[PPT] - Online Task Remapping Strategies for Fault-tolerant Network-on-Chip PowerPoint Presentation

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Online Task Remapping Strategies for Fault-tolerant Network-on-Chip Multiprocessors

Onur Derin, Deniz Kabakcı, Leandro Fiorin

ALaRI Faculty of Informatics University of Lugano Lugano, Switzerland derino@alari.ch

NOCS’11 - Pittsburgh

May 3, 2011

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Outline

Problem ILP formulation of the optimal mapping problem of KPN applications onto NoC Minimization of the communication cost Minimization of the total computation time Online Task Remapping Optimal Task Remapping Center of Gravity method (CoG) Nonidentical Multiprocessor Scheduling Heuristics (NMS) Localized NMS Heuristic (LNMS) Case study Results

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Introduction

Continuity of service support in the MADNESS NoC platform

starting point

Kahn Process Networks as the computation model xpipes-based NoC from Uni. Cagliari, NORMA model, message-passing support

Main tasks

a middleware to execute KPN on NoCs fault detection/masking via self-testing and self-checking reconfiguration via online task remapping task migration from faulty nodes fault-tolerant interconnect

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Problem

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RISC RISC RISC RISC RISC DSP DSP DSP DSP t11 t10 t6 t12 t4 t5 t9 t8 t7 t2 t1 t3 e 1

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Figure: A KPN application running on a 3x3 mesh

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Problem: Where should the tasks on the faulty core be moved?

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Figure: Processing node n5 becomes faulty

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Approach

Solve the task mapping problem onto NoC-based heterogeneous multiprocessors optimally Consider different fault scenarios and find new optimal remappings Propose heuristics for the problem Compare their performances with the optimal results

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Mapping problem

Given a KPN task graph Given an architecture graph and a deterministic routing algorithm Find the optimal mapping such that computation time and amount of communication is

ptimized
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ILP formulation of the mapping problem

A task graph gt = (Vt, Et) is composed of tasks t ∈ Vt and data dependencies e ∈ Et ⊆ Vt × Vt. An architecture graph ga = (Vn, En) is composed of processing nodes n ∈ Va and bidirectional communication links l ∈ Ea ⊆ Va × Va. A task binding βt : Vt → Va is an assignment of tasks t ∈ Vt to nodes n ∈ Va. A communication binding βc : Et → E i

a is an assignment of

data dependencies e ∈ Et to paths of length i in the architecture graph ga. A path p of length i is given by i-tuple p = (l1, l2, ..., li).

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ILP formulation of the mapping problem

path : (Va, Va) → E i

a is a function that implements a

deterministic routing algorithm and returns a path between two given nodes. Path set P is the set of paths between all node pairs: P = {pk : pk = path(ni, nj), ∀ni, nj ∈ Va ∧ ni = nj} The task graph can be annotated with demand values where demand di on a data dependency ei ∈ Et, denotes the required bandwidth between the two tasks. The architecture graph can be annotated with capacity values where capacity on an architectural link li ∈ Ea, ci, denotes the maximum bandwidth of the communication link between two architectural nodes. Core type set C consists of core types Ci and lists the types of cores available in a given NoC platform.

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Minimization of the communication cost Decision variables

X NT

ij

= 1, if tj ∈ Vt is bound onto node ni ∈ Va 0,

therwise

Y PE

ij

= 1, if ej ∈ Et is mapped to pi ∈ P 0,

therwise
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Minimization of the communication cost Parameters

MTE

ij

=    1, if ∃tk, ej = (ti, tk) ∈ Et −1, if ∃tk, ej = (tk, ti) ∈ Et 0,

therwise

MNP

ij

=    1, if source(pj) = ni −1, if sink(pj) = ni 0,

therwise

MPL

ij

= 1, if lj ∈ pi 0,

therwise
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Minimization of the communication cost Constraints

Constraint 1 (routing): Task mapping and communication binding are constrained with each other due to the routing algorithm implemented in the NoC. X NTMTE = MNPY PE (1) Constraint 2 (task mapping): A task can be mapped exactly on

ne node.

X TN1|Va| = 1|Vt| (2) Constraint 3 (communication mapping): A data dependency can be mapped at most on one path. Y EP1|P| ≤ 1|Et| (3)

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Minimization of the communication cost

Constraint 4 (capacity): Total bandwidth demand on a link lj should not exceed the capacity of the link cj. MLPY PEd ≤ c (4) Objective 1 (communication cost): The total traffic on the links is the sum of all demands di on the links of the paths that arise according to a given mapping: min: dT Y EPMPL 1|Ea| (5)

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Minimization of the total computation time Parameters

MTC

cap ij =

1, if Cj ∈ C is capable of realizing task ti ∈ Vt 0,

therwise

T TC

cap ij =

completion time of ti on Cj,

if MTC

cap ij = 1

0, if MTC

cap ij = 0

MNC

ij

= 1, if ni ∈ Va is of core type Cj ∈ C 0,

therwise
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Minimization of the total computation time Constraints

Constraint 5 (capability): All tasks should be mapped on cores that are capable of implementing those tasks. MTC = X TNMNC ≤ MTC

cap

(6)

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Minimization of the total computation time

Objective 2 (total execution time): We calculate the total computation time of the application by finding the maximum of the sum of the execution times of tasks mapped on the same core. min: max(T N) = max(X NT(((X TNMNC) . T TC

cap ) 1|C|))

(7) We apply some linearization techniques to this formula for max() and xij ∗ xkl The analytical model for the adopted objectives is valid

for acyclic KPN applications in cases where communication is faster with respect to computation when the network is not overloaded (no congestion)

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The mapping tool

based on IBM ILOG CPLEX API multi-objective ILP problem solved with ε-constraint method

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Optimal Task Remapping New constraints

Constraint (faulty core): Given a faulty node nf , a new constraint is added to the ILP formulation that forbids mapping of tasks on the faulty node nf .

|Vt|

j=1

X NT

fj

= 0 (8) Constraint (migrate only tasks on the faulty core): Given a faulty node nf and an initial task mapping MNT, a new constraint is added to limit the reconfiguration just to the tasks that are running on the faulty node nf . X NT

ij

= MNT

ij

, 1 ≤ i ≤ |Va|, 1 ≤ j ≤ |Vt|, i = f (9)

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Optimal Task Remapping

Why not encode optimal remapping solutions for every fault scenario? number of scenarios, N N =

|Va|

i=1

|Va| i

− 1 = 2|Va| − 1

number of bits, B B = (2|Va| − 1) p |Vt| ⌈log(|Va|)⌉ For |Va| = 9, |Vt| = 12, p = 5, we have B = 14.97 Kbytes We may need heuristics!

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Center of Gravity method (CoG) Idea

We transform the problem to finding the center of gravity of masses by considering the weights of communication as the masses

f the peer tasks.

coordi =

tj∈peers(ti) coord( map(tj) ) weight(tj, ti)
tj∈peers(ti) weight(tj, ti)

, ti ∈ Lf coord(ni) = ⌊coordi + (0.5, 0.5)⌋ considers only communication

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Nonidentical Multiprocessor Scheduling Heuristics (NMS) Idea

The objective regarding computation is equivalent to the scheduling of independent tasks on nonidentical processors in order to minimize the makespan. Three heuristics: NMS-A, NMS-B, NMS-C Different complexities: O(n), O(n log n), O(n2) No absolute winner considers only computation

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NMS Heuristics NMS-A

The task ti ∈ Lf is scheduled on the core that minimizes its finishing time.

NMS-B

For each task ti ∈ Lf , Algorithm NMS-B first orders the tasks in Lf according to decreasing min{T TN

cap ij : 1 ≤ j ≤ |Va|}, and then calls Algorithm NMS-A.

NMS-C

This algorithm iteratively schedules the tasks by choosing a task from Lf that gives the least finishing time.

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Localized NMS Heuristics (LNMS) Idea

We limit the region of nodes where we employ the NMS heuristics. considers both communication and computation apply NMS heuristics on a region: LNMS-A, LNMS-B, LNMS-C region is parametrized in size and centered around center of gravity

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Case study

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Figure: MPEG-2 Decoder KPN graph

15 seconds long video with resolution 704 × 576 pixels and 25 fps d =                          1.0 34.6 28.1 28.1 28.1 28.1 65.0 34.6 28.1 28.1 28.1 28.1 65.0 15.2                          (in MBps)

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Case study

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Figure: The given 3x3 NoC architecture

ci = 100 MBps, 1 ≤ i ≤ |Ea| C = {C1, C2} = {RISC, DSP} MTC

cap = 112×2

T TC

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                     0.13 0.20 6.68 8.52 0.06 0.04 2.00 1.25 2.00 1.25 0.05 0.04 0.06 0.04 2.00 1.25 2.00 1.25 0.05 0.04 12.33 8.51 0.18 0.30                      (in seconds)

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Results

Figure: Pareto curves for optimal mapping of three applications with 12, 24 and 36 tasks

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Results (MPEG2 decoder - 3x3 NoC - n5 faulty)

Figure: Pareto curves for optimal mappings and optimal remappings (unlimited task migration)

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Results (MPEG2 decoder - 3x3 NoC - n5 faulty)

Figure: Comparison of results between heuristics, optimal remappings and the initial mapping (limited task migration)

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Results (MPEG2 decoder - 3x3 NoC - all single faults)

Figure: Degradation achieved by Pareto-optimal limited remappings for all single fault scenarios Figure: Degradation achieved by proposed heuristics for all single fault scenarios

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Conclusions

We proposed an ILP formulation to the task mapping problem

nto heterogeneous NoC multiprocessors with deterministic

routing optimizing the total execution time and total network traffic. We proposed ILP-based optimal solution to the remapping problem due to faulty nodes. We proposed heuristics and evaluated them in comparison to the optimal remapping results. ILP is not scalable but it makes sense to use it for the remapping problem.

Future work

get results for bigger task and node sizes implement on the MADNESS NoC platform

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