modelling network performance with a spatial stochastic
TRANSCRIPT
![Page 1: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/1.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Modelling network performance with a spatialstochastic process algebra
Vashti GalpinLaboratory for Foundations of Computer Science
University of Edinburgh
17 June 2010
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 2: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/2.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 3: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/3.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 4: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/4.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 5: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/5.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 6: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/6.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 7: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/7.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 8: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/8.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 9: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/9.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Introduction
I model network performance
I introduce spatial concepts to a stochastic process algebra
I analysis using continuous time Markov chains (CTMCs)
I demonstrate through an example
I other approaches to network modelling
I using the same spatial stochastic process algebra
I using a process algebra with stochastic, continuous anddiscrete aspects
I conclusions and further work
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 10: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/10.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]
I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 11: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/11.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 12: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/12.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 13: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/13.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 14: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/14.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 15: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/15.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 16: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/16.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 17: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/17.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Motivation
I PEPA [Hillston 1996]I compact syntax, rules of behaviour
P(α,r)−−−→ P ′
P + Q(α,r)−−−→ P ′
I transitions labelled with (α, r) ∈ A× R+
I interpret as continuous time Markov chain or ODEs
I various analyses to understand performance
I add a general notion of location
I location names, cities
I points in n-dimensional space
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 18: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/18.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PL
I structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 19: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/19.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 20: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/20.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 21: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/21.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → R
I weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 22: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/22.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 23: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/23.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 24: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/24.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 25: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/25.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 26: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/26.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 27: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/27.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Spatial stochastic process algebra
I locations, L and collections of locations, PLI structure over PL, weighted graph G = (L,E ,w)
I undirected hypergraph or directed graph
I E ⊆ PL and w : E → RI weights modify rates on actions between locations
I L ∈ PL α ∈ A M ⊆ A r > 0
I sequential components
S ::= (α@L, r).S | S + S | Cs@L
I locations defined at sequential level only
I model components
P ::= P BCM
P | P/M | C
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 28: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/28.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Parameterised operational semantics
I define abstract process algebra parameterised by threefunctions
I transitions labelled with A×PL × R+
I Prefix
(α@L, r).S(α@L′,r)−−−−−→ S
L′ = apref ((α@L, r).S)
I CooperationP1
(α@L1,r1)−−−−−−→ P ′1 P2
(α@L2,r2)−−−−−−→ P ′2
P1 BCM
P2(α@L,R)−−−−−→ P ′
1BCM
P ′2
α ∈ M
L = async(P1,P2, L1, L2) R = rsync(P1,P2, L1, L2, r1, r2)
I other rules defined in the obvious manner
I instantiate functions to obtain concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 29: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/29.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Parameterised operational semantics
I define abstract process algebra parameterised by threefunctions
I transitions labelled with A×PL × R+
I Prefix
(α@L, r).S(α@L′,r)−−−−−→ S
L′ = apref ((α@L, r).S)
I CooperationP1
(α@L1,r1)−−−−−−→ P ′1 P2
(α@L2,r2)−−−−−−→ P ′2
P1 BCM
P2(α@L,R)−−−−−→ P ′
1BCM
P ′2
α ∈ M
L = async(P1,P2, L1, L2) R = rsync(P1,P2, L1, L2, r1, r2)
I other rules defined in the obvious manner
I instantiate functions to obtain concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 30: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/30.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Parameterised operational semantics
I define abstract process algebra parameterised by threefunctions
I transitions labelled with A×PL × R+
I Prefix
(α@L, r).S(α@L′,r)−−−−−→ S
L′ = apref ((α@L, r).S)
I CooperationP1
(α@L1,r1)−−−−−−→ P ′1 P2
(α@L2,r2)−−−−−−→ P ′2
P1 BCM
P2(α@L,R)−−−−−→ P ′
1BCM
P ′2
α ∈ M
L = async(P1,P2, L1, L2) R = rsync(P1,P2, L1, L2, r1, r2)
I other rules defined in the obvious manner
I instantiate functions to obtain concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 31: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/31.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Parameterised operational semantics
I define abstract process algebra parameterised by threefunctions
I transitions labelled with A×PL × R+
I Prefix
(α@L, r).S(α@L′,r)−−−−−→ S
L′ = apref ((α@L, r).S)
I CooperationP1
(α@L1,r1)−−−−−−→ P ′1 P2
(α@L2,r2)−−−−−−→ P ′2
P1 BCM
P2(α@L,R)−−−−−→ P ′
1BCM
P ′2
α ∈ M
L = async(P1,P2, L1, L2) R = rsync(P1,P2, L1, L2, r1, r2)
I other rules defined in the obvious manner
I instantiate functions to obtain concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 32: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/32.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Parameterised operational semantics
I define abstract process algebra parameterised by threefunctions
I transitions labelled with A×PL × R+
I Prefix
(α@L, r).S(α@L′,r)−−−−−→ S
L′ = apref ((α@L, r).S)
I CooperationP1
(α@L1,r1)−−−−−−→ P ′1 P2
(α@L2,r2)−−−−−−→ P ′2
P1 BCM
P2(α@L,R)−−−−−→ P ′
1BCM
P ′2
α ∈ M
L = async(P1,P2, L1, L2) R = rsync(P1,P2, L1, L2, r1, r2)
I other rules defined in the obvious manner
I instantiate functions to obtain concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 33: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/33.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Parameterised operational semantics
I define abstract process algebra parameterised by threefunctions
I transitions labelled with A×PL × R+
I Prefix
(α@L, r).S(α@L′,r)−−−−−→ S
L′ = apref ((α@L, r).S)
I CooperationP1
(α@L1,r1)−−−−−−→ P ′1 P2
(α@L2,r2)−−−−−−→ P ′2
P1 BCM
P2(α@L,R)−−−−−→ P ′
1BCM
P ′2
α ∈ M
L = async(P1,P2, L1, L2) R = rsync(P1,P2, L1, L2, r1, r2)
I other rules defined in the obvious manner
I instantiate functions to obtain concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 34: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/34.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenario
I arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 35: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/35.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenario
I arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 36: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/36.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 37: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/37.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 38: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/38.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 39: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/39.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 40: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/40.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 41: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/41.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 42: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/42.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 43: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/43.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Concrete process algebra for modelling networks
I networking performance
I scenarioI arbitrary topology
I single packet traversal through network
I processes can be colocated
I want to model different topologies and traffic
I choose functions to create process algebra
I each sequential component must have single fixed location
I communication must be pairwise and directional
I let PL = L ∪ (L × L), singletons and ordered pairs
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 44: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/44.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Functions for concrete process algebra
I functions
apref (S) =
{` if ploc(S) = {`}⊥ otherwise
async(P1,P2, L1, L2) =
{(`1, `2) if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
rsync(P1,P2, L1, L2, r1, r2)
=
r1
rα(P1)
r2rα(P2)
min(rα(P1), rα(P2)) · w((`1, `2))
if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 45: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/45.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Functions for concrete process algebra
I functions
apref (S) =
{` if ploc(S) = {`}⊥ otherwise
async(P1,P2, L1, L2) =
{(`1, `2) if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
rsync(P1,P2, L1, L2, r1, r2)
=
r1
rα(P1)
r2rα(P2)
min(rα(P1), rα(P2)) · w((`1, `2))
if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 46: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/46.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Functions for concrete process algebra
I functions
apref (S) =
{` if ploc(S) = {`}⊥ otherwise
async(P1,P2, L1, L2) =
{(`1, `2) if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
rsync(P1,P2, L1, L2, r1, r2)
=
r1
rα(P1)
r2rα(P2)
min(rα(P1), rα(P2)) · w((`1, `2))
if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 47: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/47.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Functions for concrete process algebra
I functions
apref (S) =
{` if ploc(S) = {`}⊥ otherwise
async(P1,P2, L1, L2) =
{(`1, `2) if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
rsync(P1,P2, L1, L2, r1, r2)
=
r1
rα(P1)
r2rα(P2)
min(rα(P1), rα(P2)) · w((`1, `2))
if L1 ={`1}, L2 ={`2}, (`1, `2) ∈ E
⊥ otherwise
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 48: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/48.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Example networkSenderA
P1B
P2 P3C P4D
P5E
P6
Receiver
F
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
PEPA model
Sender@Adef= (prepare, ρ).Sending@A
Sending@Adef=
∑6i=1(cSi , rS).(ack, rack).Sender@A
Receiver@Fdef=
∑6i=1(ciR , r6).Receiving@F
Receiving@Fdef= (consume, γ).(ack, rack).Receiver@F
Pi@`idef= (cSi ,>).Qi@`i +
∑6j=1,j 6=i (cji , r).Qi@`i
Qi@`idef= (ciR ,>).Pi@`i +
∑6j=1,j 6=i (cij , r).Pi@`i
Networkdef= (Sender@A BC
∗(P1@B BC
∗(P2@C BC
∗(P3@C BC
∗(P4@D BC
∗(P5@E BC
∗(P6@F BC
∗Receiver@F )))))))
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 50: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/50.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Graphs
I rates: r = rR = rS = 10
I 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
SenderA
P1B
P2 P3C P4D
P5E
P6
Receiver
F
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 51: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/51.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Graphs
I rates: r = rR = rS = 10
I 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
SenderA
P1B
P2 P3C P4D
P5E
P6
Receiver
F
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 52: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/52.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Graphs
I 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
SenderA
P1B
P2 P3C P4D
P5E
P6
Receiver
F
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
Graphs
I G2 represents no connectivity between C and E
A B C D E F
A 1 1
B 1 1
C 1 1 0
D 1 1 1
E 0 1 1
F 1 1 1 1
SenderA
P1B
P2 P3C P4D
P5E
P6
Receiver
F
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 54: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/54.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Graphs
I 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
SenderA
P1B
P2 P3C P4D
P5E
P6
Receiver
F
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 55: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/55.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Analysis
I cumulative density function of passage time
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
Pro
b
Time
Comparison of different network models
networkrnetworkr-fastl
networkr-noCEnetworkr-slowCE
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
Evaluation
I uniform description for each node in the network
I network topology captured by graph
I graph modifications capture network variations
I existing analysis framework
I abstract process algebra is flexible
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 57: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/57.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Evaluation
I uniform description for each node in the network
I network topology captured by graph
I graph modifications capture network variations
I existing analysis framework
I abstract process algebra is flexible
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 58: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/58.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Evaluation
I uniform description for each node in the network
I network topology captured by graph
I graph modifications capture network variations
I existing analysis framework
I abstract process algebra is flexible
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 59: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/59.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Evaluation
I uniform description for each node in the network
I network topology captured by graph
I graph modifications capture network variations
I existing analysis framework
I abstract process algebra is flexible
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 60: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/60.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Evaluation
I uniform description for each node in the network
I network topology captured by graph
I graph modifications capture network variations
I existing analysis framework
I abstract process algebra is flexible
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 61: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/61.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 62: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/62.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 63: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/63.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 64: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/64.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 65: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/65.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 66: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/66.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 67: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/67.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 68: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/68.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 69: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/69.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 70: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/70.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Different concrete process algebras
I multiple packets
I each located node in network is one or more buffers
I similar approach
I throughput, loss rates
I wireless sensor networks
I actual physical location
I weights capture performance characteristics over distance
I scope for many other scenarios
I different types of networks
I virus transmission in vineyards
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 71: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/71.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 72: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/72.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 73: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/73.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 74: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/74.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 75: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/75.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 76: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/76.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 77: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/77.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 78: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/78.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
And now for something slightly different
I Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi
I process algebra to model discrete, stochastic and continuousbehaviour
I semantic model
I piecewise deterministic Markov processes
I transition-driven stochastic hybrid automata
I delay-tolerant networks
I packets modelled as a continuous flow
I periods of connectivity modelled stochastically
I full buffers modelled discretely
I determine storage required at nodes
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 79: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/79.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 80: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/80.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 81: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/81.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 82: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/82.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 83: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/83.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 84: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/84.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 85: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/85.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 86: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/86.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 87: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/87.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 88: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/88.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
Conclusion and further work
I conclusion
I stochastic process algebra with location
I designed to be flexible
I useful for modelling network performance
I further research
I explore how it can be applied in modelling networks
I explore how it can be applied elsewhere
I comparison with other location-based formalism
I theoretical results for abstract process algebra
I behavioural equivalences
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 89: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/89.jpg)
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
![Page 90: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/90.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related research
I PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of location
I PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 91: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/91.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of location
I PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 92: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/92.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of location
I PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 93: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/93.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of location
I PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 94: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/94.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of location
I PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 95: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/95.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 96: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/96.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 97: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/97.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semantics
I locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 98: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/98.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semanticsI locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 99: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/99.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semanticsI locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 100: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/100.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semanticsI locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aims
I prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 101: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/101.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semanticsI locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aimsI prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010
![Page 102: Modelling network performance with a spatial stochastic](https://reader031.vdocument.in/reader031/viewer/2022021305/62073a2549d709492c2f3bb8/html5/thumbnails/102.jpg)
Introduction Motivation Syntax and semantics Example Other approaches Conclusion
More comments
I related researchI PEPA nets (Gilmore et al)
I StoKlaim (de Nicola et al)
I biological models – BioAmbients, attributed π-calculus
I locations and collections of locationI PL = 2L, powerset
I PL = L ∪ (L × L), singletons and ordered pairs
I different choices for PL give different semanticsI locations associated with processes and/or actions
I singleton locations versus multiple locations
I longer terms aimsI prove results for parametric process algebra
I then apply to concrete process algebra
Vashti Galpin
Modelling network performance with a spatial stochastic process algebra June 2010