CSE 522 Real-Time Scheduling (3)

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CSE 522 Real-Time Scheduling (3)

Computer Science & Engineering DepartmentArizona State University

Tempe, AZ 85287

Dr. Yann-Hang Leeyhlee@asu.edu(480) 727-7507

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Priority Inversion in Synchronization

1(H)

Blocked

2(M)

3(L)

Time

1 :{…P(S1)…V(S1)…}

3 :{…P(S1)…V(S1)…} S1 unlocked

Attempt to lock S1 (blocked) S1 locked

S1 unlocked

S1 locked

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Priority Inversion

Delay to a task’s execution caused by interference from lower priority tasks is known as priority inversion

Priority inversion is modeled by blocking time Identifying and evaluating the effect of sources of

priority inversion is important in schedulability analysis

Sources of priority Inversion Synchronization and mutual exclusion Non-preemtable regions of code FIFO (first-in-first-out) queues

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Accounting for Priority Inversion

Recall that task schedulability is affected bypreemption: two types of preemption

can occur several times per period can occur once per period

execution: once per periodblocking: at most once per period for each request to

a source

The schedulability formulas are modified to add a “blocking” or “priority inversion” term to account for inversion effects

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UB Test with Blocking

Include blocking while calculating effective utilization for each tasks:

Hn Preemption(can hit n times) Execution

Blocking H1 Preemption(can hit once)

1n Hk

kii

i

i

i

Hj j

ji e

p1

pB

pe

pe

f

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Blocking is also included in the RT test

Perform test as before, including blocking effect

RT Test with Blocking

i

1jji0

j

1i

1j j

nii1n

eBa where

epaeBa

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Consider the following examplePeriodic tasks

What is the worst case blocking effect (priority inversion) experienced by each task ?

Example: Considering Blocking

25 msec

100 msec

50 msec

200 msec

100 msec

300 msec

10 msec30 msec

Data Structure

1

2

3

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Example: Adding Blocking Task 2 does not use the data structure. Task 2 does

experiences no priority inversion Task 1 shares the data structure with 3 . Task 1 could have to

wait for 3 to complete its critical section. But worse, if 2 preempts while 1 is waiting for the data structure, 1 could have to wait for 2’s entire computation.

This is the resulting tabletask Period Execution

TimePriority Blocking

delayDeadline

1100 25 High 30+50 100

2200 50 Medium 0 200

3300 100 Low 0 300

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UB Test for Example

UB test with blocking:

1n Hk

kii

i

i

i

Hj j

ji e

p1

pB

pe

pe

f

00.105.110080

10025

pB

pef

1

1

1

11

)2(U5.020050

10025

pe

pef

2

2

1

12

)3(U84.0300100

20050

10025

pe

pe

pef

3

3

2

2

1

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Not schedulable

with additional RT test, 3 is shown to be schedulable

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Synchronization Protocols

No preemption Basic priority inheritance Highest locker’s priority Priority ceiling

Each protocol prevents unbounded priority inversion.

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Nonpreemption Protocol

2:{…P(S1)…V(S1)…}4:{…P(S1)…V(S1)…}

readyblocked

ready

ready

S1 locked S1 unlocked

Time

1(H)

4(L)

2

3

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Advantages and Disadvantages

Advantages: Simplicity Use with fixed-priority and dynamic-priority systems No priori knowledge about resource requirement by each task Good when all critical sections are short

Disadvantages: Every task can be blocked by every lower priority task, even

when there is no resource sharing between the tasks. Blocking time: max(csi)

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Basic Inheritance Protocol (BIP)

2:{…P(S1)…V(S1)…}4:{…P(S1)…V(S1)…}

ready

ready

S1 locked S1 unlocked

1(H)

4(L)

2

3

blocked

attempts to lock S1

S1 unlockedS1 locked

ready

inherits the priority of 2

after 2 is blocked

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Some Notations

Ji is the i-th job in Task T. i = Assigned priority of Job Ji

i(t) = current priority of Ji

If the decision to change the priority of Job Ji is made at t = t1 then i(t1

-) = priority at and immediately before, i(t1

+) = priority immediately after the priority change

= nonexistent priority, lower than the lowest priority

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Terminology and Assumptions At time t1, job Ji requests resource Rk. Rk Jl: Resource Rk is held by Job Jl

Ji Rk: Job Ji is blocked waiting for resource Rk to be released (Ji Rk Jl)

Scheduling Rules: Ready Jobs scheduled on processors preemptively in a

priority driven manner according to their current priorities, i(t).

At job release time the priority is equal to its assigned priority if Ji is release at t = t’, then i(t’) = i

Resource allocation: If a resource is free then it is allocated when requested if not free then the request is denied and the requesting job is

blocked

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Priority Inheritance Rules

Scheduling Rule: same as the assumptions Allocation Rule: same as the assumptions Priority-Inheritance Rule:

if Ji Rk Jl and l(t1-) = priority of Jl at t = t1

then l(t1+) = i(t1)

until Jl releases Rk at t2 when l(t2+) = l(t1

-)

L. Sha, R. Rajkumar, J. Lehoczky, “Priority Inheritance Protocols: An Approach to Real-Time Synchronization”, IEEE Transactions on Computers, Vol. 39, No. 9, pp. 1175-1185, 1990

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Properties of Priority Inheritance For each resource (semaphore), a list of blocked tasks must be

stored in a priority queue. A task (job) i uses its assigned priority, and uses (inherits) the

highest dynamic priority of all the tasks it blocks when it is in its critical section and blocks some higher priority tasks.

Priority inheritance is transitive; that is, if taski blocks j and j blocks k , then i can inherit the priority of k.

When taski releases a resource, which priority it should use?

Chained blocking if requesting multiple resources (nested mutex requests)

Direct blocking and indirect (inheritance) blocking (when the lower priority task inherits the higher priority task’s priority).

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Implementation Issues of BIP PI semaphore and basic semaphore Priority is changed when acquiring and releasing a lock When release a lock, can the priority be restore to the one

before acquiring? Need to maintain a list of PI semaphores locked by a task

when holding multiple locks and release one when a PI semaphore is deleted when a task waiting for a PI semaphore quits the waiting (due to

timeout) when the priority of a task waiting for a PI semaphore is changed

Note that for each semaphore, a queue for all waiting tasks

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Example Of Chained Blocking (BIP)1:{…P(S1)…P(S2)…V(S2)…V(S1)…}2:{…P(S1)…V(S1)…}3:{…P(S2)…V(S2)…}

S2 locked S2 unlocked

3(L)

1(H)

2(M)

B

Attempts to lock S1(blocked)

Attempts to lock S2(blocked)

B

S1 locked S1 unlocked

B

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Deadlock: Using BIP

1 :{…P(S1)…P(S2)…V(S2)…V(S1)..} 2 :{…P(S2)…P(S1)…V(S1)…V(S2)..}

S2 locked Attempts to lock S1 (blocked)

Attempts to lock S2 (blocked)Locks S1

B

2 (M)

1 (H)

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Blocking Time Under BIP Example

T1 = {.. P(A) .3. P(B) .2. V(B) .1. V(A) ..}T2 = {.. P(C) .2. V(C) ..}T3 = {.. P(A) .1. P(B) .2. V(B) .2. V(A) .. }T4 = {.. P(A) .1. P(C) .1. P(B) .3. V(B) .1. V(C) .1. V(A).. }

direct blocking by indirect blocking by blocking time

T2 T3 T4 T2 T3 T4 T2 T3 T4

T1 N Y Y 5 7

T2 N Y Y Y 5 7

T3 Y Y 7

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Priority Ceiling Protocol (PCP)

2:{…P(S1)…V(S1)…} 3:{…P(S2)…V(S2)…}4:{…P(S1)…V(S1)…}

ready

ready

1(H)

2

3

B

attempts to lock S1 S1 locked S1 unlocked

S1 locked S1 unlocked

4(L)

attempts to lock S2 S2 locked

blocked by ceiling

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Basic Priority Ceiling Rules (1) (R) = priority ceiling of resource R – the highest

priority of the tasks that request R S(t) = system priority ceiling -- the highest priority

ceiling of the resources that are in use at time t Scheduling Rule: same as the assumptions Allocation Rule:

if Ji Rk Jl at t = t1 then block Ji (no change) Rk free at t1,

if i(t1) > S(t1), then Rk Ji

else (i.e. i(t1) S(t1) )if for some Rx Ji and (Rx) = S(t1), then Rk Ji [ Ji holds a resource Rx whose priority ceiling is S(t1) ]

else deny and block (Ji Rk)

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Basic Priority Ceiling Rules (2) Priority-Inheritance Rule:

if Ji Rk at t = t1 and is blocked by Jl (and l(t1-) = priority

of Jl) either Rk Jl, (Jl holds the resource Rk)

or Jl Rx and (Rx) = S(t1) i(t1) then l(t1

+) = i(t1) (inherited priority) until Jl releases all Rx with (Rx) i(t1), l(t2

+) = l(t1-) at t

= t2.

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Blocking in PCP

A task TH can be blocked by a lower-priority task TL in three ways: directly, i.e.

when TL inherits a priority higher than the priority H of TH.

When TH requests a resource the priority ceiling of resources held by TL is equal to or higher than H:

X TLTH

request for allocated to

X TLT TH

( > H)

Y TLTH

(H X)

X

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Blocked At Most Once (PCP)

1:{…P(S1)…P(S2)…V(S2)…V(S1)…}2:{…P(S1)…V(S1)…}3:{…P(S2)…V(S2)…}

S2 locked S2 unlocked

3(L)

1(H)

2(M)

attempts to lock S1(blocked)

B

S1 locked S1 unlocked

attempts to lock S1(blocked)

S2 locked S2 unlocked

S1 locked S1 unlocked

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Deadlock Avoidance: Using PCP

Locks S2

Locks S1

Unlocks S1

Unlocks S2

Attempts to lock S1 (blocked)

Locks S1

Locks S2

C

1 :{…P(S1)…P(S2)…V(S2)…V(S1)..} 2 :{…P(S2)…P(S1)…V(S1)…V(S2)..}

2 (M)

1 (H)

Unlocks S2 Unlocks

S1

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Stack Sharing Sharing of the stack among tasks eliminates stack space

fragmentation and so allows for memory savings:

However: Once job is preempted, it can only resume when it returns to be on top

of stack. Otherwise, it may cause a deadlock. Stack becomes a resource that allows for “one-way preemption”.

T1

Ti

Tn

no stack sharing

T1

Ti

Tn

stack sharing

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Stack-Based Priority Ceiling Protocol To avoid deadlocks: Once execution begins, make

sure that job is not blocked due to resource access allow preemption only if the priority is higher than the ceiling

of the resources in use

Update Current Ceiling in the usual manner If no resource allocated, S (t) =

Scheduling Rule: Ji released and blocked until i(t) > S(t) When not blocked jobs are scheduled in the usual manner.

Allocation Rule: Allocate when requested

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Stack-Based PCP (cont)

The Stack-Based Priority-Ceiling Protocol is deadlock-free: When a job begins to execute, all the resources it will ever need are

free. Otherwise, S(t) would be higher or equal to the priority of the job. Whenever a job is preempted, all the resources needed by the

preempting job are free. The preempting job can complete, and the preempted job can resume.

Worst-case blocking time of Stack-Based Protocol is the same as for Basic Priority Ceiling Protocol.

Stack-Based Protocol smaller context-switch overhead 2 context switches since once execution starts, job cannot be blocked

(may be preempted) 4 context switches for PCP since a job may be blocked at most once

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SRP + EDF

Let 1, 2, . . . , n denote the tasks, and R1,R2, . . . , Rm denote the non-preemptable resources. Each resource Rj is statically assigned a ceiling (Rj), which is

set equal to the minimum relative deadline parameter of any task that may access it:

(Rj) = min{Di | i accesses Rj} A system ceiling is computed each instant during runtime. This is

set equal to the minimum ceiling of any resource that is currently being held by some job.

At any instant in time, a job generated by i may begin execution only if it is the earliest-deadline active job, and Di is strictly less than the system ceiling.

(From “Resource sharing in EDF-scheduled systems: a closer look,” by Sanjoy K. Baruah, RTSS’06)

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Ceiling-Priority Protocol

Re-formulation of stack-based priority ceiling protocol for multiple stacks (no stack-sharing)

Update Current Ceiling in the usual manner Scheduling Rule:

No resources held by Ji, i(t) = i

Resource held by Ji,i(t) = max((Rx)) for all resource Rx

held by Ji

FIFO scheduling among jobs with equal priority Allocation Rule:

Allocate when requested Also called: Priority ceiling emulation, highest locker

protocol, Immediate priority ceiling protocol (ICPP)

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Comparison

Worst case performance of stack-based and basic ceiling protocols are the same

Stack-based version supported by the Real-Time systems Annex of Ada95 Jobs must not self-suspend

When jobs do not self-suspend, stack-based and ceiling-priority protocols yield the same schedules.

Stack-based and ceiling-priority have the same worst-case blocking time.

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Highest Locker’s Priority Protocol

2:{…P(S1)…V(S1)…}4:{…P(S1)…V(S1)…}

ready

ready

S1 locked S1 unlocked

1(H)

4(L)

2

3

BB

run with the priority of 2

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Summary of Synchronization ProtocolsProtocol Bounded Priority

InversionBlocked at Most

OnceDeadlock

AvoidanceNonpreemptible critical sections

Yes Yes1 Yes1

Highest locker's priority

Yes Yes1 Yes1

Basic inheritance Yes No No

Priority Ceiling Yes Yes2 Yes1

1 Only if tasks do not suspend within critical sections2 PCP is not affected if tasks suspend within critical sections.

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BIP and PCP BIP

no penalty when the locks are not contended, which covers the vast majority of time-constrained systems.

many extra context switches are avoided, and medium priority tasks are not preempted unnecessarily,

excellent average performance CPP (highest locker protocol)

change a thread's priority twice regardless of whether there is contention for the lock or not

higher overhead and many unnecessary context switches and blocking in unrelated tasks

worst-case priority inversion control, it handles nested locks well, and can avoid deadlock in some cases

static analysis of the system to find the priority ceiling