Scheduling Algorithms for Multiprogramming in a Hard-Real-Time Environments Gracia Yuen

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Scheduling Algorithms for
Multiprogramming in a
Hard-Real-Time Environments

Gracia Yuen
UM
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Agenda
1
Target of the presentation
2
Background
3
A Fixed Priority Scheduling Algorithm
5
A Deadline Driven Scheduling Algorithm
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A Mixed Scheduling Algorithm
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Algorithm Comparison
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Conclusion
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Target of the presentation

• Discuss the proper algorithm of multiprogram
  scheduling for services in Hard-Real-Time
  environment on a single processor.
• Based on existed two ideas
• 1. Fixed priority scheduling
• 2. Dynamically assigning priority scheduling.
• try to find an optimum combination idea for
  the Hard-Real-Time services.

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Background
2-1
Requirements Background
2-2
Definition of Concept
2-3
Constraint Conditions of Modeling
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Background 2-1 Requirements Background

• 1. Design is triggered requirements.
• The rapidly increased computer use for
  ControlMonitoring of industrial processes.
• 2. The validity of embedded realtime system
  includes
• 1) the correctness of the program logic
• 2) meet the time constraint condition.

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Background 2-1 Requirements Background

• 3. Based on the requirements of Real-Time,
  real-time system can be divided as
• 1) Hard-real-time
• it is mandatory to meet the deadline of
  response time
• 2) Soft-real-time
• a statistical distribution of response
  times is acceptable

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Background 2-1 Requirements Background

• 4. Based on scheduling, real-time system can be
  divided as
• 1) Static Scheduling
• Algorithms are based on RMS
• 2) Dynamic Scheduling
• Algorithms are based on EDF or LLF.

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Background 2-1 Requirements Background

• 5. Based on Real-Time Scheduling, real-time
  system can be divided as
• 1) single processor scheduling
• 2) centralized multiprocessor scheduling
• 3) distributed processor scheduling

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Background 2-1 Requirements Background

• 6. Based on whether or not preemption is
  available, real-time system can be divided as
• 1) preemptive scheduling
• 2) non-preemptive scheduling
• 7. This paper is discussed Only on
• 1) single process system
• 2) preemptive scheduling

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Background 2-2 Definition of Concept

• 2. Function
• 1) More than 1 functions on a computer
• 2) Associated with a set of tasks
• 3. Task
• 1) Time-driven
• 2) Processes a fixed time to elapse/task.
• gt service is guaranteed in the time.
• 3) Preemptive

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Background 2-3 Constraint Conditions of Modeling

• 1. Task
• 1) Periodic task
• 1gt independent
• 2gt has deadline
• consist of run-ability constraints
  Only
• no queuing problem for individual
  task
• 3gt constant interval between tasks
• Note Periodic task is one scenarios of tasks in
  time-critical control monitoring functions.

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Background 2-3 Constraint Conditions of Modeling

• 4gt run-time of each task is constant
• run-time is an approximation value
• the maximum processing time for a
  task
• task ti
• tast requirest period Tm
  1/requiret-rate
• 2) Non-Periodic task
• 1gt Initialization or Failure RR
• 2gt no critical deadline

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Background 2-3 Constraint Conditions of Modeling

• 2. Assumptions
• The requests for all tasks for which hard
  deadlines exist are periodic, with constant
  interval between requests.
• Deadlines consist of run-ability constraints only
  i.e. each task must be completed before the
  next request for it comes.
• gteliminates queuing problem for the
  individual task.

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Background 2-3 Constraint Conditions of Modeling

• 2. Assumptions
• The tasks are independent in that requests for a
  certain task do not depend on the initiation or
  the completion of requests for other tasks.
• Run-time for each task is constant for that task
  and does not vary with time. Run-time here refers
  to the time which is taken by a processor to
  execute the task without interruption.

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Background 2-3 Constraint Conditions of Modeling

• 2. Assumptions
• Any non-periodic tasks in the system are special
  they are initialization or failure-recovery
  routines they displace periodic tasks while they
  themselves are being run, and do not themselves
  have hard, critical deadlines.
• Delays caused by the single processor, the
  preemptive scheduling and task switching, are
  ignored.

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Background 2-3 Constraint Conditions of Modeling

• 3. Scheduling algorithms will be discussed
• 1) Fixed priority scheduling
• 2) Dynamic priority scheduling
• priorities of tasks might change from
  request
• to request.
• 3) Mixed scheduling algorithm
• the priority of some tasks are fixed and
  others are vary from request to request.

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A Fixed Priority Scheduling Algorithm
3-1
Scheduling Algorithm Concepts
3-2
Modeling
3-3
Theorem Proof
3-4
Processor Utilization
3-5
Relaxing the Utilization Bound
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A Fixed Priority Scheduling Algorithm

• 1. Scheduling Algorithm Concepts
• 1) Deadline of a request for a task (point of
  time)
• the time of the next request for the same
  task
• if t is the deadline of an unfulfilled
  request,
• gt an overflow occurs at t
• 2) Critical Instant for a task (point of
  time)
• is used to determine the algorithm
• If t critical instant,
• a request for the task will have the largest
  
• response time

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A Fixed Priority Scheduling Algorithm

• 3) response time of a request for a task
  (duration)
• the time span t(request), t(the end of
  the response to the request)
• 4) Critical time zone for a task (duration)
• the time interval t(a critical instant),
• t(the end of the response to
  the corresponding request of the task)

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A Fixed Priority Scheduling Algorithm
Obviously, the fixed one is a RMS algorithm.
(Rate-Monotonic Scheduling)
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A Fixed Priority Scheduling Algorithm
2. Modeling 1) Allocation of Priority
Priority is inversely proportional to Period of
request 2) Schedulability Analysis CPU
Utilization U sum(Ci/Ti) Ult1
Otherwise, the tasks can not be scheduled in the
single processor system.

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A Fixed Priority Scheduling Algorithm
2. Modeling 3) Defination si is a period
task and defined as si(Ti,Ci,Di) Ti is the
Request_Period of si the reciprocal(the
request rate) task with lower
Request_Period will have higher Priority
task with higher Rquest_Rate will have higher
Priority Ci is the respective
rum-times(processor time spent) Di is the end
of the request period
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A Fixed Priority Scheduling Algorithm

• 3. Theorem Proof
• 1)Theorem 1
• A critical instant for any task occurs
  whenever the task is requested simultaneously
  with requests for all higher priority tasks.
• Proof
• The delay in the completion of si is the
  largest
• when t2 coincide with t1

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A Fixed Priority Scheduling Algorithm

• Effect
• I. One of the values of this result is that a
  simple direct calculation can determine whether
  or not a given Priority assignment will yield a
  feasible scheduling algorithm.
• If 1gt it can schedule a set of tasks
• 2gt the requests for all tasks at their
  critical instants are fulfilled before their
  respective deadlines.
• gt it is a feasible scheduling algorithm.

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A Fixed Priority Scheduling Algorithm
T12, T25 C11, C21

• (a) (T1 higher priority) Feasible
• (b) (T1 higher priority) C2 can be increased to 2
• (c) (T2 higher priority) C1 and C2 can be at most
  1

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A Fixed Priority Scheduling Algorithm

• Q In figure2, for task 2, plz answer below
  items
• deadline,
• critical instant,
• the end of respond end,
• response time,
• critical time zone?
• My understanding
• as the critical time zone in Figure 2, for
  task2, the end of the response is 5, actually
  task2 is finished to response at 2. right?
• a new request can come at t5, gt 5 is
  deadline.

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A Fixed Priority Scheduling Algorithm

• A1, all the tasks have periodic requests,
• A4, run-times is constant.
• gt otherwise,critical time zone can be defined
  as the time zone between its request and
  deadline, if the task has the highest priority.

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A Fixed Priority Scheduling Algorithm

• Effect
• II.Every fixed priority assignments rule can be
  scheduled by the RMPA(rate-monotonic priority
  assignment).
• Reason Precondition is (T12) lt (T2 5)
• 1) Priority(S1) gt Priority(S2)
• need to meet (T2/T1)C1 C2 lt T2
• Request_Rate(S1) gt Request_Rate(S2)
• 2) Priority(S1) lt Priority(S2)
• need to meet C1 C2 lt T1, Or
• (T2/T1)C1 (T2/T1)C2 lt
  (T2/T1)T1 lt T2
• gt the algorithm is feasible for both of the two
  cases.

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A Fixed Priority Scheduling Algorithm

• Effect
• gt More generally,
• the rule of Priority assignment is to assign
  priority to tasks according to their
  Request_Rate, independent of their of their
  run-times(C1,C2)
• gt task with higher Request_Rate will have a
  higher Priority. Or,
• task with lower Request_Period(T1,T2)
  will have a higher Priority.

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A Fixed Priority Scheduling Algorithm

• Effect
• for(T12) lt (T2 5)
• gt Request_Period(T1) lt Request_Period(T2)
• gt S1 has higher Request_Rate
• gt S1 has a higher Priority
• The way to assign Priority to tasks is
  called RMPA(Rate Monotonic Priority Assignment)
• The algorithm of RMPA is called
• RMS(Rate-Monotonic Scheduling)

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A Fixed Priority Scheduling Algorithm

• 3. Theorem Proof
• 2) Theorem 2
• If a feasible priority assignment exists for
  some task set, the rate-monotonic priority is
  feasible for that task set.
• If a static scheduling algorithm exists for
  some task set, RMS is feasible for the task set.

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3
A Fixed Priority Scheduling Algorithm

• Proof Exchange Algorithm
• 1gt Assumption
• If a static scheduling algorithm, RMS1, exists
  for some task set
• Sa,Sb is 2 tasks of adjacent priorities in the
  task set, and Priority(Sa)gt Priority(Sb),
• But, Request_Period Ta gt Tb

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A Fixed Priority Scheduling Algorithm

• 2gt Proving process
• Obviously, it differs with definition of RMS.
• In order to be in accord with RMS
• gt Action exchange the priorities of Sa,Sb
• gt the resultant priority assignment is still
  feasible.
• 3gt Conclusion
• RMPA can be obtained from any Priority
  ordering by a sequence of pairwise priority
  re-ordering.

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A Fixed Priority Scheduling Algorithm

• 4gt Significance
• Advantage
• RMS is proved as the optimum of static
  scheduling algorithm, more feasible, little
  overhead
• Disadvantage
• Processor Utilization is not high
• When n?8,
• Processor utilizationln2 70.

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A Fixed Priority Scheduling Algorithm

• 5gt Question?
• scenario Priority Inversion
• in real-time system, resources are shared by
  real-time tasks, it may happens that a lower
  priority task will block the processing of a task
  with higher priority.
• gt deadlock happens!!!
• gt RMS cannot provide a proper schedule for
  the set of task.
• Any solution?

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A Fixed Priority Scheduling Algorithm

• 6gt Solution
• Control the time of priority inversion to
  be limited
• Based on requirements, it needs some
  protocol to ensure that.

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A Fixed Priority Scheduling Algorithm

• 4. Processor Utilization
• 1) The least upper bound to PU in a fixed
  priority systems.
• PU factor
• Ci increases, or Ti decreases,
• gt U is improved.
• Note Precondition is all tasks satisfy their
  deadlines at their Critical _Instant.

U S (Ci/Ti) Trequest periods 1/Tfrequency Cru
n-time
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A Fixed Priority Scheduling Algorithm

• 4. Processor Utilization
• 2) Significance
• the least upper bound of UP factor is
• the minimum of the PU factors over all sets of
  tasks that fully utilize the processor.
• For all task sets whose PU factor is below
  this bound, there exists a fixed priority
  assignment which is feasible.
• For PU factor is above this bound can only be
  achieved if the of the tasks are suitably
  related.

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A Fixed Priority Scheduling Algorithm

• 4. Processor Utilization
• 2) Significance
• The least upper bound to be determined is the
  infimum of the utilization factors corresponding
  to the RMPA over all possible Request_Period and
  run-times for the tasks.
• The least upper bound is firstly determined
  for two tasks, then extended for an arbitrary
  number of tasks.

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A Fixed Priority Scheduling Algorithm

• 4. Processor Utilization
• 3) Theorem 3
• For a set of 2 tasks with fixed priority
  assignment, the least upper bound to the PU
  factor is U 2(2(1/2)-1)
• Such as if the Request_Period, Tb, for the
  lower Priority task is a multiple of the other
  tasks Request_Period, Ta.
• for U 1- f(1-f)/(If), ITb/Ta, f
  Tb/Ta
• gt when f 0, PU factor U1

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3
A Fixed Priority Scheduling Algorithm

• 4. Processor Utilization
• 4) Theorem 4
• For a set of m tasks with fixed priority
  order, and
• the restriction that the ratio between any
  two Request_Period, Tb/Talt2,
• the least upper bound to the PU factor is
• U m(2 1/m -1)

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3
A Fixed Priority Scheduling Algorithm

• 4. Processor Utilization
• 5) Theorem 5
• For a set of m tasks with fixed priority
  order,
• the least upper bound to PU is U m(2 1/m
  -1)
• gt to determine the least upper bound of the
  PU factor, we need only consider task sets in
  which the ratio between any two
  Request_Period,Tb/Ta, is less than 2

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A Fixed Priority Scheduling Algorithm

• 5. Relaxing the Utilization Bound
• Limitation
• for real-time guaranteed service, the least
  upper bound can approach ln2 for large task sets.
  
• How to improve the situation?
• if f Tm/Ti0, for i1,2,,(m-1).
• But, it cannot always be done.

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A Fixed Priority Scheduling Algorithm

• 5. Relaxing the Utilization Bound
• alternative solution
• 1. buffer the lower priority task, Sm, and
  perhaps several of the lower priority tasks.
• 2. relax their head deadlines.
• suppose
• 1. the entire task set has a finite period
• 2. the buffered tasks are executed in some
  reasonable fashion.

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A Fixed Priority Scheduling Algorithm

• 5. Relaxing the Utilization Bound
• gt Delay_Timem amount of buffering required
• can be computed.
• gt Dynamic fashion is a better solution,
• with PU factor 100.

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A Deadline Driven Scheduling Algorithm
4-1
DDSA Policy of Priority setting
4-2
Necessary and sufficient condition
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A Deadline Driven Scheduling Algorithm

• DDSA
• Deadline Driven Scheduling Algorithm
• it is Dynamic Scheduling Algorithm
• called in the paper.
• Policy of Priority setting
• Priority is assigned to a task according to
  the deadline of its current request.

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A Deadline Driven Scheduling Algorithm

• Dynamic Scheduling Algorithm
• that means,
• if the deadline of the tasks current request
  is the nearest,
• gta task will be assigned the highest priority
• if the deadline of the tasks current request
  is the furthest,
• gt a task will be assigned the lowest priority

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A Deadline Driven Scheduling Algorithm

• 2. Necessary and sufficient condition for the
  feasibility of the algorithm.
• Theorem 6
• When the DDSA is used to schedule a set of
  tasks on a single processor, there is no
  processor idle time prior to an overflow.

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A Deadline Driven Scheduling Algorithm

• 2. Necessary and sufficient condition for the
  feasibility of the algorithm.
• Theorem 7
• For a given set of tasks, the DDSA is
  feasible if and only if,
• (C1/T1) (C2/T2) (Cm/Tm) lt 1
• Judgment is rest on
• if the total demand gt the available processor
  time
• gt it is not a feasible scheduling algorithm

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A Mixed Scheduling Algorithm
5-1
Concept
5-2
Mathematical results
Theorem Proof
Processor Utilization
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A Mixed Scheduling Algorithm

• 1. Concept
• MSA are combinations of RMSA and DDSA
• 2. Mathematical results
• 1)Theorem 8
• If a set of tasks are scheduled by the DDSA
  on a processor whose availability function is
  sublinear, then there is no processor idle
  period to an overflow.

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A Mixed Scheduling Algorithm

• 2) Theorem 9
• A necessary and sufficient condition for the
  feasibility of the DDSA with respect to a
  processor with availability function ak(t) is
• t/Tk1 Ck1 t/Tk2 Ck2 t/Tm
  Cmltak(t)
• for all ts which are multiples of Tk1, or
  Tk2,, or Tm.

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A Mixed Scheduling Algorithm

• Notes
• ak(t) is a non-decreasing function of t.
• ak(t) is sublinear, if for all t and all T,
• a(T)lt a(tT) a(t)
• Significance
• 100 utilization is not achievable
  universally by the MSA.

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Algorithm Comparison
6-1
Advantages
6-2
Comparison
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Algorithm Comparison

• Advantage
• URMSA lt UMSA lt UDDSA
• The least upper bound is considerably less
  restrictive for the MSA than RMSA.
• URMSA is only slightly greater than the worst
  case of UMSA.
• gt MSA is preferred.

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Algorithm Comparison

• Comparison
• Example
• If T13, T24, T35, a1(20)13,
• C11, C21, C32
• Here we go
• to prove MSA is prefferred.

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Algorithm Comparison

• Based on the reasoning of Theorem 1,
• gt C1 C2C3 lt T1
• 1 1 C3 lt3
• gt C3max lt 1
• gt URMSA 1/31/41/578.3

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Algorithm Comparison

• Based on Theorem 7,
• gt C1/T1 C2/T2 C3/T3 lt 1
• 1/3 1/4 C3/5 lt1
• gt C3max lt 25/12 2.0833
• gt UDDSA 1/31/42.0833/5
• 1/31/4(25/12)/5 100

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Algorithm Comparison

• Based on Theorem 9,
• gt if k1, then t/T2C2 t/T3C3 lt a1(20)
• 20/41 20/5C3 lt 13
• gt C3max 2
• for U C1/T1 C2/T2 C3/T3
• gt UMSA 1/31/42/598.3

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Conclusion

• Problems associated with multiprogramming are
  focused in a hear-real-time environment typified
  by process control and monitoring, using some
  assumptions which characterize that application.

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Conclusion

• 3. Conclusion
• for all fixed priority scheduling algorithm
• which assigns priority to tasks in a
  monotonic relation to their Request_Rate was
  shown to be optimum among the class of all fixed
  priority scheduling algorithms.
• The least upper bound of PU factor is on the
  order of 70 for large task sets.

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Conclusion

• 3. Conclusion
• Dynamic Deadline Driven Scheduling Algorithm
• is shown to be globally optimum and capable
  of achieving 100

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Conclusion

• 3. Conclusion
• Mixed Scheduling Algorithm
• appears to provide most of the benefits of
  the Deadline Driven Scheduling Algorithm, and yes
  may be readily implemented in existing computers.

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• Q A