Scheduling Aperiodic and Sporadic Jobs in Priority- Driven Systems

Scheduling Aperiodic and
Sporadic Jobs in Priority-
Driven Systems
Outline
Liu: Chapter 7
Ingo Sander
ingo@kth.se
IL2212 Embedded Software 1
l� System Model and Assumptions
l� Scheduling Aperiodic Jobs
l� Scheduling Sporadic Jobs
IL2212 Embedded Software 2
1

Assumptions
l� Single Processor
l� Independent preemptable periodic tasks
l� Parameters of all periodic tasks are known
l� Periodic tasks meet their deadlines
l� Aperiodic and sporadic jobs are independent
of each other
l� Parameters of sporadic jobs become known
after release
System Model
Rejected Jobs
Sporadic
Jobs
Aperiodic
Jobs
Periodic
Jobs
Acceptance
Test
IL2212 Embedded Software 3
In each queue jobs are sorted
based on priority
Processor
IL2212 Embedded Software 4
2

Scheduling Algorithms
l� Aperiodic jobs
l� are always accepted
l� Scheduler tries to complete aperiodic jobs as
soon as possible
Scheduling Algorithms
l� Sporadic jobs
IL2212 Embedded Software 5
l� Scheduler decides, if job can be accepted or must
be rejected
l� Job is accepted and scheduled, if all other scheduled
jobs still meet their deadlines
l� Otherwise job is rejected
IL2212 Embedded Software 6
3

Scheduling Algorithm
l� A scheduling algorithm is correct, if it only
produces correct schedules of the system
l� A correct schedule is a schedule where
periodic tasks and accepted sporadic tasks
always meet their deadlines
IL2212 Embedded Software 7
Optimality of Algorithms
l� An aperiodic job scheduling algorithm is
optimal if it minimizes either
l� the response time of the aperiodic job at the head
of the aperiodic job queue, or
l� the average response time of all the aperiodic
jobs for the given queueing discipline
IL2212 Embedded Software 8
4

Optimality of Algorithms
l� A sporadic job scheduling algorithm is
optimal, if it
l� accepts each sporadic job newly offered to the
system and schedules the job to complete in time
if and only if the new job can be correctly
scheduled in time by some means
IL2212 Embedded Software 9
Scheduling Aperiodic Jobs
l� In the following several different algorithms to
schedule aperiodic jobs are discussed
l� Assumption here:
l� No sporadic jobs
IL2212 Embedded Software 10
5

Background Execution
l� Aperiodic jobs are only scheduled and
executed at times, when there is no periodic
or sporadic job ready for execution
Background Execution
T 1
T 2
0 3 6 9
0 3 6 9
Background A
A
0.1
0.8
IL2212 Embedded Software 11
T 1 = (3,1), T 2 = (10,4)
IL2212 Embedded Software 12
6

Background Execution
l� Advantage: simple algorithm
l� Disadvantage: aperiodic jobs are often
executed very late
l� Possible improvement: slack stealing (as
shown in chapter 5 for clock-driven systems)
l� slack stealing can greatly improve the
performance, but is much more complex in
priority-driven systems
Periodic Server
IL2212 Embedded Software 13
l� A task that behaves more or less like a
periodic task and is created to execute
aperiodic jobs is called a periodic server
l� A periodic server is defined partially by
execution time e S and period p S
l� The parameter e S is the execution budget of
the server
l� The ratio u S = e S / p S is the size of the server
IL2212 Embedded Software 14
7

Periodic Server
l� When the server is scheduled and executes
aperiodic jobs, it consumes its budget at the
rate of 1 per time unit
l� The budget is exhausted, when it reaches 0
l� A time instant when the budget is replenished
(reloaded) is called replenishment time
Periodic Server
IL2212 Embedded Software 15
l� A periodic server is backlogged whenever the
aperiodic job queue is non-empty
l� It is idle when the queue is empty
l� The server is eligible for execution only when
it is backlogged and has non-zero budget
IL2212 Embedded Software 16
8

Polling Server
l� A polling server (p s , e s ) is a periodic server
l� When executed, it executes an aperiodic job,
if the aperiodic job queue is non-empty
l� Poller suspends execution or is suspended
by the scheduler either
l� when it has executed for e s , or
l� when the aperiodic job queue becomes empty
Polling Server
l� Consumption Rules
IL2212 Embedded Software 17
l� The budget is immediately consumed when the
server is not scheduled
l� Replenishment Rules
l� The budget is replenished to e s at the beginning of
each period
l� Example: Liu, Figure 7.2b, p.193
IL2212 Embedded Software 18
9

Polling Server
T 1 = (3,1), T 2 = (10,4), Poller =(2.5, 0.5)
Poller
T 1
T 2
0 2.5 5.3
9
0 3 6 9
0 3 6 9
A
0.1
0.8
Polling Server
IL2212 Embedded Software 19
l� Aperiodic jobs that arrive after the release
time of the poller must wait until next polling
period
l� Execution budget is not preserved
l� Simple to prove correctness
IL2212 Embedded Software 20
10

Bandwidth-Preserving Servers
l� A bandwidth-preserving server is a periodic
server
l� Compared to polling server bandwidth
preserving servers try to preserve their
budget when they are not executed
l� Additional rules for consumption and
replenishment
IL2212 Embedded Software 21
Bandwidth-Preserving Servers
l� A backlogged bandwidth-preserving server is
ready for execution when it has budget
l� Scheduler keeps track of the consumption of
the server budget
l� If budget is exhausted server becomes idle
IL2212 Embedded Software 22
11

Bandwidth-Preserving Servers
l� Scheduler moves server back to ready
queue, when budget is replenished and
server is backlogged
l� If a new aperiodic job arrives an idle server
becomes backlogged and is put into the
ready queue when it has budget
Deferrable Server
IL2212 Embedded Software 23
l� Simplest bandwidth preserving server
l� Consumption rule
l� The execution budget of the server is consumed
at the rate of one unit per time whenever the
server executes
l� Replenishment rule
l� The execution budget of the server is set to e s at
multiples of its period
l� Server is not allowed to cumulate budget
from period to period
IL2212 Embedded Software 24
12

Deferrable Server (RMS)
T DS = (3,1), T 1 = (2,3.5,1.5), T 2 =(6.5, 0.5)
T DS
T 2
0 2.8 5.3
9
T 1
2 3 6 9
0 3 6 9
1.7
Budget
1.0
0.5
2.8
A
IL2212 Embedded Software 25
Schedulability of Deferrable
Servers
l� Time Demand Analysis can be used to determine
whether all jobs remain schedulable in the presence
of a deferrable server
l� Time Demand Function (if deferred server has
highest priority)
Blocking
Server
IL2212 Embedded Software 26
13

Deferrable Server
Time Demand Analysis
Time Demand
6
5
4
3
2
1
0
T DS = (3,1), T 1 = (2,3.5,1.5), T 2 =(6.5, 0.5)
w 1 (t)
w 2 (t)
y(t) = t
1 2 3 4 5 6 7 8
Deferrable Server
Time
IL2212 Embedded Software 27
Schedulability of Deferrable
Servers
l� There is no known schedulability utilization
that ensures the schedulability of a fixedpriority
system in which a deferrable server is
scheduled at an arbitrary priority
l� Some special cases are discussed in the
book (Liu p.201)
IL2212 Embedded Software 28
14

Limitations of Deferrable
Servers
l� Deferrable servers may be scheduled longer
than its execution time in a time interval as
long as its period
l� Lower priority task may be delayed longer by
a deferrable server than by a periodic task
with same period and execution time
Deferrable server does not behave as a periodic task
Sporadic Server
l� Bandwidth preserving server
IL2212 Embedded Software 29
l� More complex consumption and
replenishment rules ensure that each
sporadic server with period p s and budget e s
never demands more processor time than the
periodic task (p s , e s ) in any time interval
IL2212 Embedded Software 30
15

A simple Fixed-Priority
Sporadic Server
l� Definitions (Liu p.205)
l� t r denotes the latest actual replenishment time
l� t f denotes the first instant after t r at which the
server begins to execute
l� t e denotes the latest effective replenishment time
A simple Fixed-Priority
Sporadic Server
l� Definitions (Liu p.205)
IL2212 Embedded Software 31
l� At any time t, BEGIN is the beginning instant of the earliest
busy interval among the latest contiguous sequence of
busy intervals of the higher priority subsystem T H that
started before t
l� END is the end of the latest busy interval in the above
defined sequence if this interval ends before t and equal to
its infinity if the interval ends after t
l� Server Busy Interval: Begins when an aperiodic job
arrives at an empty aperiodic job queue and ends
when the queue becomes empty again
IL2212 Embedded Software 32
16

Fixed-Priority Simple Sporadic
Server
l� Consumption Rules (Liu p.206)
l� At any time t after t r , the server’s execution budget
is consumed at the rate of 1 per unit time until the
budget is exhausted when either one of the
following to conditions are true. When these
conditions are not true, the server holds its budget
l� C1 The server is executing
l� C2 The server has executed since t r and END < t
IL2212 Embedded Software 33
Fixed-Priority Simple Sporadic
Server
l� Replenishment Rules (Liu p.206)
l� R1 Initially when the system begins execution
and each time when the budget is replenished,
the execution budget = e s , and t r = the current
time
l� R2 At time t f , if END = t f , t e = max(t r , BEGIN). If
END < t f , t e = t f . The next replenishment time is
set at t e + p s
IL2212 Embedded Software 34
17

Fixed-Priority Simple Sporadic
Server
l� Replenishment Rules (Liu p.206)
l� R3 The next replenishment occurs at the next
replenishment time, except under the following
conditions. Under these conditions,
replenishment is done at times stated below
a) If the next replenishment time t e + p s is earlier than t f ,
the budget is replenished as soon as it is exhausted
b) If the system T becomes idle before the next
replenishment time t e + p s and becomes busy again at
t b , the budget is replenished at min(t e + p s , t b )
IL2212 Embedded Software 35
Simple Fixed-Priority Sporadic
Server
l� Example: Liu, Figure 7-8, p.207
IL2212 Embedded Software 36
18

T 1
T 2
T S
Simple Fixed-Priority Sporadic
Server - Example
T3 0 3 6 9 12 15 18 21 24
1.0
2.0
2.0
Budget
1.5
1.0
0.5
3
T 1 = (3,0.5), T 2 = (4,1), T 3 = (19,4.5) T S =(5, 1.5)
A1
C1
C1
C2
7
A2
C1
C1
C2
0 3 6 9 12 15 18 21 24
15.5
C1
C1
A3
IL2212 Embedded Software 37
Simple Fixed-Priority Sporadic
Server - Example
t t r t f t e BEGIN END
3.5 0 3.5 3 3 3.5 R2: t e = max(0,3.0)
=> t r + = te + t s = 8.0
3.5
5.0
IL2212 Embedded Software 38
C1
C2
C2
C1: Server executes
C2: Queue Empty, higher
priority jobs idle
8 R3: Replenishment
9.5 8 9.5 3 8 9.5 R2: t e = max(8,8)
=> t r + = te + t s = 13.0
19

Simple Fixed-Priority Sporadic
Server - Example
t t r t f t e BEGIN END
13.5 13 13.5 13 12 13.5 R2: t e = max(13,12)
=> t r + = te + t s = 18.0
13.5 System T idle!
R3b: t r + = min(te + p s , t b )= 15.0,
since system (T 1 ) becomes
busy at 15
15.5 15 15.5 15 15.5 R2: t e = max(15,15)
=> t r + = te + t s = 20.0
18.5 System T idle!
R3b: t r + = min(te + p s , t b )= 19.0,
since system (T 3 ) becomes
busy at 19
IL2212 Embedded Software 39
Fixed-Priority Sporadic Server
l� Sporadic server is more complex than polling or
deferrable servers due to more complex
consumption and replenishment rules
l� Main advantage: schedulability easy to demonstrate
l� A sporadic server can be treated like a periodic task
when we check for schedulability
l� System with sporadic server may be schedulable
while the corresponding deferrable server is not
l� More complex sporadic servers exist (Liu: 7.3.2)
IL2212 Embedded Software 40
20

Sporadic Dynamic-Priority
Servers
l� Sporadic servers can also be used for
dynamic-priority (deadline-driven) systems
l� Rules have to be adapted to EDF or LST
l� Also here sporadic server can be treated as
normal task for schedulability analysis
IL2212 Embedded Software 41
Other Bandwidth Preserving
Servers
l� Other bandwidth preserver algorithms are
based on general processor sharing (GPS)
algorithms (deadline-driven algorithms)
l� Examples:
l� Constant utilization server
l� Total bandwidth server
l� Weighted round-robin server
l� Exact functionality not discussed in course,
instead see Liu: 7.4
IL2212 Embedded Software 42
21

Scheduling Sporadic Jobs
l� Sporadic jobs
l� Scheduler decides, if job can be accepted or must
be rejected
l� Job is accepted and scheduled, if all other scheduled
jobs still meet their deadlines
l� Otherwise job is rejected
l� Sporadic job is denoted by S i (r i , d i , e i )
IL2212 Embedded Software 43
Acceptance Test in Fixed-
Priority System
l� Sporadic server can be used to execute
sporadic jobs in a fixed-priority system
l� The sporadic server (p s , e s ) has e s units of
processor time every p s units of time
IL2212 Embedded Software 44
22

Acceptance Test in Fixed-
Priority Systems
l� For each new sporadic job S (r, d, e) it must
be checked, if
l� new job can be scheduled together with the
sporadic jobs that have deadline before d
l� sporadic jobs with deadline larger or equal to d
can still be scheduled
l� Acceptance test is quite complex, but may
still be feasible for many systems
IL2212 Embedded Software 45
Acceptance Test in Fixed-
Priority Systems
l� Accepted sporadic jobs are ordered among
themselves on EDF basis
l� For the first sporadic job S 1 (t, d s,1 ,e s.1 ) the
server has at least floor((d s,1 – t)/p s ) e s units of
processor time available
l� Thus first job is accepted, if the slack of the
job
σ s,1 (t) = floor((d s,1 – t)/p s ) e s – e s,1
is larger than or equal to 0.
IL2212 Embedded Software 46
23

Acceptance Test in Fixed-
Priority Systems
l� When there are already n accepted sporadic jobs in
the system, the scheduler computes the slack σ s,i of
S i according to
where ξ s,k is the execution time of the completed
portion of the sporadic job S k
IL2212 Embedded Software 47
Acceptance Test in Fixed-
Priority Systems
l� If the slack σ s,i for the new sporadic job is not less
than 0, we have to check, if all accepted jobs can
still meet their deadline
l� For each sporadic job S k which has an equal or later
deadline the S i we have to check, if the slack σ s,k is
larger than the execution time of the new sporadic
job e s,i
l� The new sporadic job is only accepted, if this is the
case for all accepted sporadic jobs
IL2212 Embedded Software 48
24

Summary
l� Servers can be used for the efficient
scheduling of aperiodic and sporadic jobs
l� Servers have consumption and
replenishment rules, which can be arbitrarily
complex
l� Implementation overhead can be significant
IL2212 Embedded Software 49
25