Lock-free and Wait-free Slot Scheduling Algorithms - PowerPoint Presentation

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Lock-free and Wait-free Slot Scheduling Algorithms

Pooja Aggarwal

Smruti R. SarangiComputer Science, IIT Delhi, India

1Slide2
Outline

Motivation Related WorkParallel Slot

Scheduler DesignPerformance Results

Summary2Slide3

time

Thread

i

Thread

j

How to schedule the requests

Real-Time System

t

1

t

2

t

i

3Slide4

Slot SchedulingTreats time as a discrete quantityGlobally-visible reservation system

Requires advance algorithm for parallel scheduling

4Slide5

T

0

T

1

T

2

T

n-2

T

n-1

T

n

T

1

T

1

T

1

T

2

T

2

time

Shared Resource

Reservation System

5Slide6
Related Work

In 1982 Ousterhout proposed the matrix representation of time-slices

and processors to facilitate running jobs simultaneouslyThe real-time scheduler

for the Rialto operating system, based on CPU reservations, bears a great deal of similarity to slot scheduling. Generic scheduling using locksIn 2009 Mhamdi et. al. gave online variants of scheduling problem for a message passing based

system

In

2011 Keller et. al. propose an

offline version

of the algorithm that has a known task

dependence graph

.

We propose a novel, parallel, and

Linearizable non-blocking slot scheduling algorithms

6Slide7

Nx1 Problem

N

M

FREE

BUSY

7Slide8

NxM

Nx1 Problem

N

M

8Slide9

Time Slots

P3

1xM Problem

T

0

T

1

T

2

T

3

T

4

T

i

T

i+1

T

i+2

P2

P2

P2

P3

P3

P3

9

Resource can process one request per slotSlide10

2

2

busy Free

Empty slot

2

4

4

2

time

NxM

Problem

10Slide11

Problems with LockingDeadlock – no progress

Priority

Inversion – lower-priority process preempted while holding lockConvoying – lockholder de-scheduledStarvation – a process never completes

11Slide12
Lock-free

AlgorithmOptimistic approach

a lock-free algorithm can run in four phases: complete

one's own operationassist an obstructing operation (internal helping)abort an obstructing operationand waitFast execution when low contention

Avoids

blocking and priority

inversion

Avoids

deadlock

12Slide13
Wait-free Algorithm

Per-operation progress guarantees

Every operation is guaranteed to complete in a finite number of

stepsFaster thread helps the slower threadWait-free = Lock-free + Starvation free

13Slide14
Basic Helping Mechanism

Each thread is assigned a priority based on the initial timestamp of its request Shared

Data Structure is used to store the requests

Each thread requesting for slotsFirst chooses a monotonically increasing request ID (reqid)Announce the requesthelps all threads with a non-larger reqid

REQUEST

entry

per thread

requestId

state

path

threadId

timeSlot

numSlots

9

SOFT

null

1

3

4

10

NEW

null

2

10

4

11

NEW

null

3

7

4

NEED TO HELP

Announcing the request

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Optimized

Helping CriteriaDrawback of basic scheme:Helping even if no starvation

even when there is no contentionmany threads help same operations

large redundant workOptimization:REQUEST_THRESHOLDHELP_THRESHOLDINTERNAL HELPING

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Parallel Slot Scheduler Design Schedule operation is accomplished in 3 three atomic steps

Announce the request

concurrent processes realize that there is an operation-in-progressTemporary ReservationTry to reserve the earliest possible available slotsPermanent Reservationfinalizing the reserve slots

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FSM of a

Request

NEW

SOFT

FORCEHARD

DONE

CANCEL

FAIL

Make temporary reservation

Finished reserving the required slots

Make permanent reservation

POINT

of LINEARIZABILITY

POINT of LINEARIZABILITY

Cancelled by other thread or cancelled itself

Could not find empty slot

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Schedule Operation

requestId

state

path

threadId

timeSlot

numSlots

EMPTY

SOFT

9

NEW

null

1

3

4

1

1

1

SOFT

HARD

(3,1)

(3,1),(4,2),(5,2)

1

(3,1),(4,2),(5,2),(6,5)

FORCEHARD

POINT

of LINEARIZABILITY

1

1

1

1

DONE

10

NEW

null

6

4

3

6 6

SOFT

(4,1),(5,1)

CANCEL

NEW

null

6 6 6

SOFT

(7,5),(8,5),(9,5)

FORCEHARD

6 6 6

DONE

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State Transitions’ of a Slot

Tstamp

reqId

tid

state

slotno

round

EMPTY

SOFT

HARD

Temporary Reservation

Permanent Reservation

threadId

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20

Role of Saving Slot

4 4 4 4

2

1 1

2

Already booked

Temporary Reservation

Reserved 4 slots

Reserved 2 slotsSlide21

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Role of Round

1 1 1

2 2

NEW

SOFT

CANCEL

2 2

NEW

SOFT

CANCEL

NEW

2

SOFT

round is 1

round is 2

Round is 3

With every cancellation, round is increment

CASSlide22

22

Selecting a Slot

4 4 4 4

6 6

1

2 2

1

1

1

BOOKED

FREE

SOFT, 2

SOFT, 4

Another

helper reserved slot

1

1

1

1

Another helper

Booked the slot

5

7

SOFT,2Slide23

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Issues and Resolutions

ABA issue Time-Stamp

M

ultiple rollbacksCANCEL-THRESHOLDMultiple reservationsPATH arraySHADOW array

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Setup

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Workload

The inter-request distances are truncated normal distributions

Box-Muller

transform is used to generate the normal variantsExperiment is executed till one of the thread completes all its iterationsEach thread performs 1000 iterationsEach experiment is performed 10 times, and mean values are reported

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Mean time per request (

treq)

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Lock is 100 times slowerSlide28
Work Done

We run the system till the fastest thread completes κ requests

.

wk = tot requests/(κ ×NUMTHREADS).

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Wait-free Work done is around 10 % moreSlide29

Sensitivity: Request-threshold

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Summary

First lock-free and wait-free algorithm for four variants of the generic slot scheduling problemLock-free is fastest of the three approaches

Wait-freedom incurs an inherent trade-offbounds the completion time of a single operation

Total Work done is moreAll our algorithms are linearizableProposed design scheme might be applicable for other wait-free data structures30Slide31

Thank you!Questions?

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