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Modelling network performance with a spatial stochastic process - - PowerPoint PPT Presentation

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Introduction Motivation Syntax and semantics Example Other approaches Conclusion Modelling network performance with a spatial stochastic process algebra Vashti Galpin Laboratory for Foundations of Computer Science University of Edinburgh

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SLIDE 1

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Modelling network performance with a spatial stochastic process algebra

Vashti Galpin Laboratory for Foundations of Computer Science University of Edinburgh 17 June 2010

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 2

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-3
SLIDE 3

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance ◮ introduce spatial concepts to a stochastic process algebra

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 4

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance ◮ introduce spatial concepts to a stochastic process algebra ◮ analysis using continuous time Markov chains (CTMCs)

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 5

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance ◮ introduce spatial concepts to a stochastic process algebra ◮ analysis using continuous time Markov chains (CTMCs) ◮ demonstrate through an example

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-6
SLIDE 6

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance ◮ introduce spatial concepts to a stochastic process algebra ◮ analysis using continuous time Markov chains (CTMCs) ◮ demonstrate through an example ◮ other approaches to network modelling

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 7

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance ◮ introduce spatial concepts to a stochastic process algebra ◮ analysis using continuous time Markov chains (CTMCs) ◮ demonstrate through an example ◮ other approaches to network modelling

◮ using the same spatial stochastic process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 8

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance ◮ introduce spatial concepts to a stochastic process algebra ◮ analysis using continuous time Markov chains (CTMCs) ◮ demonstrate through an example ◮ other approaches to network modelling

◮ using the same spatial stochastic process algebra ◮ using a process algebra with stochastic, continuous and

discrete aspects

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-9
SLIDE 9

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Introduction

◮ model network performance ◮ introduce spatial concepts to a stochastic process algebra ◮ analysis using continuous time Markov chains (CTMCs) ◮ demonstrate through an example ◮ other approaches to network modelling

◮ using the same spatial stochastic process algebra ◮ using a process algebra with stochastic, continuous and

discrete aspects

◮ conclusions and further work

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 10

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 11

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

◮ compact syntax, rules of behaviour

P

(α,r)

− − − → P′ P + Q

(α,r)

− − − → P′

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-12
SLIDE 12

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

◮ compact syntax, rules of behaviour

P

(α,r)

− − − → P′ P + Q

(α,r)

− − − → P′

◮ transitions labelled with (α, r) ∈ A × R+ Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-13
SLIDE 13

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

◮ compact syntax, rules of behaviour

P

(α,r)

− − − → P′ P + Q

(α,r)

− − − → P′

◮ transitions labelled with (α, r) ∈ A × R+ ◮ interpret as continuous time Markov chain or ODEs Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 14

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

◮ compact syntax, rules of behaviour

P

(α,r)

− − − → P′ P + Q

(α,r)

− − − → P′

◮ transitions labelled with (α, r) ∈ A × R+ ◮ interpret as continuous time Markov chain or ODEs ◮ various analyses to understand performance Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 15

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

◮ compact syntax, rules of behaviour

P

(α,r)

− − − → P′ P + Q

(α,r)

− − − → P′

◮ transitions labelled with (α, r) ∈ A × R+ ◮ interpret as continuous time Markov chain or ODEs ◮ various analyses to understand performance

◮ add a general notion of location

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-16
SLIDE 16

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

◮ compact syntax, rules of behaviour

P

(α,r)

− − − → P′ P + Q

(α,r)

− − − → P′

◮ transitions labelled with (α, r) ∈ A × R+ ◮ interpret as continuous time Markov chain or ODEs ◮ various analyses to understand performance

◮ add a general notion of location

◮ location names, cities Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-17
SLIDE 17

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Motivation

◮ PEPA [Hillston 1996]

◮ compact syntax, rules of behaviour

P

(α,r)

− − − → P′ P + Q

(α,r)

− − − → P′

◮ transitions labelled with (α, r) ∈ A × R+ ◮ interpret as continuous time Markov chain or ODEs ◮ various analyses to understand performance

◮ add a general notion of location

◮ location names, cities ◮ points in n-dimensional space Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 18

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 19

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 20

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL and w : E → R Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 22

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL and w : E → R ◮ weights modify rates on actions between locations Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 23

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL and w : E → R ◮ weights modify rates on actions between locations

◮ L ∈ PL

α ∈ A M ⊆ A r > 0

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 24

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL and w : E → R ◮ weights modify rates on actions between locations

◮ L ∈ PL

α ∈ A M ⊆ A r > 0

◮ sequential components

S ::= (α@L, r).S | S + S | Cs@L

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 25

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL and w : E → R ◮ weights modify rates on actions between locations

◮ L ∈ PL

α ∈ A M ⊆ A r > 0

◮ sequential components

S ::= (α@L, r).S | S + S | Cs@L

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 26

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL and w : E → R ◮ weights modify rates on actions between locations

◮ L ∈ PL

α ∈ A M ⊆ A r > 0

◮ sequential components

S ::= (α@L, r).S | S + S | Cs@L

◮ locations defined at sequential level only

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 27

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Spatial stochastic process algebra

◮ locations, L and collections of locations, PL ◮ structure over PL, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL and w : E → R ◮ weights modify rates on actions between locations

◮ L ∈ PL

α ∈ A M ⊆ A r > 0

◮ sequential components

S ::= (α@L, r).S | S + S | Cs@L

◮ locations defined at sequential level only ◮ model components

P ::= P ⊲

⊳

M P | P/M | C Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 28

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Parameterised operational semantics

◮ define abstract process algebra parameterised by three

functions

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 29

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Parameterised operational semantics

◮ define abstract process algebra parameterised by three

functions

◮ transitions labelled with A × PL × R+

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 30

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Parameterised operational semantics

◮ define abstract process algebra parameterised by three

functions

◮ transitions labelled with A × PL × R+ ◮ Prefix

(α@L, r).S

(α@L′,r)

− − − − − → S L′ = apref ((α@L, r).S)

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 31

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Parameterised operational semantics

◮ define abstract process algebra parameterised by three

functions

◮ transitions labelled with A × PL × R+ ◮ Prefix

(α@L, r).S

(α@L′,r)

− − − − − → S L′ = apref ((α@L, r).S)

◮ Cooperation

P1

(α@L1,r1)

− − − − − − → P′

1

P2

(α@L2,r2)

− − − − − − → P′

2

P1 ⊲

⊳

M P2

(α@L,R)

− − − − − → P′

1 ⊲

⊳

M P′

2

α ∈ M L = async(P1, P2, L1, L2) R = rsync(P1, P2, L1, L2, r1, r2)

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 32

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Parameterised operational semantics

◮ define abstract process algebra parameterised by three

functions

◮ transitions labelled with A × PL × R+ ◮ Prefix

(α@L, r).S

(α@L′,r)

− − − − − → S L′ = apref ((α@L, r).S)

◮ Cooperation

P1

(α@L1,r1)

− − − − − − → P′

1

P2

(α@L2,r2)

− − − − − − → P′

2

P1 ⊲

⊳

M P2

(α@L,R)

− − − − − → P′

1 ⊲

⊳

M P′

2

α ∈ M L = async(P1, P2, L1, L2) R = rsync(P1, P2, L1, L2, r1, r2)

◮ other rules defined in the obvious manner

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 33

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Parameterised operational semantics

◮ define abstract process algebra parameterised by three

functions

◮ transitions labelled with A × PL × R+ ◮ Prefix

(α@L, r).S

(α@L′,r)

− − − − − → S L′ = apref ((α@L, r).S)

◮ Cooperation

P1

(α@L1,r1)

− − − − − − → P′

1

P2

(α@L2,r2)

− − − − − − → P′

2

P1 ⊲

⊳

M P2

(α@L,R)

− − − − − → P′

1 ⊲

⊳

M P′

2

α ∈ M L = async(P1, P2, L1, L2) R = rsync(P1, P2, L1, L2, r1, r2)

◮ other rules defined in the obvious manner ◮ instantiate functions to obtain concrete process algebra

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 34

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 35

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 36

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 37

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology ◮ single packet traversal through network Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 38

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 39

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated

◮ want to model different topologies and traffic

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 40

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated

◮ want to model different topologies and traffic ◮ choose functions to create process algebra

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-41
SLIDE 41

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated

◮ want to model different topologies and traffic ◮ choose functions to create process algebra

◮ each sequential component must have single fixed location Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 42

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated

◮ want to model different topologies and traffic ◮ choose functions to create process algebra

◮ each sequential component must have single fixed location ◮ communication must be pairwise and directional Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-43
SLIDE 43

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated

◮ want to model different topologies and traffic ◮ choose functions to create process algebra

◮ each sequential component must have single fixed location ◮ communication must be pairwise and directional

◮ let PL = L ∪ (L × L), singletons and ordered pairs

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Functions for concrete process algebra

◮ functions

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 45

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Functions for concrete process algebra

◮ functions

apref (S) =

  • ℓ

if ploc(S) = {ℓ} ⊥

  • therwise

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 46

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Functions for concrete process algebra

◮ functions

apref (S) =

  • ℓ

if ploc(S) = {ℓ} ⊥

  • therwise

async(P1, P2, L1, L2) =

  • (ℓ1, ℓ2)

if L1 ={ℓ1}, L2 ={ℓ2}, (ℓ1, ℓ2) ∈ E ⊥

  • therwise

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 47

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Functions for concrete process algebra

◮ functions

apref (S) =

  • ℓ

if ploc(S) = {ℓ} ⊥

  • therwise

async(P1, P2, L1, L2) =

  • (ℓ1, ℓ2)

if L1 ={ℓ1}, L2 ={ℓ2}, (ℓ1, ℓ2) ∈ E ⊥

  • therwise

rsync(P1, P2, L1, L2, r1, r2) =        r1 rα(P1) r2 rα(P2) min(rα(P1), rα(P2)) · w((ℓ1, ℓ2)) if L1 ={ℓ1}, L2 ={ℓ2}, (ℓ1, ℓ2) ∈ E ⊥

  • therwise

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 48

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Example network

Sender A P1 B P2 P3 C P4 D P5 E P6 Receiver F

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 49

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

PEPA model

Sender@A

def

= (prepare, ρ).Sending@A Sending@A

def

= 6

i=1(cSi, rS).(ack, rack).Sender@A

Receiver@F

def

= 6

i=1(ciR, r6).Receiving@F

Receiving@F

def

= (consume, γ).(ack, rack).Receiver@F Pi@ℓi

def

= (cSi, ⊤).Qi@ℓi + 6

j=1,j=i(cji, r).Qi@ℓi

Qi@ℓi

def

= (ciR, ⊤).Pi@ℓi + 6

j=1,j=i(cij, r).Pi@ℓi

Network

def

= (Sender@A ⊲

⊳

∗ (P1@B ⊲

⊳

∗ (P2@C ⊲

⊳

∗ (P3@C ⊲

⊳

∗

(P4@D ⊲

⊳

∗ (P5@E ⊲

⊳

∗ (P6@F ⊲

⊳

∗ Receiver@F))))))) Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 50

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Graphs

◮ rates: r = rR = rS = 10

Sender A P1 B P2 P3 C P4 D P5 E P6 Receiver F

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 51

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Graphs

◮ rates: r = rR = rS = 10 ◮ the weighted graph G describes the topology

A B C D E F A 1 1 B 1 1 C 1 1 1 D 1 1 1 E 1 1 1 F 1 1 1 1

Sender A P1 B P2 P3 C P4 D P5 E P6 Receiver F

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 52

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Graphs

◮ G1 represents heavy traffic between C and E

A B C D E F A 1 1 B 1 1 C 1 1 0.1 D 1 1 1 E 0.1 1 1 F 1 1 1 1

Sender A P1 B P2 P3 C P4 D P5 E P6 Receiver F

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 53

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Graphs

◮ G2 represents no connectivity between C and E

A B C D E F A 1 1 B 1 1 C 1 1 D 1 1 1 E 1 1 F 1 1 1 1

Sender A P1 B P2 P3 C P4 D P5 E P6 Receiver F

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-54
SLIDE 54

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Graphs

◮ G3 represents high connectivity between colocated processes

A B C D E F A 1 1 B 1 1 C 1 10 1 D 1 1 1 E 1 1 1 F 1 1 1 10

Sender A P1 B P2 P3 C P4 D P5 E P6 Receiver F

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 55

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Analysis

◮ cumulative density function of passage time 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 2 3 4 5 6 7 8 9 10 Prob Time Comparison of different network models networkr networkr-fastl networkr-noCE networkr-slowCE

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 56

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Evaluation

◮ uniform description for each node in the network

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-57
SLIDE 57

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Evaluation

◮ uniform description for each node in the network ◮ network topology captured by graph

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 58

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Evaluation

◮ uniform description for each node in the network ◮ network topology captured by graph ◮ graph modifications capture network variations

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 59

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Evaluation

◮ uniform description for each node in the network ◮ network topology captured by graph ◮ graph modifications capture network variations ◮ existing analysis framework

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 60

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Evaluation

◮ uniform description for each node in the network ◮ network topology captured by graph ◮ graph modifications capture network variations ◮ existing analysis framework ◮ abstract process algebra is flexible

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 61

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-62
SLIDE 62

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-63
SLIDE 63

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-64
SLIDE 64

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-65
SLIDE 65

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates

◮ wireless sensor networks

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-66
SLIDE 66

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates

◮ wireless sensor networks

◮ actual physical location Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-67
SLIDE 67

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates

◮ wireless sensor networks

◮ actual physical location ◮ weights capture performance characteristics over distance Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-68
SLIDE 68

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates

◮ wireless sensor networks

◮ actual physical location ◮ weights capture performance characteristics over distance

◮ scope for many other scenarios

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-69
SLIDE 69

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates

◮ wireless sensor networks

◮ actual physical location ◮ weights capture performance characteristics over distance

◮ scope for many other scenarios

◮ different types of networks Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-70
SLIDE 70

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Different concrete process algebras

◮ multiple packets

◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates

◮ wireless sensor networks

◮ actual physical location ◮ weights capture performance characteristics over distance

◮ scope for many other scenarios

◮ different types of networks ◮ virus transmission in vineyards Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-72
SLIDE 72

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous

behaviour

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-73
SLIDE 73

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous

behaviour

◮ semantic model

◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-74
SLIDE 74

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous

behaviour

◮ semantic model

◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata

◮ delay-tolerant networks

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-75
SLIDE 75

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous

behaviour

◮ semantic model

◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata

◮ delay-tolerant networks

◮ packets modelled as a continuous flow Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-76
SLIDE 76

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous

behaviour

◮ semantic model

◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata

◮ delay-tolerant networks

◮ packets modelled as a continuous flow ◮ periods of connectivity modelled stochastically Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-77
SLIDE 77

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous

behaviour

◮ semantic model

◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata

◮ delay-tolerant networks

◮ packets modelled as a continuous flow ◮ periods of connectivity modelled stochastically ◮ full buffers modelled discretely Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-78
SLIDE 78

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

And now for something slightly different

◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous

behaviour

◮ semantic model

◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata

◮ delay-tolerant networks

◮ packets modelled as a continuous flow ◮ periods of connectivity modelled stochastically ◮ full buffers modelled discretely ◮ determine storage required at nodes Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-79
SLIDE 79

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-80
SLIDE 80

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-81
SLIDE 81

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-82
SLIDE 82

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-83
SLIDE 83

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance

◮ further research

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-84
SLIDE 84

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance

◮ further research

◮ explore how it can be applied in modelling networks Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-85
SLIDE 85

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance

◮ further research

◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-86
SLIDE 86

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance

◮ further research

◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere ◮ comparison with other location-based formalism Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-87
SLIDE 87

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance

◮ further research

◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere ◮ comparison with other location-based formalism ◮ theoretical results for abstract process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-88
SLIDE 88

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Conclusion and further work

◮ conclusion

◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance

◮ further research

◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere ◮ comparison with other location-based formalism ◮ theoretical results for abstract process algebra ◮ behavioural equivalences Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 89

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

Thank you

This research was funded by the EPSRC SIGNAL Project

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

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SLIDE 90

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-91
SLIDE 91

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-92
SLIDE 92

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-93
SLIDE 93

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-94
SLIDE 94

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-95
SLIDE 95

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-96
SLIDE 96

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset ◮ PL = L ∪ (L × L), singletons and ordered pairs Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-97
SLIDE 97

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset ◮ PL = L ∪ (L × L), singletons and ordered pairs

◮ different choices for PL give different semantics

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-98
SLIDE 98

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset ◮ PL = L ∪ (L × L), singletons and ordered pairs

◮ different choices for PL give different semantics

◮ locations associated with processes and/or actions Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-99
SLIDE 99

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset ◮ PL = L ∪ (L × L), singletons and ordered pairs

◮ different choices for PL give different semantics

◮ locations associated with processes and/or actions ◮ singleton locations versus multiple locations Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-100
SLIDE 100

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset ◮ PL = L ∪ (L × L), singletons and ordered pairs

◮ different choices for PL give different semantics

◮ locations associated with processes and/or actions ◮ singleton locations versus multiple locations

◮ longer terms aims

Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-101
SLIDE 101

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset ◮ PL = L ∪ (L × L), singletons and ordered pairs

◮ different choices for PL give different semantics

◮ locations associated with processes and/or actions ◮ singleton locations versus multiple locations

◮ longer terms aims

◮ prove results for parametric process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010

slide-102
SLIDE 102

Introduction Motivation Syntax and semantics Example Other approaches Conclusion

More comments

◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) ◮ biological models – BioAmbients, attributed π-calculus

◮ locations and collections of location

◮ PL = 2L, powerset ◮ PL = L ∪ (L × L), singletons and ordered pairs

◮ different choices for PL give different semantics

◮ locations associated with processes and/or actions ◮ singleton locations versus multiple locations

◮ longer terms aims

◮ prove results for parametric process algebra ◮ then apply to concrete process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010