1 lic presentation memory aware task assignment and scheduling for multiprocessor embedded systems...
TRANSCRIPT
1
Lic Presentation
Memory Aware Task Assignment and Scheduling for Multiprocessor
Embedded Systems
Radoslaw Szymanek / Embedded System Design
http://www.cs.lth.se/home/Radoslaw_Szymanek
2
Outline
• Introduction
• Problem Formulation and Motivational Example
• CLP Introduction
• CLP Modeling
• Optimization Heuristic and Experimental Results
• Conclusions
3
System Level Synthesis (SLS)
• Multiprocessor embedded systems are designed using CPU’s, ASIC’s, buses, and interconnection links
• The application areas range from signal and image processing to multimedia and telecommunication
• Task graph representation for application
• The main design activities are task assignment and scheduling for a given architecture
• Memory constraints (code and data memory)
4
SLS with memory constraints
annotated task graph
target architecture
P1
ROM RAM
P2
ROM RAM
P3
ROM RAM
A1
RAM
B1
L1
L2
5
• Data dominated application represented as directed bipartite acyclic task graph
• Each task is annotated with execution time, code and data memory requirements
• Heterogeneous architecture
• Both tasks and communications are atomic and they must be performed in one step
• Find a good CLP model
• Find a good heuristic for memory constrained time minimization task assignment and scheduling satisfying all constraints
Problem Assumptions and Formulation
6
Motivation
• SoC multiprocessor architectures
• Co-design methodology needs tool support
• Memory consideration to decrease cost and power consumption
• System Level design for fast evaluation
7
Motivating example (memory)
task graph
DC2t
4
86
DC2
DC3
t
4
86
architecture
P1 L1
C1
C3 C2C2
P1L1P2
C3
P1L1P2
DC3t
4
86
t
4
86
DC2
DC3
P1 P2
P1 P2
DC1
ScheduleData Memory
Task - 1kB code memory, 4kB data memory, Communication - 2kB data memory
P2
8
CLP Introduction
“Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it.”
Eugene C. Freuder
CONSTRAINTS, April 1997
9
CLP Introduction
• Relatively young and attractive approach for modeling many types of optimization problems
• Many heterogeneous applications of constraints programming exist today
• State decision variables which constitute to solution
• State constraints which must be satisfied by solution
• Search for solutions using knowledge you can derive from constraints
10
Constraints properties
• may specify partial information — need not uniquely specify the values of its variables,
• non-directional — typically one can infer a constraint on each present variable,
• declarative — specify relationship, not a procedure to enforce this relationship,
• additive — order of imposing constraints does not matter,
• rarely independent — typically they share variables.
11
A simple constraint problem
1. Specify all decision variables and their initial domains
CLP description
TP1, TP2, TP3 :: 1..2,
TS1, TS2, TS3 :: 0..10,
Cost :: 0..10,
Natural language description
There are three tasks, namely, T1, T2, and T3. Each of these tasks can execute on any of two available processors, P1 and P2. Tasks T1 and T2 send data to task T3.
The tasks should be assigned and scheduled in such a way that the schedule length does not exceed 10 seconds.
12
A simple constraint problem
2. Specify all constraints and additional variables
The execution time of task T1 is four seconds on processor P1 and two seconds on processor P2.
Task T2 requires three and five seconds to complete execution on processor P1 and P2 respectively.
Task T3 always needs three seconds for execution.
If TP1 = 1 then TD1 = 4.
If TP1 = 2 then TD1 = 2,
If TP2 = 1 then TD2 = 3,
If TP2 = 2 then TD2 = 5,
TD3 = 3,
13
A simple constraint problem
Tasks T1 and T2 must execute on different processors.
Tasks T1 and T2 send data to task T3. If two communicating tasks are executed on different processors there must be at least one second delay between them so the data can be transferred.
The tasks should be assigned and scheduled in such a way that the schedule length does not exceed 10 seconds.
TP1 != TP2,
If TP1 != TP3 then D1 = 1 else D1 = 0,
TS1 + TD1 + D1 <= TS3,
[…],
Cost >= TS1 + TD1,
Cost >= TS2 + TD2,
Cost >= TS3 + TD3.
14
Search Tree
15
Modeling
• Constraint Logic Programming (finite domain, CHIP solver)
• Global constraints (cumulative, diffn, sequence, etc.) reduce model complexity of the synthesis problem and exploit specific features of the problem
• Global constraints are useful for modeling placement problems and graph problems
• Problem-specific search heuristic for NP-hard problem
16
CLP Model
Decision variables for task
• TS – start time of the task execution
• TP – resource on which task is executed
• TDP – exact placement of task local data in memory
Additional variables for task
• TD – task duration
• TCM and TDM denote the amount of code and data memory for task execution
17
CLP Model
Decision variables for data
• DS – start time of the data communication
• DB – resource on which data is communicated
• DCP and DPP – exact placement of data in memory of the producer and consumer processor
Additional variables for data
• DD – data communication duration
18
CLP Model – Task Requirements
TS
TP
TD
1
time
PU
a) execution time
TP
1
TCM
PU
CM
b) code memory
TS
TDP
TD
TDM
DM
c) data memory
time
19
CLP Model – Data Requirements
DS
DB
DD1
CU
communication time
timeTSp
DPPDA
DM
data mem (prod)
timeDS+DD DS
DCPDA
DM
data mem (cons)
time
TSc + TDc
20
Simple Example
P2
P1
P2
P1
B1T2
C1T3T1
D1_eD1_p
D2_p D2_c
D3_e
D2_eD1_c
T1
D1 D2
T2 T3
Diffn constraint
21
Code Memory Constraint
Processor
Code Memory Limit
T5
T2T7 T6
T3T4
T8
T1
22
Constraints types
• precedence constraints
• processing resources constraints
• communication resource constraints
• pipelining constraints
• code memory constraints
• data memory constraints
23
data memory estimate no. 1 holds?
Task Assignment and Scheduling Heuristic
Undo all decision – choose a task which consumes the most data
data memory estimate no. 2 holds?
Assign data memory
Schedule communications that Ti is minimal
Assign the task to a processor with the minimal implementaion cost ci
Choose a task from ready task set with min(max(Ti)) – minimize schedule length
Y
Y N
N
24
Execution Cost
1IndL
LIndL )1(*
LIndL-
-LIndL-)1(*
-L Ind 1-
1
12
22
21
1
in
in
in
in
in
in
in
in
in
in
in
in
in
in
in
in
exec
ATS
dATS
dInd
ACM
cATS
d
ACM
c
IndATS
d
ACM
cACM
c
c
Ind = LowTS/PTS – LowCM/PCM
ATS = available time slots, ACM – available code memory
i-th task, n-th processor
25
Data and Communication Cost
otherwise0
32
procMprocAM
0ΔdprocAM
Δdc
ni
n
i
data
i-th task, n-th processor
iD
2
)imax(DD)imin(DDccomm
26
• Estimate no. 1
where S (Sn) is a set of tasks already scheduled on a processor (processor Pn), tasks tj are direct successors of task ti, and dij is amount of data communicated between ti and tj.
• Estimate no. 2 uses the global constraint diffn and it takes time into account
Estimates
StSt
ijn
inj
dP,
1 )(
27
MATAS System
28
Synthesis Results - H.261 example
DCT
FB1
IN
BMA
FIR
PRAE Q
IQ IDCT REK FB2
C96
553
64
96
96
96 96
96
96
96 96 96
Video Coding Algorithm H.261
29
Experimental results H.261 example
EXP.
#
ALG
ORIT
HM
PIPE
LIN
E D
EPTH
DEA
DLI
NE
AVER
AG
E EX
ECU
TIO
N
TIM
E
D
ATA
MEM
ORY
TIM
E
D
ATA
MEM
.
1 both 1 2871 2871 2683 - -
2 greedy 4 6743 1686 3812 0 0
3 memory 4 6781 1696 3259 1% -16%
30
Experimental results(random task graphs)
Experiment setup Result
Each CPU Data Mem. Code Mem.
Exp.
#
algo
rith
m
data
m
emor
y si
ze [
kb]
code
m
emor
y si
ze [
kb]
dead
line
[ms]
utili
zatio
n [k
b]
peak
[kb
]
utili
zatio
n [k
b]
peak
[kb
]
# s
olut
ions
1 greedy 100 100 171 243 78 319 98 22
2 greedy 75 100 182 233 68 310 96 8
3 greedy 100 75 169 257 79 294 75 4
4 greedy 75 75 - - - - - 0
5 memory 75 75 295 222 64 247 65 22
31
Main Contributions
• Definition of the extended task assignment and scheduling problem
• Inclusion of memory constraints to decrease the cost for data dominated applications
• Specialized search heuristic to solve resource constrained task assignment and scheduling
• CLP modeling framework to facilitate an efficient, clean, and readable problem definition
32
Conclusions and Future Work
• The synthesis problem modeled as a constraint satisfaction problem and solved by the proposed heuristic,
• Good coupling between model and search method for efficient search space pruning,
• Memory constraints and pipelined designs taken into account,
• Heterogeneous constraints can be modeled in CLP, important advantage over other approaches
Need for our own constraint engine implementation, approximate solutions, mixture of techniques
Need for better lower bounds, problem specific global constraints, designer interaction during search
33
Lic Presentation
Memory Aware Task Assignment and
Scheduling for MultiprocessorEmbedded Systems
Radoslaw Szymanek / Embedded System Design
http://www.cs.lth.se/home/Radoslaw_Szymanek
34
Related Work
• J. Madsen, P. Bjorn-Jorgensen, “Embedded System Synthesis under Memory Constraints”, CODES ‘99 (GA, only RAM)
• S. Prakash and A. Parker, “Synthesis of Application-Specific Heterogeneous Multiprocessor Systems”, VLSI Signal Processing, ‘94 (MILP, no ASIC’s, optimal)