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

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Modelling network performance with a spatial stochastic process algebra Vashti Galpin Laboratory for Foundations of Computer Science University of

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Modelling network performance with a spatial stochastic process algebra

Vashti Galpin Laboratory for Foundations of Computer Science University of Edinburgh 26 May 2009

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs)

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ related research

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ related research

◮ PEPA nets (Gilmore et al) Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ related research

◮ PEPA nets (Gilmore et al) ◮ StoKlaim (de Nicola et al) Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Introduction

◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Outline

Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivating example

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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ PEPA [Hillston 1996]

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ 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 Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ 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 ◮ analyses to understand performance Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Motivation

◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ 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 ◮ analyses to understand performance

◮ new ingredient: general notion of location

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

◮ PL = 2L, powerset Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

◮ PL = 2L, powerset ◮ PL = P ∪ (P × P), singletons and ordered pairs Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

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

◮ structure over locations, weighted graph G = (L, E, w)

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

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

◮ structure over locations, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

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

◮ structure over locations, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

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

◮ structure over locations, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL ◮ w : E → R Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Locations

◮ L locations

◮ location names, cities ◮ points in n-dimensional space

◮ collections of locations

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

◮ structure over locations, weighted graph G = (L, E, w)

◮ undirected hypergraph or directed graph ◮ E ⊆ PL ◮ w : E → R ◮ weights modify rates on actions between locations Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Syntax

◮ L locations, PL collection of locations

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Syntax

◮ L locations, PL collection of locations ◮ L ∈ PL

α ∈ A M ⊆ A r > 0

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Syntax

◮ L locations, PL collection of 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Syntax

◮ L locations, PL collection of locations ◮ L ∈ PL

α ∈ A M ⊆ A r > 0

◮ sequential components

S ::= (α@L, r).S | S + S | Cs@L

◮ sequential constant definition

Cs@L

def

= S

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Syntax

◮ L locations, PL collection of locations ◮ L ∈ PL

α ∈ A M ⊆ A r > 0

◮ sequential components

S ::= (α@L, r).S | S + S | Cs@L

◮ sequential constant definition

Cs@L

def

= S

◮ model components

P ::= P ⊲

⊳

M P | P/M | C Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Syntax

◮ L locations, PL collection of locations ◮ L ∈ PL

α ∈ A M ⊆ A r > 0

◮ sequential components

S ::= (α@L, r).S | S + S | Cs@L

◮ sequential constant definition

Cs@L

def

= S

◮ model components

P ::= P ⊲

⊳

M P | P/M | C

◮ model constant definition

C

def

= P

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics

◮ transitions labelled with A × PL × R+

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics

◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics

◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics

◮ 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)

◮ parameterised by three functions

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics

◮ 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)

◮ parameterised by three functions ◮ other rules defined in the obvious manner

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra ◮ determines what transitions are possible

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra ◮ determines what transitions are possible ◮ different choices for PL give different semantics

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra ◮ determines what transitions are possible ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra ◮ determines what transitions are possible ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra ◮ determines what transitions are possible ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra ◮ determines what transitions are possible ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Parameterised operational semantics (cont.)

◮ instantiation of functions gives concrete process algebra ◮ determines what transitions are possible ◮ 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Concrete process algebra for modelling networks

◮ networking performance

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Concrete process algebra for modelling networks

◮ networking performance ◮ scenario

◮ arbitrary topology Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Functions for concrete process algebra

◮ functions

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance 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 AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications ◮ theoretical results Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications ◮ theoretical results ◮ semantic equivalences Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications ◮ theoretical results ◮ semantic equivalences ◮ translation into PEPA Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications ◮ theoretical results ◮ semantic equivalences ◮ translation into PEPA ◮ results from graph theory Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications ◮ theoretical results ◮ semantic equivalences ◮ translation into PEPA ◮ results from graph theory

◮ conclusions

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications ◮ theoretical results ◮ semantic equivalences ◮ translation into PEPA ◮ results from graph theory

◮ conclusions

◮ presentation of a very general stochastic process algebra with

locations

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Further work and conclusions

◮ further work

◮ other specific applications ◮ theoretical results ◮ semantic equivalences ◮ translation into PEPA ◮ results from graph theory

◮ conclusions

◮ presentation of a very general stochastic process algebra with

locations

◮ use for modelling network performance in a general way Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009

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Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion

Thank you

This research was funded by the EPSRC SIGNAL Project

Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009