Real-time Scheduling Review

Venkita Subramonian

venkita@cs.wustl.edu

Research Seminar on Software Systems

February 2, 2004

Main Topics for Discussion

Single Processor Scheduling

End-to-end Scheduling

Holistic Scheduling

What is a Real-time System?

Real-time systems have been defined as: “those systems in which the correctness of the system depends not only on the logical result of the computation, but also on the time at which the results are produced"; J. Stankovic, "Misconceptions About Real-Time

Computing," IEEE Computer, 21(10), October 1988.

Real-time does not necessarily mean “Real fast”.

Predictability is key in real-time systems

“There was a man who drowned crossing a stream with an average depth of six inches” – J. Stankovic

Real-time Scheduling

Job (Jij): Unit of work, scheduled and executed by system. Jobs repeated at regular or semi-regular intervals modeled as periodic

Task (Ti): Set of related jobs.

Jobs scheduled and allocated resources based on a set of scheduling algorithms and access control protocols.

Scheduler: Module implementing scheduling algorithms

Schedule: assignment of all jobs to available processors, produced by scheduler.

Valid schedule: All jobs meet their deadline

Clock-driven scheduling vs Event(priority)-driven scheduling

Fixed Priority vs Dynamic Priority assignment

Scheduling Periodic Tasks

In hard real-time systems, set of tasks are known apriori

Task Ti is a series of periodic Jobs Jij. Each task has the following parameters

pi - period, minimum interrelease interval between jobs in Task Ti.

ei - maximum execution time for jobs in task Ti.

rij - release time of the jth Job in Task i (Jij in Ti).

i - phase of Task Ti, equal to ri1.

ui - utilization of Task Ti = ei / pi

In addition the following parameters apply to a set of tasks

H - Hyperperiod = Least Common Multiple of pi for all i: H = lcm(pi), for all i.

U - Total utilization = Sum over all ui.

Schedulable utilization of an algorithm Us

If U < Us the set of tasks can be guaranteed to be scheduled

Fixed Priority Algorithms

Rate Monotonic scheduling Priority assignment based on rates of tasks Higher rate task assigned higher priority Schedulable utilization = 0.693 (Liu and Leyland) If U < 0.693, schedulability is guaranteed Tasks may be schedulable even if U > 0.693

Deadline Monotonic scheduling Priority assignment based on relative deadlines of tasks Shorter the relative deadline, higher the priority Useful when relative deadline ≠ period

Both of the above usually done off-line since fixed priority assigned at task level

Online dispatcher enforces the schedule by dispatching higher priority jobs before lower priority jobs

Dynamic Priority Algorithms

Online scheduler assigns priorities for jobs released

Dispatcher dispatches the highest priority job

Suitable for scheduling aperiodic as well as periodic tasks

Earliest Deadline First (EDF) Priority assignment based on absolute deadline of jobs Job with closest deadline assigned highest priority Schedulable utilization = 1

Least Laxity First (LLF) Laxity = Absolute Deadline – Worst case computation time Priority assignment based on laxity of jobs Job with minimum laxity assigned highest priority Schedulable utilization = 1

Dynamic Priority algorithms provide better processor utilization than Fixed Priority algorithms

Hybrid algorithms

Not all algorithms are robust in overload situations

To improve predictability for critical tasks, use a combination of fixed and dynamic priority algorithms

Tasks divided based on criticality – critical and non-critical

Critical tasks scheduled using fixed priority assignment

Non-critical tasks scheduled based on dynamic priority assignment

Examples - Maximum Urgency First, RM + MLF

Blocking factors

Sometimes a higher priority job cannot run because Currently running lower priority job is non-preemptive (priority-

inversion) E.g., non-preemptable system call

Self-suspension E.g., i/o operations, remote calls

Above blocking delays need to be taken into account while doing schedulability analysis

Blocking delay should include Maximum blocking time due to non-preemptability of lower

priority tasks Maximum own self suspension time and maximum self-

suspension time of all higher priority tasks Context switches

ORB endsystem example (1/2)

Client ServerC

Reactor

3 wait

Re

acto

r

Servant

Deadlock here

Callback

1 2 4

5

Wait-on-Connection

ReplyHandler in ORB waits on socket connection for the reply

Blocking call to recv() One less thread listening on

the Reactor for new requests

No interference from other requests that arrive when reply is pending

However, could cause deadlocks on nested upcalls.

Wait-on-Reactor

ReplyHandler waits in reactor for the reply

Reactor gets a chance to process other requests while replies are pending

Interleaving of request reply processing, hence interference from other requests while reply is pending

Ideal for single threaded processing

Client ServerC

Reactorwait

Re

acto

r

Servant

Callback6

Deadlock avoided bywaiting on reactor

1

342

5

ORB endsystem example (2/2)

f1 f4

f7 f2 f5

f8 f3 f6

P

Wait-on-Reactor strategy could cause interleaved request/reply processing

Blocking factor could be bounded or unbounded Based on the upcall duration And number of intervening upcalls

Blocking factors may affect real-time properties of other end-systems Call-chains can have

a cascading blocking effect

f2f5

f3f6

f5 replyqueued

f3 returns

f5 replyprocessed

f2 returns

Blocking factor for f2

Algorithm selection

Periodic RMS/MUF/DM

Periodic, Blocking RMS/MUF/DM with Priority Ceiling

Periodic?, Predictable Overload behavior

MUF, RM+MLF

Maximum Utilization EDF,MLF

Single Processor

End to End Scheduling

End-to-end task model

A task is composed of multiple subtasks running on multiple processors Remote method invocation Non-local event Messages

Subtasks are subject to precedence constraints Task = a chain of subtasks

A task is subject to an end-to-end deadline Does not care about the response time of a particular subtask

End-to-End scheduling should address Task allocation : bind tasks to processors Synchronization protocols : to enforce precedence constraints Subdeadline assignment Schedulability analysis

Thanks to Dr. Lu for permitting to use material from CS520 slides

Task Allocation

Strategies Offline, static allocation Allocate a task when it arrives Re-allocate (migrate) a task after it starts

NP-hard: heuristics needed

Bin-Packing formulation Pack subtasks to bins (processors) with limited capacity

“Size” of a subtask Ti,j: ui,j = ei,j/pi “Capacity” of each bin is its utilization bound, e.g., 0.69 (RMS) or 1

(EDF) under ideal assumptions Goal: minimize the number of bins subject to the capacity

constraints

Thanks to Dr. Lu for permitting to use material from CS520 slides

The Synchronization Problem

Given that Priorities are assigned to subtasks in a task chain using some fixed

priority assignment algorithm

How do we coordinate the release of subtasks in a task chain so that Precedence constraints among subtasks are satisfied subtask deadlines are met end-to-end deadlines are met

Synchronization Protocols

Direct Synchronization (DS) Protocol Simple and straightforward

Phase Modification (PM) Protocol Proposed by Bettati Extension called Modified Phase Modification (MPM) Protocol

Release Guard Protocol Proposed by Sun

Synchronization Protocol - Example

P1 P2

(4,2)T1

(6,2)T2,1

(6,2)T2,2

(6,3)T3

Ti,j – jth subtask of task Ti

(period,execution time)

Period = relative deadline of parent task

Task T3 has a phase of 4 time units

Direct Synchronization Protocol

Greedy strategy

On completion of subtask A synchronization signal sent to the next processor Successor subtask competes with other tasks/subtasks on the

next processor

Direct Synchronization Illustrated

On P1

On P2

T1

T2,1

T2,2

T3

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

Phase of T3

T3 misses

deadline

P1 P2

(4,2)T1

(6,2)T2,1

(6,2)T2,2

(6,3)T3

Phase Modification Protocol

Proposed by Bettati

Release subtasks periodically According to the periods of their parent tasks

Each subtask given its own phase

Phase determined by subtask precedence constraints

Phase Modification Protocol Illustrated (1/2)

T1,1

T1,2

T1,3

T1,1 T1,2 T1,3

Actual response time

Estimated worst case response time

Phase of T1,2 Phase

of T1,3

p1

p1

p1

Phase Modification Protocol Illustrated (2/2)

On P1

On P2

T1

T2,1

T2,2

T3

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

Phase of T3

P1 P2

(4,2)T1

(6,2)T2,1

(6,2)T2,2

(6,3)T3

Phase of T2,2

Phase Modification Protocol - Analysis

Periodic Timer interrupt to release subtasks

Centralized clock or strict clock synchronization

Task overruns could cause Precedence constraint violations

Modified PM Protocol Illustrated (1/2)

T1,1

T1,2

T1,1 T1,2 T1,3

Actual response time

Estimated worst case response time

p1

Overrun ∆

p1 + ∆

Modified PM Protocol Illustrated (2/2)

On P1

On P2

T1

T2,1

T2,2

T3

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

Phase of T3

P1 P2

(4,2)T1

(6,2)T2,1

(6,2)T2,2

(6,3)T3

Synch signal delayed

Modified PM Protocol - Analysis

MPM protocol behavior the same as PM under ideal conditions Ideal conditions – Clocks synchronized, no overrun

MPM protocol does not need clock synchronization

Precedence constraints preserved even in the case of overruns

Upper bound on End-to-End Response time of task Ti

Ri,k is the response time of the kth subtask of Ti

ni is the number of subtasks for the task Ti

Lower bound on End-to-End Response time of task Ti

1

1,

in

kkiR

in

kkiR

1,

+ Actual Response time of nith subtask

Lower bound high, hence high average EER time, but low output jitter

Release Guard Protocol

Proposed by Sun

A guard variable – release guard - associated with each subtask

Release guard used to control release of each subtask Contains next release time of subtask

Synchronization signals just like MPM

Release guard updated On getting synchronization signal During idle time

Release Guard Protocol Illustrated

On P1

On P2

T1

T2,1

T2,2

T3

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

2 4 6 8 10 12

Phase of T3

P1 P2

(4,2)T1

(6,2)T2,1

(6,2)T2,2

(6,3)T3

g1,2 = 4+6=10 g1,2 = 9

Idle time detected

Release Guard Protocol - Analysis

Shares the same advantages as MPM

Upper bound on EER still the same as MPM Since upper bound on release time enforced by release guard

Ri,k is the response time of the kth subtask of Ti

ni is the number of subtasks for the task Ti

in

kkiR

1,

Lower bound on EER less than that of MPM If there are idle times Results in lower average EER

Subdeadline Assignment

Subdeadline -> priorities under EDF & DM

Optimal subdeadline assignment is NP-hard Offline: heuristic search algorithms Online: simpler heuristics

Effective Deadline (ED): Work backwards from the end-to-end deadline

Slack assignment Assign all slack to 1st subtask Assign slack proportionally to execution time Assign more slack to subtasks on busier processors

Thanks to Dr. Lu for permitting to use material from CS520 slides

Holistic Scheduling

Combine processor scheduling with communication bus scheduling to provide an integrated schedulability analysis

Calculate bounds on end-to-end delays in distributed systems including communication delays

Typically used in hard real-time systems to calculate the worst case end-to-end response time of tasks

Algorithm selection

Use MPMP or RG if Information about all tasks are available a priori System has global clock sync

Otherwise only RG can be used

Use MPMP for low jitter and RG for lower average EER

References

Synchronization Protocols in Distributed Real-Time Systems, ICDCS 96 Jun Sun, Jane Liu

Real-time Systems Jane Liu

Holistic Schedulability for Distributed Hard Real-time Systems, Microprocessing and Microprogramming - Euromicro Journal 1994 (Special Issue on Parallel Embedded Real-Time Systems) Ken Tindell, John Clark

VEST: An Aspect-Based Composition Tool for Real-Time Systems, RTAS 2003 Stankovic, Lu, et.al

DM with phase offset

Distributed Task - conceptual Period=P1

T1

Actual Distributed Scheduling ProblemProc 1

Proc 2

Proc 3

D11 Phase Offset

D11 where D11 < P1 => DM

= Communication delayD12 Phase Offset D13

T11

T12

T13

Distributed Task - conceptual Period=P1

T1

Actual Distributed Scheduling ProblemProc 1

Proc 2

Proc 3

D11 Phase Offset

D11 where D11 < P1 => DM

= Communication delayD12 Phase Offset D13

T11

T12

T13