Sandtids systemer 2.modul

el.

Henriks 1. forsøg m. Power Point

Real Time Systems

• Specifications -> Task Set

• Task Specifications

• Scheduling

• Fixed Priority Scheduling

• Dependent tasks

• Dynamic Priority Scheduling

• Aperiodic Tasks

Task Specifications

• A task is a collection of jobs J1,J2,J3,…

• A job is a set of instructions to be executed

• A job is specified in time by: a ready time r, a computation time c and a deadline d

The job life cycle

Time

Running

Completed C

Scheduled S

Ready r

Computation time c Deadline d

Pre-emptied

Task Specifications

• Periodic tasks

• Aperiodic tasks

• Sporadic tasks

• Hard Real Time

• Real Time

• Soft Real Time

• Non Real Time

Task Specifications

r1Time

r4

T

r2

T T T

Periodic Task

r3

Task Specifications

r1Time

r4r2

Aperiodic Task

r3

T3

0 < Ti, 0 < c << T , (Ti < c)

T1 T2

Task Specifications

r1Time

r4r2

Sporadic Task

r3

T3

0 < c << Tmin < Ti

T1 T2

Task Specifications

• Hard Real Time: d <= Tmin (T), (periodic,sporadic)

• Real Time: d > Tmin (T), (periodic, sporadic)

• Soft Real Time: C < d (periodic,aperiodic)

• Non Real Time

Scheduling

• For periodic and sporadic tasks: {Ti, ci}, ci / Ti = U < 1 (stable),

(U>1, unstable)

• For aperiodic tasks: ri = ci / Ti, U= ri < 1

Scheduling

• Pre emptive• Non Pre emptive

• Fixed Schedules• Cyclic Schedules• Round Robin• Fixed Priorities• Rate/Deadline

Monotonic• Dynamic Priorities• Earliest Deadline First

Fixed Schedules

• Ready times need to be known a priori

• Only very light run time load

• Table based

• Less flexible

• Cyclic schedules are fixed schedules

Cyclic Schedules

• All periods are multiples of dT

• LCM: is the Least Common Multiple

• Schedule is made for [0, dt * LCM]

• If CPU is idle at dT * LCM the schedule may be reused in subsequent intervals.

• Applicable both for Pre emptive and Non Pre Emptive Schedules

Cyclic Schedules (example)

• T1=2,c1=1,d1=2

• T2=3,c2=3/2,d2=3

Task

Time

1 2 3 4 5 6

Round Robin

• Time line divided into slots dT• Tasks are granted execution time cyclically.• When a job has executed for dT or is

completed CPU access is passed on.• Non pre emptive if dT is infinite.• Critical instant when grant is just passed on

when job is ready along with jobs from all other tasks

Round Robin (example)

• T1=2,c1=1,d1=2

• T2=3,c2=3/2,d2=3, dT=1/2

1 2 3

Task

Time

Task

Time 1 2

Test for task 2 Test for task 1

Fixed Priorities

• Tasks are assigned priorities in order

• A task is ready if its latest job is still not completed

• A task is running if it is ready and it has highest priority among ready tasks.

• Both pre emptive and non preemptive

Fixed priorities (example)

• T1=2,c1=1,d1=2

• T2=3,c2=3/2,d2=3 , preemptive

Task

Time

1 2 3 4 5 6

Task 2 missed deadline

Fixed priorities (properties)

• Flexible

• Medium run time demands

• Not optimal

• Typically better then Round Robin

• Well known schedulability criteria

Fixed Priorities (schedulability)

• Critical Instant Theorem (Liu,Layland) Worst case completion time is when launced along with jobs from all other tasks simultaneously.

• Utilization U < N (2N-1) -> 0.7 < 1 !!• Completion time:

exist t <= di : t => i[t / Tj] cj + ci

Fixed Priorities (example)• T1=2,c1=1,d1=2

• T2=3,c2=3/2,d2=3 , preemptive

c2=3/2

c1=1

T1=2

C2=3½ > d2=3 1 2 3

Time

Work

Priority Order

• Priorities according to importance or time efficiency.

• DMA: d1 < d2 < d3 < .. < dN

• DMA (Deadline Monotonic) / RMA (Rate Monotonic) is optimal when d<=T / d=T

• No general optimal order when d>T

Dependent tasks

• Inter Process Communication (IPC)

• Critical regions

• Producer Consumer

• Rendezvous

• All introduce dependence

Critical regions (example)

2

3Time

Running

W(S)

W(S)

1

S(S)

Priority inversion

W(S)

Priority Ceiling

• Priority ceil C(S) of semaphore S is the highest (minimum) priority of all tasks locking S

• Runtime:– if prio < min {C(Si)| Si locked} when attempting a

lock on S then lock and active. – else suspend. Task locking S inherits prio (if lower)

until unlock.

• Whenever a semaphore is unlocked the suspend queue is inspected to see if any task may be resumed.

Priority Ceiling (assumptions and properties)

• Assumption: Critical regions nicely nested.

• Property: No deadlocks possible

• Property: No task is blocked by lower priority tasks for more than the duration of 1 critical region.

Critical regions with PC (example)

2

3Time

Running

W(S)

W(S), suspended

1

3 -> prio(1)

W(S)

S(S), 3 -> low prio.

Fixed Priorities with PC (schedulability)

• Completion time: exist t <= di : t => i[t / Tj] cj + ci + Bi

• Bi is the duration of the longest critical region possibly blocking taui

• Lower priority tasks also block through priority inheritance

Dynamic priority scheduling

• At every scheduling point considers states of every job.

• Heavy run time load.

• Includes fixed schedules and fixed priorities as special cases – thus stronger

• Earliest Deadline First (EDF) and Least Laxity First (LLF) are special cases.

Ealiest Deadline First (EDF)

• At every scheduling point runs job with closest deadline.

• Optimal among all schedules.

• U < 1 sufficient for d=T

• No priority according to importance possible.

EDF (example)

• T1=2,c1=1,d1=2

• T2=3,c2=3/2,d2=3

Task

Time

1 2 3 4 5 6

d1,1 d2,1 d1,2 d2,2 d1,3

RMA/DMA missed deadline

Aperiodic tasks

• Low (close to zero) minimum interarrival time Tmin

• May be seen from probabilistic and worst case viewpoints

• Probabilistic viewpoint uses mean inter arrival times T and queueing theory.

• Worst case view uses Tmin. OK if c/Tmin < available CPU fraction.

• Aperiodic server or background task

Probabilistic viewpoint (queueing)

• Assumes Poisson arrivals and exponential distributed service times. (Approximation.)

• l=1/T : arrival rate, u: service rate.

• Load (utilization) r = l/u

• Mean queue length Q = r / (1-r)

• Mean waiting time W = Q/l = 1 / (u –l) (Littles theorem)

Worst case v.p.

• Higher priority computation times Ki

• Higher priority utilization Ui

• W.C. Completion time for n jobs of taui: Cn < min{t | t > n ci + Ki + t*Ui} => Cn < (n ci + Ki) / (1-Ui)

• W.C. Waiting Wn = Cn – rn < Cn - (n-1)*Tmin < n (ci / (1-Ui) –Tmin) + Ki / (1-Ui) +Tmin = (ci +Ki ) / (1-Ui) for n=1

Worst Case V.P.

1 2 3 4 5 6 n

Waiting timeKi / (1- Ui) + Tmin

1

Ci/(1-Ui) - Tmin

(ci + Ki) / (1- Ui)

Sporadic Tasks

• Tmin >> c• Typically hard real time (alarm not.) d << Tmin• No queueing.• If aperiodic server T < d << Tmin (high load)• Sporadic server accesible at all times, however

allways Tmin between every use.• Ticket issued at start up time. New ticket at

n*Tmin if used – else old ticket left.• High responsiveness – low load.

Sporadic Server (example)

Time

Tickets

r1

Tmin

1

r2 r4 r3

The End