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POLITECNICO DI MILANO
Task Scheduling Techniques on Task Scheduling Techniques on
Dynamically Reconfigurable SystemsDynamically Reconfigurable Systems
Roberto Cordone: [email protected]
Francesco Redaelli: [email protected]
Reconfigurable Computing Italian MeetingReconfigurable Computing Italian Meeting19 December 2008
Room S01, Politecnico di Milano - Milan (Italy)
22
OutlineOutline
Aims
ILP model
Heuristic solution
Experimental Results
Concluding Remarks
3
AimsAims
(A1) Definition of a formal model for
the scheduling problem in a partially
dynamically reconfigurable scenario
(A2) Development of a heuristic
method to solve in reasonable time
the proposed scheduling problem
(A3) Validation of the proposed ILP
model and heuristic scheduler
4
An ILP model for placement and schedulingAn ILP model for placement and scheduling
It derives from the general model by a heuristic definition of
partitioning and mapping
1. choose a specific partition xs and build the TDG:
• each node i is a task
• each arc (i,j) a precedence induced by one or more
precedences between the operations in i and those in j
2. choose a specific mode mi for each task i:
size, reconfiguration and latency depend on I
3. each RU is a column of a FPGA (U = {1,…,|U|}),
the device is homogeneous and γu is uniform:a task can be implemented anywhere, given enough RUs
4. Additional (technological) constraint:
limited number of simultaneous reconfigurations
5
The decision variablesThe decision variables
pihk = 1 if task i is present on the device at time h
starting from column k; pihk = 0 otherwise
rih = 1 if the reconfiguration of task i starts at time h ;
rih = 0 otherwise
mi = 1 if task i exploits module reuse (no reconfiguration);
mi = 0 otherwise
τi is the start time of task i (reconfiguration if no module reuse,
execution otherwise)
ti is the execution start time of task i
6
The placement and scheduling model (1)The placement and scheduling model (1)
Different tasks do not overlap
A task has a single leftmost RU
A task cannot be placed too far on the right
Minimize the completion time
Subject to
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The placement and scheduling model (2)The placement and scheduling model (2)
A task either exploits module reuse or it is reconfigured
If there is no module reuse, the task starts with the
reconfiguration
If there is module reuse, the task is directly executed
If no module reuse occurs, the execution start follows the task
start at least by the reconfiguration time
8
The placement and scheduling model (3)The placement and scheduling model (3)
A task is removed at the end of its execution
A task occupies the device continuously from the start to the
execution end
All precedences are respected
The number of simultaneous reconfigurations is limited
9
The placement and scheduling model (4)The placement and scheduling model (4)
Let aij = 1 if tasks i and j are mapped onto the same mode;
aij = 0 otherwise
If a task exploits module reuse, its execution is preceded by the
execution of a compatible task using the same RUs
If a task exploits module reuse and its execution is preceded by
an incompatible task on overlapping RUs, a compatible task must
be executed between them using the same RUs as the first one
for
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NapoleonNapoleon
ReconfigurationReconfiguration--Aware Scheduler Aware Scheduler 1 of 21 of 2
Napoleon: heuristic reconfiguration-aware scheduler, list-based with priority function the ALAP value of a node. It allows out of order scheduling for particular task graphs.
It tries to exploits at best
• Configuration prefetching
• Module reuse
It also uses anti-fragmentation techniques to improve the quality of the solution
It tries to build a solution taking into account the constraintsfound in the ILP formulation of the problem
11
NapoleonNapoleon
ReconfigurationReconfiguration--Aware Scheduler Aware Scheduler 2 of 22 of 2
Anti-Fraqmentation Techniques:
farthest placement
Ti: execution of task i
Ri: configuration of task i
limited deconfiguration
12
Experimental Results Experimental Results
ASAP
ALAP
DyASAP
They have been chosen as the most representative for the solution of our problem in the literature
ASAPS
ALAPS
DyASAPS
ASAPB
ALAPB
DyASAPB
ASAPLIU
ALAPLIU
DyASAPLIU
GLPK [http://gnuwin32.sourceforge.net/packages/glpk.htm]
has been used to solve the ILP instances
Benchmark
Ten task graphs with ten nodes [BBD06a]
9135 task graphs with a number of nodes in a 10-1000 range
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Results Results 1 of 31 of 3
[BBD06a] S. Banerjee, E. Bozorgzadeh, N. D. Dutt
“Integrating physical constraints in HW-SW Partitioning for
Architectures with partial dynamic reconfiguration”, IEEE
Transactions on very large scale integration system, vol.
14, no. 11, november 2006
14
Results Results 3 of 33 of 3
9135 task graphs with a number of nodes in a 10-1000 range
15
Conclusions and Future WorksConclusions and Future Works
Conclusions:
ILP model formulation for the scheduling problem in a partially
dynamically reconfigurable scenario --> (A1)
Napoleon heuristic method based on the ILP formulation --> (A2)
Napoleon obtains schedule length (in average) 18.6% better than
the other algorithms --> (A3)
Future works
Integrate Napoleon into a general framework, to create a
scheduling/reconfiguration-aware partitioning
Integrate Napoleon in DRESD-HLR to complete the design flow to
implement large applications onto partially dynamically
reconfigurable devices
Try new anti-fragmentation techniques
16
QuestionsQuestions
