CprE 458/558: Real-Time Systems

1
CprE 458/558 Real-Time Systems

• Combined Scheduling of
• Periodic and Aperiodic Tasks

2
Assumptions Issues

• RMS scheduling algorithm used
• All periodic tasks start at time t0 (same as
  before)
• Periodic tasks relative deadlines are equal to
  end of period
• Arrival times of aperiodic tasks unknown
• Schedulability of periodic tasks
• Response time for aperiodic tasks
• Implementation considerations

3
Background Scheduling Algorithm

• No server is created.
• Aperiodic tasks are executed when there is no
  periodic task to execute.
• Simple, but no guarantee on aperiodic
  schedulability

Periodic tasks
RMS
CPU
High priority Queue
Aperiodic tasks
FIFO/EDF
Low priority Queue
4
Normal RMS schedule Notice the holes
Task set Ti (ci, pi) T1 (2,6) and T2 (4,10)
Schedulability check 2/6 4/10 0.33 0.40
0.73 2(v2 -1) 0. 82
Background scheduling basic idea -- Scheduling
aperiodic tasks in holes like this
T1
T11
T12
Hole
0
2
6
8
10
T2
T21
T22
6
0
2
10
Schedule continues
5
Background Scheduling Example
T1
Hole1 2 units
Hole2 2 units
T13
T14
T11
T12
18
0
2
6
8
10
T2
T21
T22
T22
6
14
16
18
0
2
10
12
Aperiodic tasks
A1
A2
6
14
16
18
0
2
10
12
RMS
Periodic tasks
CPU
High priority Queue
FIFO
Aperiodic tasks
Low priority Queue
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Combined Scheduling

• Creating a periodic server Ts(Cs, Ps) for
  processing aperiodic workload. Create one or more
  server tasks.
• Aperiodic tasks are scheduled in the periodic
  servers time slots. This policy could be based
  on deadline, arrival time, or computation time.
• Algorithms all algorithms behave the same
  manner when there are enough aperiodic tasks to
  execute
• - Polling Server (bandwidth non-preserving)
• - Deferrable Server (bandwidth preserving)
• - Priority Exchange Server (bandwidth
  preserving)
• - Sporadic Server (bandwidth preserving)

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Polling Server

• A periodic server is created.
• If there are no aperiodic tasks at an invocation
  of the server (as per RMS), the server suspends
  itself during its current period and gets invoked
  again at its next period.
• If there are enough aperiodic tasks in an
  invocation, it serves up to Cs capacity.
• The computation time allowance for the server is
  replenished at the start of its period
• Include Ts in the task set and do schedulability
  test
• Poor response time for aperiodic tasks

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Polling server Example
This aperiodic task cannot be scheduled now as
there is no server available till time 5
Task set Ti (ci, pi) T1 (1,4) , T2 (2,6)
and Ts (2,5)
Task set Ti (ci, pi) T1 (1,4) , T2 (2,6)
and Ts (2,5)
T1
8
12
16
24
0
4
20
Server becomes available and schedules aperiodic
task A1 for 2 units
Server becomes available and can schedule for 2
units. However, aperiodic task A2 needs only 1
T2
24
1
3
6
7
10
12
13
15
18
20
Waits till time 10
Waits till time 15
Preempted by T1
Aperiodic tasks
A1
A2
A3
A3
2
8
10
13
15
16
17
18
24
5
0
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Polling server Example (no animations)
Task set Ti (ci, pi) T1 (1,4) , T2 (2,6)
and Ts (2,5)
T1
8
12
16
24
0
4
20
T2
24
1
3
6
7
10
12
13
15
18
20
Aperiodic tasks
A1
A2
A3
A3
2
8
10
13
15
16
17
18
24
5
0
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Polling server Schedulability Analysis

• Schedulability analysis involves
• Schedulability of periodic tasks
• Schedulability of Aperiodic tasks
• Schedulability of periodic tasks can be evaluated
  by introducing a periodic task equivalent to the
  server. Therefore, the schedulability test is

?i1 to n (Ci / Pi) (Cs / Ps) (n1)2 1/(n1)
-1
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Polling server Schedulability Analysis

• Aperiodic task guarantees
• Consider a single aperiodic task Ai, arrived at
  ra, with computation time Ca and deadline Da.
  Since an aperiodic task can wait at most for one
  period before receiving service, if Ca Cs the
  request is certainly completed within two server
  periods. Thus it is guaranteed if 2Ps Da

Ca
Cs
Ps
Ps
da
0
ra
Da gt Ps
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Polling server Schedulability Analysis

• Aperiodic task guarantees
• For arbitrary computation times, the aperiodic
  task is certainly completed in ceil(Ca/Cs) server
  periods hence it is guaranteed if
• Ps ceil(Ca/Cs) Ps Da

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Deferrable Server

• A periodic server task is created.
• When the server is invoked with no outstanding
  aperiodic tasks, the server does not execute but
  defers its assigned time slot.
• When an aperiodic task arrives, the server is
  invoked (as per RMS) to execute aperiodic tasks
  and maintains its priority.

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Deferrable Server (Contd.)

• The computation time allowance for the server is
  replenished at the start of its period.
• Provides better response time for aperiodic tasks
  than Polling server
• Under overload, deadlines are missed predictably.
• Similar schedulability test like polling server

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Deferrable Server Example
Task set Ti (ci, pi) T1 (1,4) , T2 (2,6)
and Ts (2,5)
T1
8
12
16
24
0
4
20
Why is A2 not scheduled at time 8 itself???
T2
Dont need to wait till time 10
Dont need to wait till time 5
24
1
3
6
8
10
12
13
15
18
20
T1 runs from 8 to 9 and hence Ts a lower priority
task cannot run till 9
Aperiodic tasks
A1
A2
4
9
2
8
24
0
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Priority Exchange Server

• A periodic server task is created.
• When the server invoked, the server runs if there
  are any outstanding aperiodic tasks.
• If no aperiodic task exists, the high priority
  server exchanges its priority with a lower
  priority periodic task for a duration of Cs,
  where Cs is the remaining computation time of
  the server.

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Priority Exchange Server (Contd.)

• In this way, the priority of the server
  decreases, but its computation time is
  maintained.
• The computation time allowance for the server is
  replenished at the start of its period.
• As a consequence, the aperiodic tasks get low
  preference for execution. Offers worse response
  time compared to Deferrable Server.
• Better schedulability bound for periodic task set
  compared to Deferrable Server.

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Priority Exchange server example
Aperiodic task exists to utilize the server
capacity
TH
Cs
TS
Tf
TL
No more Aperiodic tasks to utilize the server
capacity
Server executing at TLs priority when there are
aperiodic tasks to serve
TL executing at the servers priority
TL executing at its own priority
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Sporadic Server

• This algorithm allows to enhance the average
  response time for aperiodic tasks without
  degrading the utilization bound for periodic task
  set
• This is achieved by varying the points at which
  the computation time of the server is
  replenished, rather than merely at the start of
  each server period.
• In other words, any spare capacity (i.e., not
  being used by periodic tasks) is available for an
  aperiodic task on its arrival.

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Sporadic server example
Server has the highest priority
Task set Ti (ci, pi) T1 (3,10) , T2 (4,15)
and Ts (2,8)
And, replenishes its capacity at time
current_time period
T1
10
12
16
24
15
2
0
4
20
Server has capacity to schedule A2
T2
Server schedules the aperiodic task right away
with its capacity
Server has no capacity to handle
24
5
9
15
18
20
Aperiodic tasks
A2
A1
7
12
2
10
24
0
4
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Priority-driven preemptive scheduling- summary

• Scheduling algorithms
• RMS EDF utilization test
• RMS DMS Exact analysis
• Combined Scheduling
• Polling, Deferrable, PE, Sporadic servers
• Resource Access Control
• Priority Inversion
• Priority Inheritance Pri. Ceiling Protocols
• Schedulability tests accounting Blocking