Multi-criteria Mapping and Scheduling of Workflow Applications onto - - PowerPoint PPT Presentation

▶
multi criteria mapping and scheduling of workflow
SMART_READER_LITE
LIVE PREVIEW

Multi-criteria Mapping and Scheduling of Workflow Applications onto - - PowerPoint PPT Presentation

Apr 20, 2023 331 likes •1.54k views

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion Multi-criteria Mapping and Scheduling of Workflow Applications onto Heterogeneous Platforms Veronika Sonigo GRAAL team, LIP Ecole Normale Sup erieure de

slide-1
SLIDE 1

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Multi-criteria Mapping and Scheduling

  • f Workflow Applications
  • nto Heterogeneous Platforms

Veronika Sonigo

GRAAL team, LIP ´ Ecole Normale Sup´ erieure de Lyon

Supervisors: Anne Benoit, Harald Kosch, Yves Robert

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 1/ 48

slide-2
SLIDE 2

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Multi-criteria Mapping and Scheduling

Mapping and scheduling for parallel machines Makespan minimization → already a difficult problem Mapping and scheduling for large-scale heterogeneous platforms Need new objectives Period, reliability, latency, cost, QoS, energy, etc Multi-criteria optimization Assess problem complexity (polynomial /NP-hard instances) Design practical heuristics for important application problems New results and solutions for algorithmically challenging problems

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 2/ 48

slide-3
SLIDE 3

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Thesis outline - Today’s Presentation

Replica Placement in Tree-Networks Without Constraints QoS Constraints Bandwidth Constraints Pipeline Workflow Applications Mono-criterion Optimization Bi-criteria Optimization Example: JPEG-Encoder In-network Stream Processing Single Application - Platform Creation Multiple Applications

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 3/ 48

slide-4
SLIDE 4

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Thesis outline - Today’s Presentation

Replica Placement in Tree-Networks Without Constraints QoS Constraints Bandwidth Constraints Pipeline Workflow Applications Mono-criterion Optimization Bi-criteria Optimization Example: JPEG-Encoder In-network Stream Processing Single Application - Platform Creation Multiple Applications

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 3/ 48

slide-5
SLIDE 5

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Outline of the Talk

1

Replica Placement in Tree-Networks Framework Complexity Heuristics for Replica Cost Problem Experiments

2

Pipeline Workflow Applications Bi-criteria Complexity Results

3

In-network Stream Processing Heuristics and Experiments

4

Conclusion

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 4/ 48

slide-6
SLIDE 6

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Mimi alone at home

Internet

Problems and questions: Where to download from? How to deal with multiple users? Heterogeneity Where to place the replicas?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 5/ 48

slide-7
SLIDE 7

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Mimi alone at home

?

Internet

Problems and questions: Where to download from? How to deal with multiple users? Heterogeneity Where to place the replicas?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 5/ 48

slide-8
SLIDE 8

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Mimi alone at home

Internet

Problems and questions: Where to download from? How to deal with multiple users? Heterogeneity Where to place the replicas?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 5/ 48

slide-9
SLIDE 9

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Mimi alone at home

?

  • Problems and questions:

Where to download from? How to deal with multiple users? Heterogeneity Where to place the replicas?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 5/ 48

slide-10
SLIDE 10

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Mimi alone at home

? ? ? ?

  • Problems and questions:

Where to download from? How to deal with multiple users? Heterogeneity Where to place the replicas?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 5/ 48

slide-11
SLIDE 11

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Mimi alone at home

? ? ? ?

  • Problems and questions:

Where to download from? How to deal with multiple users? Heterogeneity Where to place the replicas?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 5/ 48

slide-12
SLIDE 12

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Mimi alone at home

? ? ? ?

  • Problems and questions:

Where to download from? How to deal with multiple users? Heterogeneity Where to place the replicas?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 5/ 48

slide-13
SLIDE 13

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Replica placement in tree networks Set of clients (tree leaves): requests with QoS or bandwidth constraints, known in advance Internal nodes may be provided with a replica; in this case they become servers and process requests (up to their capacity limit) Research questions: How many replicas required? Which locations? Total replica cost? Quality of Service?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 6/ 48

slide-14
SLIDE 14

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Replica placement in tree networks Set of clients (tree leaves): requests with QoS or bandwidth constraints, known in advance Internal nodes may be provided with a replica; in this case they become servers and process requests (up to their capacity limit) Research questions: How many replicas required? Which locations? Total replica cost? Quality of Service?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 6/ 48

slide-15
SLIDE 15

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Replica placement in tree networks Set of clients (tree leaves): requests with QoS or bandwidth constraints, known in advance Internal nodes may be provided with a replica; in this case they become servers and process requests (up to their capacity limit) Research questions: How many replicas required? Which locations? Total replica cost? Quality of Service?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 6/ 48

slide-16
SLIDE 16

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Replica placement in tree networks Set of clients (tree leaves): requests with QoS or bandwidth constraints, known in advance Internal nodes may be provided with a replica; in this case they become servers and process requests (up to their capacity limit) Research questions: How many replicas required? Which locations? Total replica cost? Quality of Service?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 6/ 48

slide-17
SLIDE 17

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Replica placement in tree networks Set of clients (tree leaves): requests with QoS or bandwidth constraints, known in advance Internal nodes may be provided with a replica; in this case they become servers and process requests (up to their capacity limit) Research questions: How many replicas required? Which locations? Total replica cost? Quality of Service?

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 6/ 48

slide-18
SLIDE 18

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

Handle all client requests, and minimize cost of replicas → Replica Placement problem Several policies to assign replicas

W = 10 5 4 3 1 2 2 3

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 7/ 48

slide-19
SLIDE 19

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

Handle all client requests, and minimize cost of replicas → Replica Placement problem Several policies to assign replicas

W = 10 5 4 3 1 2 2 3

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 7/ 48

slide-20
SLIDE 20

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

Handle all client requests, and minimize cost of replicas → Replica Placement problem Several policies to assign replicas

W = 10 5 4 3 1 2 2 3

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 7/ 48

slide-21
SLIDE 21

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

Handle all client requests, and minimize cost of replicas → Replica Placement problem Several policies to assign replicas

W = 10 5 4 3 1 2 2 3

Closest

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 7/ 48

slide-22
SLIDE 22

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

Handle all client requests, and minimize cost of replicas → Replica Placement problem Several policies to assign replicas

W = 10 5 3 1 2 2 3 4

Upwards

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 7/ 48

slide-23
SLIDE 23

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

Handle all client requests, and minimize cost of replicas → Replica Placement problem Several policies to assign replicas

W = 10 5 3 1 2 2 3 2 3 4

Multiple

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 7/ 48

slide-24
SLIDE 24

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Major contributions

Theory New access policies Problem complexity LP-based optimal solution to cost of Replica Placement Practice Heuristics for each policy Experiments to assess impact of new policies Experiments to assess impact of QoS on different policies

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 8/ 48

slide-25
SLIDE 25

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Major contributions

Theory New access policies Problem complexity LP-based optimal solution to cost of Replica Placement Practice Heuristics for each policy Experiments to assess impact of new policies Experiments to assess impact of QoS on different policies

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 8/ 48

slide-26
SLIDE 26

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Definitions and notations

Distribution tree T , clients C (leaf nodes), internal nodes N Client i ∈ C:

Sends ri requests per time unit (number of accesses to a single

  • bject database)

Quality of service qi (response time)

Node j ∈ N:

Can contain the object database replica (server) or not Processing capacity Wj Storage cost scj

Tree edge: l ∈ L (communication link between nodes)

Communication time comml Bandwidth limit BWl

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 9/ 48

slide-27
SLIDE 27

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Definitions and notations

Distribution tree T , clients C (leaf nodes), internal nodes N Client i ∈ C:

Sends ri requests per time unit (number of accesses to a single

  • bject database)

Quality of service qi (response time)

Node j ∈ N:

Can contain the object database replica (server) or not Processing capacity Wj Storage cost scj

Tree edge: l ∈ L (communication link between nodes)

Communication time comml Bandwidth limit BWl

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 9/ 48

slide-28
SLIDE 28

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Definitions and notations

Distribution tree T , clients C (leaf nodes), internal nodes N Client i ∈ C:

Sends ri requests per time unit (number of accesses to a single

  • bject database)

Quality of service qi (response time)

Node j ∈ N:

Can contain the object database replica (server) or not Processing capacity Wj Storage cost scj

Tree edge: l ∈ L (communication link between nodes)

Communication time comml Bandwidth limit BWl

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 9/ 48

slide-29
SLIDE 29

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Definitions and notations

Distribution tree T , clients C (leaf nodes), internal nodes N Client i ∈ C:

Sends ri requests per time unit (number of accesses to a single

  • bject database)

Quality of service qi (response time)

Node j ∈ N:

Can contain the object database replica (server) or not Processing capacity Wj Storage cost scj

Tree edge: l ∈ L (communication link between nodes)

Communication time comml Bandwidth limit BWl

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 9/ 48

slide-30
SLIDE 30

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Problem instances

Minimize

s∈R scs under the constraints:

Server capacity – ∀s ∈ R,

i∈C|s∈Servers(i) ri,s ≤ Ws

QoS – ∀i ∈ C, ∀s ∈ Servers(i),

l∈path[i→s] comml ≤ qi.

Link capacity – ∀l ∈ L

i∈C,s∈Servers(i)|l∈path[i→s] ri,s ≤ BWl

Restrict to case where scs = Ws: Replica Counting problem on homogeneous platforms, Replica Cost problem with heterogeneous servers.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 10/ 48

slide-31
SLIDE 31

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Problem instances

Minimize

s∈R scs under the constraints:

Server capacity – ∀s ∈ R,

i∈C|s∈Servers(i) ri,s ≤ Ws

QoS – ∀i ∈ C, ∀s ∈ Servers(i),

l∈path[i→s] comml ≤ qi.

Link capacity – ∀l ∈ L

i∈C,s∈Servers(i)|l∈path[i→s] ri,s ≤ BWl

Restrict to case where scs = Ws: Replica Counting problem on homogeneous platforms, Replica Cost problem with heterogeneous servers.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 10/ 48

slide-32
SLIDE 32

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Problem instances

Minimize

s∈R scs under the constraints:

Server capacity – ∀s ∈ R,

i∈C|s∈Servers(i) ri,s ≤ Ws

QoS – ∀i ∈ C, ∀s ∈ Servers(i),

l∈path[i→s] comml ≤ qi.

Link capacity – ∀l ∈ L

i∈C,s∈Servers(i)|l∈path[i→s] ri,s ≤ BWl

Restrict to case where scs = Ws: Replica Counting problem on homogeneous platforms, Replica Cost problem with heterogeneous servers.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 10/ 48

slide-33
SLIDE 33

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Example: existence of a solution

(b) (a) (c) W = 1 1 s2 s1 1 1 s2 s1 s2 s1 2

(a): solution for all policies (Closest, Upwards, Multiple) (b): no solution with Closest (c): no solution with Closest nor Upwards

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 11/ 48

slide-34
SLIDE 34

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Example: existence of a solution

(b) (a) (c) W = 1 1 s2 s1 1 1 s2 s1 s2 s1 2

(a): solution for all policies (Closest, Upwards, Multiple) (b): no solution with Closest (c): no solution with Closest nor Upwards

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 11/ 48

slide-35
SLIDE 35

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Example: existence of a solution

(b) (a) (c) W = 1 1 s2 s1 1 1 s2 s1 s2 s1 2

(a): solution for all policies (Closest, Upwards, Multiple) (b): no solution with Closest (c): no solution with Closest nor Upwards

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 11/ 48

slide-36
SLIDE 36

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Example: existence of a solution

(b) (a) (c) W = 1 1 s2 s1 1 1 s2 s1 s2 s1 2

(a): solution for all policies (Closest, Upwards, Multiple) (b): no solution with Closest (c): no solution with Closest nor Upwards

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 11/ 48

slide-37
SLIDE 37

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Complexity results

Homogeneous platform: Replica Counting problem, no bandwidth constraints No QoS With QoS Closest polynomial [Cidon02,Liu06] polynomial [Liu06] Upwards NP-hard NP-hard Multiple polynomial NP-hard Homogeneous platforms with bandwidth and QoS constraints: Closest remains polynomial Heterogeneous platforms: all problems are NP-hard

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 12/ 48

slide-38
SLIDE 38

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Complexity results

Homogeneous platform: Replica Counting problem, no bandwidth constraints No QoS With QoS Closest polynomial [Cidon02,Liu06] polynomial [Liu06] Upwards NP-hard NP-hard Multiple polynomial NP-hard Homogeneous platforms with bandwidth and QoS constraints: Closest remains polynomial Heterogeneous platforms: all problems are NP-hard

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 12/ 48

slide-39
SLIDE 39

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Complexity results

Homogeneous platform: Replica Counting problem, no bandwidth constraints No QoS With QoS Closest polynomial [Cidon02,Liu06] polynomial [Liu06] Upwards NP-hard NP-hard Multiple polynomial NP-hard Homogeneous platforms with bandwidth and QoS constraints: Closest remains polynomial Heterogeneous platforms: all problems are NP-hard

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 12/ 48

slide-40
SLIDE 40

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Complexity results

Homogeneous platform: Replica Counting problem, no bandwidth constraints No QoS With QoS Closest polynomial [Cidon02,Liu06] polynomial [Liu06] Upwards NP-hard NP-hard Multiple polynomial NP-hard Homogeneous platforms with bandwidth and QoS constraints: Closest remains polynomial Heterogeneous platforms: all problems are NP-hard

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 12/ 48

slide-41
SLIDE 41

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-42
SLIDE 42

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree Case 1: too many requests

r : 3 5 4 W = 10

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-43
SLIDE 43

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree Case 1: too many requests

  • i r(i) = 12

r : 3 5 4 W = 10

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-44
SLIDE 44

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree Case 1: too many requests

1 replica

  • i r(i) = 12

r : 3 5 4 W = 10

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-45
SLIDE 45

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree Case 2: QoS constraints

r : 3 5 4 W = 10 q : 1 3 2

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-46
SLIDE 46

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree Case 2: QoS constraints

1 replica q(i) < hops r : 3 5 4 W = 10 q : 1 3 2

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-47
SLIDE 47

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree Case 3: bandwidth constraints

r : 3 5 4 b : 5 2 W = 10 4 4

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-48
SLIDE 48

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree Case 3: bandwidth constraints

1 replica b(l) < r(i) r : 3 5 4 b : 5 2 W = 10 4 4

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-49
SLIDE 49

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Algo: Homogeneous Platform with QoS and Bandwidth

Basic idea: computation of the minimal necessary number of replicas in a subtree 1 replica 1 replica 2 replicas

r : 3 5 4 q : 1 3 2 W = 10 b : 5 2 4 4

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 13/ 48

slide-50
SLIDE 50

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

ORP - Optimal Replica Placement Algorithm

Preparation Tree transformation Step 1 Bottom up computation of the contribution of client requests

r : q : 1 3 2 3 5 4 b : 5 6 2 6 2 2 4 4

C(v, i) : the contribution of node v on its i-th ancestor e(v, i) : children of v that have to be equipped with a replica to minimize the contribution on the i-th ancestor of v (respecting some additional constraints).

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 14/ 48

slide-51
SLIDE 51

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

ORP - Optimal Replica Placement Algorithm

Preparation Tree transformation Step 1 Bottom up computation of the contribution of client requests Step 2 Top down replica placement

procedure Place-replica (v, i) if v ∈ C then return; end place a replica at each node of e(v, i); forall c ∈ children(v) do if c ∈ e(v, i) then Place-replica(c,0); else Place-replica(c,i+1); end end

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 15/ 48

slide-52
SLIDE 52

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Linear programming

General instance of the problem: Heterogeneous platform, QoS+bandwidth, Closest, Upwards and Multiple policies Solving over the rationals: solution for all practical values of the problem size

Not very precise bound Upwards/Closest equivalent to Multiple

Integer solving: limitation to s ≤ 50 nodes and clients Mixed bound obtained by solving the Upwards formulation

  • ver the rational and imposing only the xj being integers

Resolution for problem sizes s ≤ 400 Improved bound: if a server is used only at 50% of its capacity, the cost of placing a replica at this node is not halved as it would be with xj = 0.5 → optimal solution for Multiple

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 16/ 48

slide-53
SLIDE 53

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Linear programming

General instance of the problem: Heterogeneous platform, QoS+bandwidth, Closest, Upwards and Multiple policies Solving over the rationals: solution for all practical values of the problem size

Not very precise bound Upwards/Closest equivalent to Multiple

Integer solving: limitation to s ≤ 50 nodes and clients Mixed bound obtained by solving the Upwards formulation

  • ver the rational and imposing only the xj being integers

Resolution for problem sizes s ≤ 400 Improved bound: if a server is used only at 50% of its capacity, the cost of placing a replica at this node is not halved as it would be with xj = 0.5 → optimal solution for Multiple

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 16/ 48

slide-54
SLIDE 54

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Linear programming

General instance of the problem: Heterogeneous platform, QoS+bandwidth, Closest, Upwards and Multiple policies Solving over the rationals: solution for all practical values of the problem size

Not very precise bound Upwards/Closest equivalent to Multiple

Integer solving: limitation to s ≤ 50 nodes and clients Mixed bound obtained by solving the Upwards formulation

  • ver the rational and imposing only the xj being integers

Resolution for problem sizes s ≤ 400 Improved bound: if a server is used only at 50% of its capacity, the cost of placing a replica at this node is not halved as it would be with xj = 0.5 → optimal solution for Multiple

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 16/ 48

slide-55
SLIDE 55

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Linear programming

General instance of the problem: Heterogeneous platform, QoS+bandwidth, Closest, Upwards and Multiple policies Solving over the rationals: solution for all practical values of the problem size

Not very precise bound Upwards/Closest equivalent to Multiple

Integer solving: limitation to s ≤ 50 nodes and clients Mixed bound obtained by solving the Upwards formulation

  • ver the rational and imposing only the xj being integers

Resolution for problem sizes s ≤ 400 Improved bound: if a server is used only at 50% of its capacity, the cost of placing a replica at this node is not halved as it would be with xj = 0.5 → optimal solution for Multiple

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 16/ 48

slide-56
SLIDE 56

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics

Polynomial heuristics for Replica Cost problem

Heterogeneous platforms Heuristics with and without QoS QoS constraints: QoS of client i represents the maximum distance (number of hops) between i and server(i)

Experimental assessment of relative performance of the three policies Impact of QoS No QoS: Traversals of the tree, bottom-up or top-down QoS: Sorted lists Worst case complexity O(s2), where s = |C| + |N| is problem size

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 17/ 48

slide-57
SLIDE 57

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics

Polynomial heuristics for Replica Cost problem

Heterogeneous platforms Heuristics with and without QoS QoS constraints: QoS of client i represents the maximum distance (number of hops) between i and server(i)

Experimental assessment of relative performance of the three policies Impact of QoS No QoS: Traversals of the tree, bottom-up or top-down QoS: Sorted lists Worst case complexity O(s2), where s = |C| + |N| is problem size

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 17/ 48

slide-58
SLIDE 58

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics

Polynomial heuristics for Replica Cost problem

Heterogeneous platforms Heuristics with and without QoS QoS constraints: QoS of client i represents the maximum distance (number of hops) between i and server(i)

Experimental assessment of relative performance of the three policies Impact of QoS No QoS: Traversals of the tree, bottom-up or top-down QoS: Sorted lists Worst case complexity O(s2), where s = |C| + |N| is problem size

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 17/ 48

slide-59
SLIDE 59

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics for Closest- No QoS

Closest Top Down Largest First CTDLF Traversal of the tree, treating subtrees that contains most requests first When a node can process the requests of all the clients in its subtree, node chosen as a server and traversal stopped Procedure called until no more servers are added

18 2 5 2 3 1 2 9 1 n4 n1 n2 n3

Cost

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 18/ 48

slide-60
SLIDE 60

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics for Closest- No QoS

Closest Top Down Largest First CTDLF Traversal of the tree, treating subtrees that contains most requests first When a node can process the requests of all the clients in its subtree, node chosen as a server and traversal stopped Procedure called until no more servers are added

18 2 5 2 3 1 2 9 1 n4 n1 n2 n3

Cost: 18

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 18/ 48

slide-61
SLIDE 61

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics for Closest- No QoS

Closest Top Down Largest First CTDLF Traversal of the tree, treating subtrees that contains most requests first When a node can process the requests of all the clients in its subtree, node chosen as a server and traversal stopped Procedure called until no more servers are added

8 2 5 2 3 1 2 9 1 n4 n1 n2 n3

Cost

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 18/ 48

slide-62
SLIDE 62

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics for Closest- No QoS

Closest Top Down Largest First CTDLF Traversal of the tree, treating subtrees that contains most requests first When a node can process the requests of all the clients in its subtree, node chosen as a server and traversal stopped Procedure called until no more servers are added

8 2 5 2 3 1 2 9 1 n4 n1 n2 n3

Solution cost: 17

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 18/ 48

slide-63
SLIDE 63

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics for Closest- QoS

Closest Big Subtree First CBSF Traversal of the tree, treating subtrees that contain most requests first When a node can process the requests of all the clients in its subtree, node chosen as a server and traversal stopped Procedure called until no more servers are added

18 2 5 2 3 1 2 9 1 n4 n1 n2 n3 q = 3 q = 1 q = 1 q = 2 q = 3

Cost

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 19/ 48

slide-64
SLIDE 64

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics for Closest- QoS

Closest Big Subtree First CBSF Traversal of the tree, treating subtrees that contain most requests first When a node can process the requests of all the clients in its subtree, node chosen as a server and traversal stopped Procedure called until no more servers are added

18 2 5 2 3 1 2 9 1 n4 n1 n2 n3 q = 3 q = 1 q = 1 q = 2 q = 3

Cost

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 19/ 48

slide-65
SLIDE 65

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Heuristics for Closest- QoS

Closest Big Subtree First CBSF Traversal of the tree, treating subtrees that contain most requests first When a node can process the requests of all the clients in its subtree, node chosen as a server and traversal stopped Procedure called until no more servers are added

18 2 5 2 3 1 2 9 1 n4 n1 n2 n3 q = 3 q = 1 q = 1 q = 2 q = 3

Cost: 27

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 19/ 48

slide-66
SLIDE 66

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Results - Percentage of success - QoS

Number of solutions for each lambda and each heuristic average(qos) = height/2

λ =

  • i∈C ri
  • j∈N Wi

20 40 60 80 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 percentage of success lambda Closest_BigSubtreeFirst Closest_SmallQoSFirst Upwards_SQoS_Started Upwards_SQoS_MinReq Upwards_DistServer_Indisp Multiple_SQoS_Close Multiple_SQoS_MinReq Multiple_MinQoS_Indisp MixedBest LP

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 20/ 48

slide-67
SLIDE 67

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Results - Relative Performance

Distance of the result (in terms of replica cost) of the heuristic to the optimal solution Tλ: subset of trees with a solution Relative performance: rperf = 1 |Tλ|

  • t∈Tλ

costLP(t) costh(t) costLP(t): optimal cost on tree t costh(t): heuristic cost on tree t; costh(t) = +∞ if h did not find any solution

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 21/ 48

slide-68
SLIDE 68

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Results - Relative Performance

Distance of the result (in terms of replica cost) of the heuristic to the optimal solution Tλ: subset of trees with a solution Relative performance: rperf = 1 |Tλ|

  • t∈Tλ

costLP(t) costh(t) costLP(t): optimal cost on tree t costh(t): heuristic cost on tree t; costh(t) = +∞ if h did not find any solution

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 21/ 48

slide-69
SLIDE 69

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Results - Relative Performance - No QoS

Heterogeneous results - similar to the homogeneous case

20 40 60 80 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 relative performance lambda ClosestTopDownAll ClosestTopDownLargestFirst ClosestBottomUp UpwardsTopDown UpwardsBigClientFirst MultipleGreedy MultipleTopDown MultipleBottomUp MixedBest

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 22/ 48

slide-70
SLIDE 70

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Results - Relative Performance - QoS

average(qos) = height/2

20 40 60 80 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 relative performance lambda Closest_BigSubtreeFirst Closest_SmallQoSFirst Upwards_SQoS_Started Upwards_SQoS_MinReq Upwards_DistServer_Indisp Multiple_SQoS_Close Multiple_SQoS_MinReq Multiple_MinQoS_Indisp MixedBest

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 23/ 48

slide-71
SLIDE 71

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Summary

No QoS: Striking effect of new policies: many more solutions to the Replica Placement problem Multiple ≥ Upwards ≥ Closest: hierarchy observed within our heuristics Best Multiple heuristic (MB) always at 85% of the optimal: satisfactory result QoS: Hierarchy also under QoS constraints Performance compared to the optimal solution: qos ∈ {1, 2}: 95% average(qos) = height/2: 85% no qos: 85% Smaller trees: results slightly less good

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 24/ 48

slide-72
SLIDE 72

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Summary

No QoS: Striking effect of new policies: many more solutions to the Replica Placement problem Multiple ≥ Upwards ≥ Closest: hierarchy observed within our heuristics Best Multiple heuristic (MB) always at 85% of the optimal: satisfactory result QoS: Hierarchy also under QoS constraints Performance compared to the optimal solution: qos ∈ {1, 2}: 95% average(qos) = height/2: 85% no qos: 85% Smaller trees: results slightly less good

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 24/ 48

slide-73
SLIDE 73

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Related work

Several papers on replica placement, but... ...all consider only the Closest policy Replica Placement in a general graph is NP-complete Wolfson and Milo: impact of the write cost, use of a minimum spanning tree for updates. Tree networks: polynomial solution Cidon et al (multiple objects) and Liu et al (QoS constraints): polynomial algorithms for homogeneous networks. Kalpakis et al: NP-completeness of a variant with bidirectional links (requests served by any node in the tree) Karlsson et al: comparison of different objective functions and several heuristics. No QoS, but several other constraints. Tang et al: real QoS constraints Rodolakis et al: Multiple policy but in a very different context

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 25/ 48

slide-74
SLIDE 74

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Related work

Several papers on replica placement, but... ...all consider only the Closest policy Replica Placement in a general graph is NP-complete Wolfson and Milo: impact of the write cost, use of a minimum spanning tree for updates. Tree networks: polynomial solution Cidon et al (multiple objects) and Liu et al (QoS constraints): polynomial algorithms for homogeneous networks. Kalpakis et al: NP-completeness of a variant with bidirectional links (requests served by any node in the tree) Karlsson et al: comparison of different objective functions and several heuristics. No QoS, but several other constraints. Tang et al: real QoS constraints Rodolakis et al: Multiple policy but in a very different context

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 25/ 48

slide-75
SLIDE 75

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Related work

Several papers on replica placement, but... ...all consider only the Closest policy Replica Placement in a general graph is NP-complete Wolfson and Milo: impact of the write cost, use of a minimum spanning tree for updates. Tree networks: polynomial solution Cidon et al (multiple objects) and Liu et al (QoS constraints): polynomial algorithms for homogeneous networks. Kalpakis et al: NP-completeness of a variant with bidirectional links (requests served by any node in the tree) Karlsson et al: comparison of different objective functions and several heuristics. No QoS, but several other constraints. Tang et al: real QoS constraints Rodolakis et al: Multiple policy but in a very different context

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 25/ 48

slide-76
SLIDE 76

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Outline of the Talk

1

Replica Placement in Tree-Networks Framework Complexity Heuristics for Replica Cost Problem Experiments

2

Pipeline Workflow Applications Bi-criteria Complexity Results

3

In-network Stream Processing Heuristics and Experiments

4

Conclusion

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 26/ 48

slide-77
SLIDE 77

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Mapping applications onto parallel platforms Difficult challenge Heterogeneous clusters, fully heterogeneous platforms Even more difficult! Structured programming approach

Easier to program (deadlocks, process starvation) Range of well-known paradigms (pipeline, farm) Algorithmic skeleton: help for mapping

Focus on pipeline applications Mapping the JPEG encoder pipeline onto a cluster of workstations.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 27/ 48

slide-78
SLIDE 78

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Mapping applications onto parallel platforms Difficult challenge Heterogeneous clusters, fully heterogeneous platforms Even more difficult! Structured programming approach

Easier to program (deadlocks, process starvation) Range of well-known paradigms (pipeline, farm) Algorithmic skeleton: help for mapping

Focus on pipeline applications Mapping the JPEG encoder pipeline onto a cluster of workstations.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 27/ 48

slide-79
SLIDE 79

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Introduction and motivation

Mapping applications onto parallel platforms Difficult challenge Heterogeneous clusters, fully heterogeneous platforms Even more difficult! Structured programming approach

Easier to program (deadlocks, process starvation) Range of well-known paradigms (pipeline, farm) Algorithmic skeleton: help for mapping

Focus on pipeline applications Mapping the JPEG encoder pipeline onto a cluster of workstations.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 27/ 48

slide-80
SLIDE 80

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Multi-criteria scheduling of workflows

Compressed Image Data

Scaling YUV Conversion Block Storage FDCT Quantizier Quantization Table Subsampling Encoder Huffman Table Entropy

Source Image Data

Workflow Several consecutive data-sets enter the application graph. Period P: time interval between the beginning of execution of two consecutive data-sets Latency L: maximal time elapsed between beginning and end of execution of a data-set Failure probability FP: the probability that a processor fails during execution

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 28/ 48

slide-81
SLIDE 81

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

The application

... ...

S1 S2 Sk Sn δ0 w1 δ1 w2 δk−1 δk wk δn wn

Cut pipeline into intervals Map each interval on a single processor... ... or replicate it to improve reliability The platform P processors Fully connected graph (i.e., a clique)

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 29/ 48

slide-82
SLIDE 82

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

The application

... ...

S1 S2 Sk Sn δ0 w1 δ1 w2 δk−1 δk wk δn wn

Cut pipeline into intervals Map each interval on a single processor... ... or replicate it to improve reliability The platform P processors Fully connected graph (i.e., a clique)

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 29/ 48

slide-83
SLIDE 83

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

The application

... ...

P1 P2 S1 S2 Sk Sn

Cut pipeline into intervals Map each interval on a single processor... ... or replicate it to improve reliability The platform P processors Fully connected graph (i.e., a clique)

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 29/ 48

slide-84
SLIDE 84

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

The application

... ...

P3 P4 P6 P1 P2 S1 S2 Sk Sn

Cut pipeline into intervals Map each interval on a single processor... ... or replicate it to improve reliability The platform P processors Fully connected graph (i.e., a clique)

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 29/ 48

slide-85
SLIDE 85

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the game

The application

... ...

P3 P4 P6 P1 P2 S1 S2 Sk Sn

Cut pipeline into intervals Map each interval on a single processor... ... or replicate it to improve reliability The platform P processors Fully connected graph (i.e., a clique)

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 29/ 48

slide-86
SLIDE 86

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Objective function?

Mono-criterion Minimize P Minimize L Minimize FP Bi-criteria How to define it? Minimize α.P + β.L? Minimize α.L + β.FP? Values which are not comparable Minimize P for a fixed latency Minimize L for a fixed period Minimize FP for a fixed latency Minimize L for a fixed failure probability

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 30/ 48

slide-87
SLIDE 87

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Objective function?

Mono-criterion Minimize P Minimize L Minimize FP Bi-criteria How to define it? Minimize α.P + β.L? Minimize α.L + β.FP? Values which are not comparable Minimize P for a fixed latency Minimize L for a fixed period Minimize FP for a fixed latency Minimize L for a fixed failure probability

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 30/ 48

slide-88
SLIDE 88

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Objective function?

Mono-criterion Minimize P Minimize L Minimize FP Bi-criteria How to define it? Minimize α.P + β.L? Minimize α.L + β.FP? Values which are not comparable Minimize P for a fixed latency Minimize L for a fixed period Minimize FP for a fixed latency Minimize L for a fixed failure probability

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 30/ 48

slide-89
SLIDE 89

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Objective function?

Mono-criterion Minimize P Minimize L Minimize FP Bi-criteria How to define it? Minimize α.P + β.L? Minimize α.L + β.FP? Values which are not comparable Minimize P for a fixed latency Minimize L for a fixed period Minimize FP for a fixed latency Minimize L for a fixed failure probability

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 30/ 48

slide-90
SLIDE 90

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

An Optimal Algorithm

Minimize L with fixed P - Homogeneous platform L(i, q) :

  • min. latency with exactly q procs mapping stages 1 to i

L(n, q) for 1 ≤ q ≤ p Init:

L(i, 1) = (

δ0 b + Pi k=1 wk s + δi b

if ≤ P ∞ else , L(1, q) = ∞ if q > 1

Recursion: L(i, q) = min

j<i

  L(j, q − 1) +

i

  • k=j+1

wk s + δi b

  • δj

b +

i

  • k=j+1

wk s + δi b ≤ P

  

... ...

w1 δ0 S1 δ1 S2 w2 δj−1 Sj δj wj Sj+1 ...

...

Si δi wi Sn δn wn Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 31/ 48

slide-91
SLIDE 91

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Exemple: Minimizing FP with fixed latency

Minimize FP with fixed latency Different speed processors - Failure heterogeneous Fixed latency: 22 10 1 w2 = 100 w1 = 1 S1 S2

s = 100 fp = 0.8 s = 1 fp = 0.1

Open complexity!

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 32/ 48

slide-92
SLIDE 92

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Exemple: Minimizing FP with fixed latency

Minimize FP with fixed latency Different speed processors - Failure heterogeneous Fixed latency: 22 10 1 w2 = 100 w1 = 1 S1 S2 10 + 101 ≫ 22

s = 100 fp = 0.8 s = 1 fp = 0.1

Open complexity!

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 32/ 48

slide-93
SLIDE 93

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Exemple: Minimizing FP with fixed latency

Minimize FP with fixed latency Different speed processors - Failure heterogeneous Fixed latency: 22 10 1 w2 = 100 w1 = 1 S1 S2 20 + 101/100 < 22 FP = (1 − (1 − 0.82)) = 0.64

s = 100 fp = 0.8 s = 1 fp = 0.1

Open complexity!

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 32/ 48

slide-94
SLIDE 94

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Exemple: Minimizing FP with fixed latency

Minimize FP with fixed latency Different speed processors - Failure heterogeneous Fixed latency: 22 10 1 w2 = 100 w1 = 1 S1 S2 30 + 101/100 > 22

s = 100 fp = 0.8 s = 1 fp = 0.1

Open complexity!

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 32/ 48

slide-95
SLIDE 95

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Exemple: Minimizing FP with fixed latency

Minimize FP with fixed latency Different speed processors - Failure heterogeneous Fixed latency: 22 10 1 w2 = 100 w1 = 1 S1 S2 10 + 1/1 + 10 × 1 + 100/100 = 22 FP : 1−(1−0.1)×(1−0.810) < 0.2

s = 100 fp = 0.8 s = 1 fp = 0.1

Open complexity!

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 32/ 48

slide-96
SLIDE 96

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Exemple: Minimizing FP with fixed latency

Minimize FP with fixed latency Different speed processors - Failure heterogeneous Fixed latency: 22 10 1 w2 = 100 w1 = 1 S1 S2

s = 100 fp = 0.8 s = 1 fp = 0.1

Open complexity!

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 32/ 48

slide-97
SLIDE 97

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Complexity Results

Bi-criteria interval mapping

Objective Failure Hom.

  • Com. Hom.

Het. P & L / polynomial NP-hard NP-hard FP & L hom. polynomial polynomial NP-hard FP & L het. polynomial

  • pen

NP-hard

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 33/ 48

slide-98
SLIDE 98

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Integer linear programming

Integer LP to solve Interval Mapping on Communication Homogeneous platforms Many integer variables: no efficient algorithm to solve Approach limited to small problem instances Absolute performance of the heuristics for such instances Bucket behavior of LP solutions

300 310 320 330 340 350 300 305 310 315 320 325 330 Optimal Latency Fixed Period P_fixed

(a) Fixed P.

300 305 310 315 320 325 330 320 330 340 350 360 370 380 390 400 Optimal Period Fixed Latency L_fixed

(b) Fixed L.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 34/ 48

slide-99
SLIDE 99

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Outline of the Talk

1

Replica Placement in Tree-Networks Framework Complexity Heuristics for Replica Cost Problem Experiments

2

Pipeline Workflow Applications Bi-criteria Complexity Results

3

In-network Stream Processing Heuristics and Experiments

4

Conclusion

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 35/ 48

slide-100
SLIDE 100

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the Game

Processors

  • p3
  • b1
  • b1
  • b2
  • b1
  • p5
  • p1
  • b1
  • b2
  • b1
  • b2

application 1

  • b3
  • p1
  • p2
  • p2
  • p4
  • p1

Applications

computation speed network card capacity application 2

Goal Minimize total processing power of the target platform while matching all application requirements. Assess impact of reusing intermediate results.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 36/ 48

slide-101
SLIDE 101

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the Game

Processors

  • p3
  • b1
  • b1
  • b2
  • b1
  • p5
  • p1
  • b1
  • b2
  • b1
  • b2

application 1

  • b3
  • p1
  • p2
  • p2
  • p4
  • p1

Applications

computation speed network card capacity application 2

Goal Minimize total processing power of the target platform while matching all application requirements. Assess impact of reusing intermediate results.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 36/ 48

slide-102
SLIDE 102

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the Game

Processors

  • p3
  • b1
  • b1
  • b2
  • b1
  • p5
  • p1
  • b1
  • b2
  • b1
  • b2

application 1

  • b3
  • p1
  • p2
  • p2
  • p4
  • p1

Applications

computation speed network card capacity application 2

Goal Minimize total processing power of the target platform while matching all application requirements. Assess impact of reusing intermediate results.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 36/ 48

slide-103
SLIDE 103

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the Game

Processors

  • p3
  • b1
  • b1
  • b2
  • b1
  • p5
  • p1
  • b1
  • b2
  • b1
  • b2

application 1

  • b3
  • p1
  • p2
  • p2
  • p4
  • p1

Applications

computation speed network card capacity application 2

Goal Minimize total processing power of the target platform while matching all application requirements. Assess impact of reusing intermediate results.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 36/ 48

slide-104
SLIDE 104

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Rule of the Game

Processors

  • p3
  • b1
  • b1
  • b2
  • b1
  • p5
  • p1
  • b1
  • b2
  • b1
  • b2

application 1

  • b3
  • p1
  • p2
  • p2
  • p4
  • p1

Applications

computation speed network card capacity application 2

Goal Minimize total processing power of the target platform while matching all application requirements. Assess impact of reusing intermediate results.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 36/ 48

slide-105
SLIDE 105

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

The Application Model

K applications OP = {op1, op2, . . . } set of operators OB = {ob1, ob2, ob3, . . . } basic

  • bjects

Computation of operator opp: wp operations, δp size of output Application tree

n4 n5

  • 1

n2 n1

  • 1
  • 2
  • 2
  • 3

n3

For application k: ρ(k) application throughput Object obj dj size of obj f (k)

j

download frequency

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 37/ 48

slide-106
SLIDE 106

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

The Platform Model

The platform P processors Fully connected graph (i.e., a clique) Objective Map operators onto processors such that processing power is minimized and all application throughputs are achieved.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 38/ 48

slide-107
SLIDE 107

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Overview of Heuristics (1)

Server selection strategies: (S1) Select the fastest processor (blocking); (S2) Select the processor with the fastest network card (blocking); (S3) Select the fastest processor (non-blocking); (S4) Select the processor with the fastest network card (non-blocking).

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 39/ 48

slide-108
SLIDE 108

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Overview of Heuristics (2)

Heuristics: Reuse of intermediate results (H1) RandomNoReuse (H3) TopDownBFS (H5) BottomUpBFS (H2) Random (H4) TopDownDFS (H6) BottomUpDFS

  • p3
  • b1
  • b1
  • b2
  • b1
  • p5
  • p1
  • b1
  • b2
  • b1
  • b2

application 1

  • b3
  • p1
  • p2
  • p2
  • p4
  • p1

application 2 Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 40/ 48

slide-109
SLIDE 109

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Results

Number of processors increases. 50 runs. 5 applications. 50 operators. Successful runs.

50 40 30 20 10

number of solutions number of processors

10 20 30 40 50 60 70

(S3) Fastest proc.

number of solutions

50 40 30 20 10 10

number of processors

20 30 40 50 60 70

(S3) Fastest proc - no reuse.

TopDownBFS TopDownDFS Random Random NoReuse BottomUpDFS BottomUpBFS

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 41/ 48

slide-110
SLIDE 110

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Results

Number of processors increases. 50 runs. 5 applications. 50 operators. Relative performance.

relative performance (cost)

0.2 0.4 0.6 0.8 1 number of processors 10 20 30 40 50 60 70

(S3) Fastest proc.

relative performance (cost)

1 0.8 0.6 0.4 0.2 10 20 30 40 50 60 70

number of processors

(S1) Fastest proc - blocking.

TopDownBFS TopDownDFS Random Random NoReuse BottomUpDFS BottomUpBFS

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 42/ 48

slide-111
SLIDE 111

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Summary

Random approach dramatically bad Neglecting reuse limits success rate and quality of solution in terms of cost Top Down approach turns out to be the best BottomUp only with BFS competitive DFS unable to reuse results efficiently (bandwidth) Strong dependency of processor selection strategy on solution quality Solid combination: TopDownBFS with fastest proc - non-blocking

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 43/ 48

slide-112
SLIDE 112

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Outline of the Talk

1

Replica Placement in Tree-Networks Framework Complexity Heuristics for Replica Cost Problem Experiments

2

Pipeline Workflow Applications Bi-criteria Complexity Results

3

In-network Stream Processing Heuristics and Experiments

4

Conclusion

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 44/ 48

slide-113
SLIDE 113

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Summary

Study of three mapping and scheduling problems Replica placement Pipeline workflows In-network stream processing

5 4 3 1 2 2 3

Complexity study: Influence of heterogeneity Multi-criteria optimization Algorithms: Optimal algorithms and NP-completeness proofs Heuristics for NP-complete instances Experiments: Absolute performance via comparison to LP MPI-application of JPEG encoder

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 45/ 48

slide-114
SLIDE 114

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Summary

Study of three mapping and scheduling problems Replica placement Pipeline workflows In-network stream processing

... ...

S1 S2 Sk Sn δ0 w1 δ1 w2 δk−1 δk wk δn wn

Complexity study: Influence of heterogeneity Multi-criteria optimization Algorithms: Optimal algorithms and NP-completeness proofs Heuristics for NP-complete instances Experiments: Absolute performance via comparison to LP MPI-application of JPEG encoder

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 45/ 48

slide-115
SLIDE 115

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Summary

Study of three mapping and scheduling problems Replica placement Pipeline workflows In-network stream processing

  • p3
  • b1
  • b1
  • b2
  • b1
  • p5
  • p1
  • b1
  • b2
  • b1
  • b2

application 1

  • b3
  • p1
  • p2
  • p2
  • p4
  • p1

application 2

Complexity study: Influence of heterogeneity Multi-criteria optimization Algorithms: Optimal algorithms and NP-completeness proofs Heuristics for NP-complete instances Experiments: Absolute performance via comparison to LP MPI-application of JPEG encoder

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 45/ 48

slide-116
SLIDE 116

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Summary

Study of three mapping and scheduling problems Replica placement Pipeline workflows In-network stream processing Complexity study: Influence of heterogeneity Multi-criteria optimization Algorithms: Optimal algorithms and NP-completeness proofs Heuristics for NP-complete instances Experiments: Absolute performance via comparison to LP MPI-application of JPEG encoder

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 45/ 48

slide-117
SLIDE 117

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Ongoing Work

Tri-criteria optimization on pipelines: Latency - reliability - period Heuristics More ambitious application: MPEG4

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 46/ 48

slide-118
SLIDE 118

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Perspectives

Replica Placement More simulations for the Replica Cost problem: shape of the trees, distribution law of the requests, degree of heterogeneity of the platforms Consider the problem with several object types Extension to more complex objective functions Pipeline Workflow Extension to fork, fork-join and tree workflows Multi-criteria: new objectives like power consumption and rental cost Stream Processing Mutable applications: Operators can be rearranged based on

  • perator associativity and commutativity rules

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 47/ 48

slide-119
SLIDE 119

Replica Placement Pipeline Workflows In-network Stream Processing Conclusion

Journals

  • A. Benoit, H. Kosch, V. Rehn-Sonigo, and Y. Robert.

Multi-criteria Scheduling of Pipeline Workflows (and Application to the JPEG Encoder)

  • Int. Journal of High Performance Computing Applications, 23, 2009

A.Benoit, V. Rehn-Sonigo, and Y. Robert. Replica Placement and Access Policies in Tree Networks. IEEE Transactions on Parallel and Distributed Systems, 19(12), 2008.

  • L. Marchal, V. Rehn, Y. Robert, and F. Vivien.

Scheduling algorithms for data redistribution and load-balancing on master-slave platforms. Parallel Processing Letters, 17(1), 2007.

Conferences

Replica Placement CoreGRID’2007, Core GRID Symposium 2007 ICCS’07, the 2007 International Conference on Computational Science. HCW’07, the 16th Heterogeneity in Computing Workshop. Pipeline Workflow Applications ICCS’08, the 2008 International Conference on Computational Science. HCW’08, the 17th Heterogeneity in Computing Workshop. HeteroPar’07, Algorithms, Models and Tools for Parallel Computing on Heterogeneous Networks (in conjunction with Cluster 2007). In-Network Stream Processing APDCM’09, the 11th Workshop on Advances in Parallel and Distributed Computational Models. Scheduling Strategies on Star Platforms PDP’2007, 15th Euromicro Workshop on Parallel, Distributed and Network-based

  • Processing. HCW’06, the 15th Heterogeneous Computing Workshop.

Veronika.Sonigo@ens-lyon.fr July 7, 2009 Mapping and Scheduling of Workflow Applications 48/ 48