chapter 3 task assignment and scheduling

Chapter 3 Task Assignment and Scheduling

3.1 Introduction3.2 Rate monotonic analysis

3.3 Other uniprocessor scheduling algorithms

3.4 Task assignment3.5 Fault-tolerant scheduling

Objective : Look at techniques for allocating & scheduling task to ensure deadline is met

Real-Time Systems (Dr Shamala) 2

Introduction

Real-time computing objective :– Execute, by appropriate deadlines it’s control tasks

Objective of Chapter:– Techniques for allocating & scheduling tasks on processors to

ensure that deadlines are met.


Scheduling

1970

Scheduling research growth

Years


The allocation/scheduling problem can be stated as follows:

Given a set of factors affecting allocation/scheduling– Tasks (consumes resources)

• number of tasks, priorities

– task characteristics• periodicity• timing constraints

– task precedence constraints (best described using precedence graph)– resource requirements– inter-task interactions We are asked to devise a feasible

allocation / schedule on a given computer


Precedence Graph

T1

T2 T3 T4

T6T5

T7

T8


Precedence Graph

The arrows indicate which task has precedence over the other task.

We denote the precedence task set of task T by <(T) that is , (T) indicates which tasks must be completed before Y can begin.


Precedence Graph (Cont.)

<(1) = <(2) = {1} <(3) = {1} <(4) = {1} <(5) = {1,2,3} or {2,3} <(6) = {1,3,4} <(7) = {1,3,4,6} <(8) = {1,3,4,6,7}

T1

T2 T3 T4

T6T5

T7

T8


Precedence Graph (Cont.)

We can also write :

i < j

to indicate that task Ti must precede task Tj. It can also be written as :

j > i The precedence operator is transitive:

i< j and j < k i < k

For economic representation:

Only the list of immediate ancestors in the precedence set:– E.g. < (5) = {2,3} since <(2) = {1}


Each task has : Each task requires resources. Eg. Processor

execution time, memory or access to a bus Resources examples: Resources may be (depending to its usage):

– Exclusively held by a task Release Time of a task- the time at which all the

data that are required to begin executing the task are available.

Deadline – the time at which the task must complete its execution. (Deadline maybe hard or soft).

Relative deadline = Absolute deadline – release time


Each task …(cont.)

Task – Periodic

• every Pi seconds, the constraints is that it has to run exactly once every period.

• Every period is generally Deadline– Sporadic

• not periodic but has an upper bound on the rate in which it has to be invoked.

• Irregular intervals– Aperiodic

• Not periodic but has no upper bound


Precedence constraints– inter-task relationship– precedence graph– ＜ (T) : precedent-task set of task T

– i ＜ j : task Ti precedes task Tj

Resource requirements– exclusive– nonexclusive

T1

T2

T3

T4

T6T5

T7

T8


Characteristics of task assignment/scheduling

– feasible schedule• a valid schedule by which every task completes by its deadli

ne

– task assignment• in case of multiple processors

– for a set of processors P, time t, set of tasks Τ, the schedule S is a function such that

• S: P × t Τ• S(i, t) : task scheduled to run on processor i at time t

– online (dynamically) vs offline scheduling (precomputed)

– Static(doesn’t change within a mode) vs dynamic priority algorithm

– preemptive vs nonpreemptive scheduling


Inter-task interactions– inter-task communication

• synchronous• asynchronous

– mutual exclusion problem (synchronization)• priority inversion• chained blocking• deadlock


Assignment / scheduling problems

Most problems pertaining are more than two processors must make do with heuristics. Heuristics are motivated by the fact that uniprocessor scheduling are tractable.

Thus, multiprocessor schedule are divided into two (2) steps:– 1) assign tasks to processors– 2) Run a uniprocessor schedule to

schedule the task allocated to each processor. If one or more schedules cannot be feasible, then we must either return to the allocation step and change the allocation or declare that a schedule cannot be found.


Developing a multiprocessor schedule

Make an allocation

Schedule each processor based on the allocation

Are all these schedules feasible

Check stopping criterion

Output schedule

Declare Failure

Stop

Change Allocation

Continue


Uniprocessor scheduling algorithms– traditional rate-monotonic (RM)– rate-monotonic deferred server (DS)– earliest deadline first (EDF)– precedence and exclusion conditions– multiple task versions– IRIS tasks

• increased reward with increased service

– mode changes

Overview


Multiprocessor scheduling– utilization balancing algorithm– next-fit algorithm– bin-packing algorithm– myopic offline scheduling algorithm– focused addressing and bidding algorithm– assignment with precedence constraints

Critical sections Fault-tolerant scheduling


Notation– n number of tasks in task set

– ci execution time of task τi

– Ti period of periodic task τi

– Ii phase of periodic task τi

– di relative deadline of task τi

– Di absolute deadline of task τi

– ri release time of task τi


Commonly Used Approaches

Weighted round-robin approach– tasks waiting in the FIFO queue– a task with weight wt get wt time slices every round– suitable for scheduling real-time traffic in high-speed

switched networks• a switch downstream can begin to transmit an earlier portion

of the message upon receipt of the portion, without having to wait for the arrival of the later portion

– no need for sorted priority queue speedup of scheduling


Priority-driven approach– never leaves any resource idle intentionally– greedy scheduling, list scheduling, work-conserving s

cheduling– most scheduling algorithms used in nonreal-time syst

ems are priority-driven– preemptive vs. nonpreemptive


Clock-driven(time-driven) approach– tasks and their timing constraints are known a priori e

xcept for aperiodic tasks– relies on hardware timers– a static schedule

• constructed off-line• cyclic schedule: periodic static schedule• clock-driven schedule: cyclic schedule for hard real-time task

s

– foreground/background approach• foreground: interrupt-driven scheduling• background: cyclic executive (“Big loop”)


code block

code block

...Loop

ISR

ISR

ISR

interrupt

Background Foreground

interrupt

ISR: interrupt service routine

Foreground/Background Systems


A clock-driven scheduler

Input: Stored schedule (tk, τ(tk)) for k = 0, 1, …, N-1Task SCHEDULER:

set the next decision point i and table entry k to 0;set the timer to expire at tk;do forever:

accept timer interrupt;if an aperiodic job is executing, preempt the job;current task τ = τ(tk);increment i by 1;compute the next table entry k = i mod N;set the timer to expire at fl(i/N)H + tk

{ fl: floor function H: hyperperiod N: #tasks in H}if the current task τ is an idle interval (or idle task), let the job at the head of the aperiodic job queue execute;else, let the task τ execute;sleep;

end SCHEDULER


3.2 Rate Monotonic Analysis

Assumptions– A1. No nonpreemptible parts in a task, and negligible

preemption cost– A2. Resource constraint on CPU time only– A3. No precedence constraints among tasks – A4. All tasks periodic– A5. Relative deadline = period


Rate-Monotonic Scheduling(RMS)

Overview– rate monotonic priority

• the higher rate, the higher priority

– schedulability guaranteed if utilization rate is below a certain limit

– for feasible schedules• fi = 1/Ti : frequency (=rate)

• ci or Ci : execution time

c fii

n

i

1

1


3.3 Other Uniprocessor Scheduling Algorithms

Period transformation for transient overload– a modified form of RM scheduling

Dynamic scheduling– earliest deadline first scheduling– least laxity first scheduling

Scheduling of IRIS tasks– imprecise computation

Scheduling of aperiodic tasks Mode change


Period Transformation

Period transformation for transient overload– changes the period to cope with transient overloads (i

n terms of RM scheduling)– actually, to cope with semantic criticality in RM sched

uling– example

• tasks: T1: T1 = 12, C1 = 4, C1+ = 7 [Ci+: worst case]

T2: T2 = 22, C2 = 10, C2+ = 14

utilization rates: average = 0.79, worst case = 1.22

• problem: if T2 is hard rt and T1 is soft (or not), how can we guarantee T2’s deadline in case of transient overload, and T1’s deadline in the average case?


(continued)

• solution: boost priority of T2 by reducing its period

replace T2 by T2’:

T2’ = T2 /2, C2’ = C2 /2, C2’+ = C2 +/2

• an alternative: lower the priority of T1 by lengthening its period

– in this case, double the value of parameters

– the new deadline must be ok


Earliest Deadline First Scheduling

Also know as Deadline Monotonic EDF scheduling

– dynamic priority based, deadline monotonic scheduling

Properties– EDF is optimal for uniprocessors– for periodic tasks with their relative deadline equal to

periods: if the total utilization of the task set is no greater than 1, the task set can be feasibly scheduled on a single processor by EDF.

– Allows preemptions.


– Procedure1. Sort task instances that require execution in time i

nterval [0, L] in reverse topological order.

2. Initialize the deadline of the kth instance of task Ti to (k-1)Ti + di, if necessary

3. Revise the deadlines in reverse topological order.

4. Select the task with earliest deadline to execute


Uniprocessor Scheduling of IRIS Tasks

Introduction– Not necessary to run to completion. Iterative algorithm

s.– Task of this type are known as increased reward w

ith increased service (IRIS)– reward function R(x)

• typically

• where r(x) is monotonically nondecreasing in x.• m, o : execution time of the mandatory and optional parts, re

spectively

moxif

moxmif

mxif

mor

xrxR

)(

)(

0

)(


3.4 Task Assignment

Assignment of tasks to processors– use heuristics cannot guarantee that an allocation

will be found that permits all task to be feasibly scheduled.

– consider communication costs precedence of task completion.

– Sometime an allocation algorithm uses communication costs as part of its allocation criterion.


Utilization-balancing algorithm

– Objective to balance processor utilization, and proceeds by allocating the tasks one by one and selecting the least utilized processor.

– Considers running multiple copies for fault-tolerance systems.

for each task Ti, doallocate one copy of Ti to each of the ri least utilized pr

ocessorsupdate the processor allocation to account for the alloc

ation of Ti

end do


A Next-fit algorithm for RM scheduling

– Used in conjunction with RM– separation of allocation and scheduling

• simplifies the scheduler to a local one• allocation: centralized, scheduler: distributed

– objectives: • to partition a task set so that each partition is scheduled later

for execution on a processor by RM scheduling• to use as few processors as possible

– task characteristics• each task has constant period and deadline constraints• independent, no precedence constraints


– allocation algorithm– n tasks– ui : utilization factor of Ti

– Pi,j : set of tasks assigned to a processor– Nk : number of class-k processors used so far

• tasks are divided into M classes such that

• assigns k class-k tasks to each class-k processor, keeping the utilization factor of the class-M processor less than ln 2

task T class- k if 2 u 2

task T class- M if 0 u 2

where 1 k < M, M >3

i

1k+1

1k

i

1M

1 1

1


– Algorithm Next-Fit-Mfor k = 1 to M do set Nk = 1;set i = 1;while i <= n do if Ti is a task from class-k, 1 <= k < M, then assign Ti to Pk,Nk

; if Pk,Nk

has currently k tasks assigned to it then set Nk = Nk +1 endif else (Ti is a task from class-M) if the total utilization factors of all the tasks assigned to PM,NM

is greater than ln2-ui then set NM = NM + 1 endif assign Ti to PM,NM

endif set i = i +1endwhileif Pk,Nk

has not task assigned to it then set Nk = Nk -1


Bin-packing assignment algorithm for EDF

– periodic independent preemptible tasks– bin-packing problem: assign tasks such that the sum

of utilization factors does not exceed 1, and minimize the number of processors needed

– first fit decreasing algorithm

Initialize i to 1. Set U(j) = 0, for all j.(L : a list of tasks with their utilizations sorted in descending orde

r, nT : # tasks )

while i <= nT do

Let j = min{k | U(k) + u(i) <= 1}. Assign the i-th task in L to pj

Set i = i + 1 . end while

L- sorted list of task so their utilization are in non-increasing


Myopic Offline Scheduling (MOS) Algorithm

– Offline Algorithm –given in advance arrival times, execution time and deadline.

– Non-pre-emptive task– Not only processor resources but also others resources such as

memory etc.

Schedule TreeSchedule Tree– MOS proceeds by building up a schedule tree.– Each node represents an assignment and scheduling of a

subset of the tasks. – The root of the schedule tree is an empty schedule.– Each child of a node consists of a schedule of its parent node,

extended by one task. – A leaf of this tree consist of the schedule of the entire task set.


Myopic Offline Scheduling (MOS) Algorithm

– algorithmi) start with an empty partial schedule

ii) determine if the current partial schedule is strongly feasible

then proceed; else backtrack

iii) extend the current partial schedule by one task(1) apply the heuristic function to the first Nk tasks in the ta

sk set

(2) choose the task with the smallest heuristic value to extend the current schedule

2 Questions – which one task & when to stop

Develop a node if it is strongly feasible. Develop a node if it is strongly feasible. If not feasible, we backtrack that is we mark that node If not feasible, we backtrack that is we mark that node

as hopeless and then go back to its parentsas hopeless and then go back to its parents


Focused addressing and bidding (FAB)

– Introduction• online• distributed environment, loosely coupled• both critical and noncritical tasks• local scheduler: handles (critical) tasks arriving at a

given node• global scheduler: schedules noncritical tasks acros

s processor boundary• global state


FAB cont.

– algorithms for global schedulingto which node the task should be sent

• noncooperative algorithm-if enough resources for critical yes; else no for non-critical.

• random scheduling algorithm-if a processor load is exceeding its threshold then another processor is chosen randomly.

• focused addressing algorithm – overloaded processor checks its surplus info. and selects a processor which it feels it is able to process the task within its deadline. Prob: surplus info may be outdated.

• bidding algorithm – simultaneous – lightly loaded to bid (Request For Bids)

• flexible algorithm <-- focused addressing + bidding


– focused addressing algorithm• FAS: focused addressing surplus, tunable paramet

er• locally unschedulable tasks sent to the node with t

he highest surplus ( > FAS)• if no such node is found, the task is rejected


– bidding algorithm• first, select k nodes with sufficient surplus

k: chosen to maximize the chances of finding a node

• a request-for-bid(RFB) message is sent to these nodes

• those nodes that receive RFB message– calculate a bid ( = likelihood that the task can b

e guaranteed)– send the bid to the bidder node if the bid > mini

mum bid req’d• the bidder sends the task to node that offers the be

st bid• if no good bid available, reject the task


– symbols• pi: a processor node with a newly arriving task that is not locall

y guaranteed• ps: a node that is selected by FA algorithm• pt: a node that receives RFB message

– the flexible algorithm (FAB algorithm)• pi selects k nodes with sufficient surplus

– if the largest value of the surplus > FAS» the node with that surplus is chosen as focused node

(ps)» pi sends the task to ps immediately» also, pi sends in parallel a RFB message to the remain

ing k-1 nodes. RFB contains info on ps

• when a node receives the RFB message– it calculates a bid, sends the bid to ps if ps exists


(continued)

• when the task reaches ps

– it first invokes the local scheduler and checks the feasibility

– if it succeeds, all the bids for the task will be ignored

if it fails, ps evaluates the bids, sends the task to the node responding with the highest bid, and sends this info to pi

• in case there is no focused node, pi will handle the bidding

• if ps cannot guarantee the task and if there is no good bid available, then corrective actions follow


(original node)

pi

network

ps (focused node)

bidding


The Buddy Strategy

Same as FAB in the sense that if the processor is overloaded it will try to offload some task to lightly loaded processor.

However, it differs in the manner in which it finds the lightly loaded tasks:

Each processor has 3 thresholds of loading:

– U:Under (TU), F: full (TF) and T: over (TV)

If a processor has a transition from F/T to U it broadcast an announcement to this effect. This broadcast is not to all processors but to a subset and this effect is known as a buddy effect.


3.5 Fault-Tolerant Scheduling

Introduction– in case of hardware failure– Systems have sufficient reserve capacity and

sufficiently fast failure-response mechanism. – multiple processors with a set of periodic tasks– multiple copies of each version of a task executed in

parallel– the approach taken : ghost copies of tasks

• embedded into the schedule• need not be identical to the primary copies• the tasks concerned are those that were to have been run by

the failing processor


Fault-tolerant schedule– should be able to run one or more copies of each vers

ion (or iteration) of a task despite the failure of up to n

sust processor

– Output of each fault-tolerant processor• has a ghost schedule + 1+ primary schedules• makes room for ghosts by shifting primary copies.

– feasible pair of a ghost schedule and a primary schedule

• if both schedules can be merged/adjusted to be feasible


Ghosts– each version of a task must have ghost copies sched

uled on nsust distinct processors

– ghosts are conditionally transparent, only if• two ghost copies may overlap in the schedule of a processor

if no other processor carries the copies of both tasks (that is, if the primary copies of both tasks are not assigned to the same processor)

• primary copies may overlap the ghosts only if there is sufficient slack time in the schedule to continue to meet all the deadlines


Algorithm FA1Ha: assignment procedure, Hs: EDF scheduling procedure

1. Run Ha to obtain a candidate allocation of copies to processors.

2. Run Hs for ghost and primary copies on a processor i.• if the resulting schedule is found infeasible, return to step 1• otherwise, record the position of the ghost copies in ghost sc

hedule Gi, and the position of the primary copies in schedule Si. (the primary copies will always be schedule according to S regardless of any ghost happen or not)

Limitation:- primary tasks are needlessly delayed when the ghost do not have to be executed. While all task will meet their deadlines, it is frequently best to complete execution of the task early to provide slack time.


Algorithm FA21. Run Ha to obtain a candidate allocation of copies to pr

ocessors.

2. Run Hs for ghost and primary copies on a processor i.• if the resulting schedule is found infeasible, return to step 1• otherwise, record the position of the ghost copies in ghost sc

hedule Gi. Assign static priorities to the primary tasks in the order in which they finish executing.

3. Run a static-priority preemptive scheduler for primary copies with the priorities to obtain Si


Exampleghosts: g4, g5, g6 primaries: h1, h2, h3

h1 h2 h3 g4 g5 g6

release time 2 5 3 0 0 9

execution time 2 2 4 2 2 2

deadline 6 8 15 5 6 12

for the primary copies of g4 and g5

case 1: they are allocated to the same processor

case 2: they are on different processors


0 5 10 15

0 5 10 15

0 5 10 15

g4

g6g4, g5

g5 g6

h1 h3 h2 h3

ghost schedule of p if g4 and g5 cannot overlap

ghost schedule of p if g4 and g5 can overlap

feasible primary schedule of p if g4 and g5 can overlap

chapter 3 task assignment and scheduling

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