high
• The priority ceiling protocols minimize the
  number of such blocking periods
• There are two different priority ceiling
  protocols
• The original ceiling protocol
• The immediate ceiling protocol

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The original priority ceiling protocol

• Each process has a static default priority
• Each resource has a static priority value, which
  is the maximum priority of the processes using
  the resource
• A process has a dynamic priority that is the
  maximum of its own priority value and any it
  inherits due to blocking higher-priority
  processes
• A process can only lock a resource if its dynamic
  priority is higher than the priority of any
  currently locked resources (excluding and
  resource that it may have locked itself)

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The immediate priority ceiling protocol

• Each process has a static default priority
• Each resource has a static priority value, which
  is the maximum priority of the processes using
  the resource
• A process has a dynamic priority that is the
  maximum of its own priority value and the
  priority of any resources it has locked