Introduction Motivation Syntax and semantics Example Other approaches Conclusion Spatial stochastic process algebra ◮ locations, L and collections of locations, P L ◮ structure over P L , weighted graph G = ( L , E , w ) ◮ undirected hypergraph or directed graph ◮ E ⊆ P L and w : E → R ◮ weights modify rates on actions between locations ◮ L ∈ P L α ∈ A M ⊆ A r > 0 ◮ sequential components S ::= ( α @ L , r ) . S | S + S | C s @ L Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Spatial stochastic process algebra ◮ locations, L and collections of locations, P L ◮ structure over P L , weighted graph G = ( L , E , w ) ◮ undirected hypergraph or directed graph ◮ E ⊆ P L and w : E → R ◮ weights modify rates on actions between locations ◮ L ∈ P L α ∈ A M ⊆ A r > 0 ◮ sequential components S ::= ( α @ L , r ) . S | S + S | C s @ L Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Spatial stochastic process algebra ◮ locations, L and collections of locations, P L ◮ structure over P L , weighted graph G = ( L , E , w ) ◮ undirected hypergraph or directed graph ◮ E ⊆ P L and w : E → R ◮ weights modify rates on actions between locations ◮ L ∈ P L α ∈ A M ⊆ A r > 0 ◮ sequential components S ::= ( α @ L , r ) . S | S + S | C s @ L ◮ locations defined at sequential level only Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Spatial stochastic process algebra ◮ locations, L and collections of locations, P L ◮ structure over P L , weighted graph G = ( L , E , w ) ◮ undirected hypergraph or directed graph ◮ E ⊆ P L and w : E → R ◮ weights modify rates on actions between locations ◮ L ∈ P L α ∈ A M ⊆ A r > 0 ◮ sequential components S ::= ( α @ L , r ) . S | S + S | C s @ L ◮ locations defined at sequential level only ◮ model components P ::= P ⊲ ⊳ M P | P / M | C Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Parameterised operational semantics ◮ define abstract process algebra parameterised by three functions Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Parameterised operational semantics ◮ define abstract process algebra parameterised by three functions ◮ transitions labelled with A × P L × R + Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Parameterised operational semantics ◮ define abstract process algebra parameterised by three functions ◮ transitions labelled with A × P L × R + ◮ Prefix L ′ = apref (( α @ L , r ) . S ) ( α @ L ′ , r ) ( α @ L , r ) . S − − − − − → S Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Parameterised operational semantics ◮ define abstract process algebra parameterised by three functions ◮ transitions labelled with A × P L × R + ◮ Prefix L ′ = apref (( α @ L , r ) . S ) ( α @ L ′ , r ) ( α @ L , r ) . S − − − − − → S ( α @ L 1 , r 1 ) ( α @ L 2 , r 2 ) → P ′ → P ′ P 1 − − − − − − P 2 − − − − − − 1 2 ◮ Cooperation α ∈ M ( α @ L , R ) → P ′ M P ′ − − − − − P 1 ⊲ M P 2 ⊳ 1 ⊲ ⊳ 2 L = async ( P 1 , P 2 , L 1 , L 2 ) R = rsync ( P 1 , P 2 , L 1 , L 2 , r 1 , r 2 ) Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Parameterised operational semantics ◮ define abstract process algebra parameterised by three functions ◮ transitions labelled with A × P L × R + ◮ Prefix L ′ = apref (( α @ L , r ) . S ) ( α @ L ′ , r ) ( α @ L , r ) . S − − − − − → S ( α @ L 1 , r 1 ) ( α @ L 2 , r 2 ) → P ′ → P ′ P 1 − − − − − − P 2 − − − − − − 1 2 ◮ Cooperation α ∈ M ( α @ L , R ) → P ′ M P ′ − − − − − P 1 ⊲ M P 2 ⊳ 1 ⊲ ⊳ 2 L = async ( P 1 , P 2 , L 1 , L 2 ) R = rsync ( P 1 , P 2 , L 1 , L 2 , r 1 , r 2 ) ◮ other rules defined in the obvious manner Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Parameterised operational semantics ◮ define abstract process algebra parameterised by three functions ◮ transitions labelled with A × P L × R + ◮ Prefix L ′ = apref (( α @ L , r ) . S ) ( α @ L ′ , r ) ( α @ L , r ) . S − − − − − → S ( α @ L 1 , r 1 ) ( α @ L 2 , r 2 ) → P ′ → P ′ P 1 − − − − − − P 2 − − − − − − 1 2 ◮ Cooperation α ∈ M ( α @ L , R ) → P ′ M P ′ − − − − − P 1 ⊲ M P 2 ⊳ 1 ⊲ ⊳ 2 L = async ( P 1 , P 2 , L 1 , L 2 ) R = rsync ( P 1 , P 2 , L 1 , L 2 , r 1 , r 2 ) ◮ other rules defined in the obvious manner ◮ instantiate functions to obtain concrete process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology ◮ single packet traversal through network Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated ◮ want to model different topologies and traffic Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated ◮ want to model different topologies and traffic ◮ choose functions to create process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated ◮ want to model different topologies and traffic ◮ choose functions to create process algebra ◮ each sequential component must have single fixed location Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated ◮ want to model different topologies and traffic ◮ choose functions to create process algebra ◮ each sequential component must have single fixed location ◮ communication must be pairwise and directional Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Concrete process algebra for modelling networks ◮ networking performance ◮ scenario ◮ arbitrary topology ◮ single packet traversal through network ◮ processes can be colocated ◮ want to model different topologies and traffic ◮ choose functions to create process algebra ◮ each sequential component must have single fixed location ◮ communication must be pairwise and directional ◮ let P L = L ∪ ( L × L ), singletons and ordered pairs Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Functions for concrete process algebra ◮ functions Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Functions for concrete process algebra ◮ functions � ℓ if ploc ( S ) = { ℓ } apref ( S ) = ⊥ otherwise Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Functions for concrete process algebra ◮ functions � ℓ if ploc ( S ) = { ℓ } apref ( S ) = ⊥ otherwise � ( ℓ 1 , ℓ 2 ) if L 1 = { ℓ 1 } , L 2 = { ℓ 2 } , ( ℓ 1 , ℓ 2 ) ∈ E async ( P 1 , P 2 , L 1 , L 2 ) = ⊥ otherwise Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Functions for concrete process algebra ◮ functions � ℓ if ploc ( S ) = { ℓ } apref ( S ) = ⊥ otherwise � ( ℓ 1 , ℓ 2 ) if L 1 = { ℓ 1 } , L 2 = { ℓ 2 } , ( ℓ 1 , ℓ 2 ) ∈ E async ( P 1 , P 2 , L 1 , L 2 ) = ⊥ otherwise rsync ( P 1 , P 2 , L 1 , L 2 , r 1 , r 2 ) r 1 r 2 r α ( P 2 ) min( r α ( P 1 ) , r α ( P 2 )) · w (( ℓ 1 , ℓ 2 )) r α ( P 1 ) = if L 1 = { ℓ 1 } , L 2 = { ℓ 2 } , ( ℓ 1 , ℓ 2 ) ∈ E ⊥ otherwise Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Example network A Sender B P 1 C P 2 P 3 D P 4 E P 5 P 6 F Receiver Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion PEPA model def Sender @ A = ( prepare , ρ ) . Sending @ A = � 6 def Sending @ A i =1 ( c Si , r S ) . ( ack , r ack ) . Sender @ A = � 6 def Receiver @ F i =1 ( c iR , r 6 ) . Receiving @ F def Receiving @ F = ( consume , γ ) . ( ack , r ack ) . Receiver @ F ( c Si , ⊤ ) . Q i @ ℓ i + � 6 def P i @ ℓ i = j =1 , j � = i ( c ji , r ) . Q i @ ℓ i ( c iR , ⊤ ) . P i @ ℓ i + � 6 def Q i @ ℓ i = j =1 , j � = i ( c ij , r ) . P i @ ℓ i def Network = ( Sender @ A ⊲ ∗ ( P 1@ B ⊲ ∗ ( P 2@ C ⊲ ∗ ( P 3@ C ⊲ ⊳ ⊳ ⊳ ⊳ ∗ ( P 4@ D ⊲ ∗ ( P 5@ E ⊲ ∗ ( P 6@ F ⊲ ∗ Receiver @ F ))))))) ⊳ ⊳ ⊳ Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Graphs ◮ rates: r = r R = r S = 10 A Sender B P 1 C P 2 P 3 D P 4 E P 5 P 6 F Receiver Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Graphs ◮ rates: r = r R = r S = 10 ◮ the weighted graph G describes the topology A Sender A B C D E F B P 1 A 1 1 B 1 1 C P 2 P 3 D P 4 1 1 1 C E P 5 D 1 1 1 E 1 1 1 P 6 F 1 1 1 1 F Receiver Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Graphs ◮ G 1 represents heavy traffic between C and E A Sender A B C D E F B P 1 A 1 1 B 1 1 C P 2 P 3 D P 4 1 1 0 . 1 C E P 5 D 1 1 1 E 0 . 1 1 1 P 6 F 1 1 1 1 F Receiver Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Graphs ◮ G 2 represents no connectivity between C and E A Sender A B C D E F B P 1 A 1 1 B 1 1 C P 2 P 3 D P 4 1 1 0 C E P 5 D 1 1 1 E 0 1 1 P 6 F 1 1 1 1 F Receiver Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Graphs ◮ G 3 represents high connectivity between colocated processes A Sender A B C D E F B P 1 A 1 1 B 1 1 C P 2 P 3 D P 4 1 10 1 C E P 5 D 1 1 1 E 1 1 1 P 6 F 1 1 1 10 F Receiver Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Analysis ◮ cumulative density function of passage time Comparison of different network models 1 0.9 0.8 0.7 0.6 Prob 0.5 0.4 0.3 0.2 networkr networkr-fastl 0.1 networkr-noCE networkr-slowCE 0 0 1 2 3 4 5 6 7 8 9 10 Time Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Evaluation ◮ uniform description for each node in the network Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Evaluation ◮ uniform description for each node in the network ◮ network topology captured by graph Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Evaluation ◮ uniform description for each node in the network ◮ network topology captured by graph ◮ graph modifications capture network variations Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Evaluation ◮ uniform description for each node in the network ◮ network topology captured by graph ◮ graph modifications capture network variations ◮ existing analysis framework Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Evaluation ◮ uniform description for each node in the network ◮ network topology captured by graph ◮ graph modifications capture network variations ◮ existing analysis framework ◮ abstract process algebra is flexible Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates ◮ wireless sensor networks Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates ◮ wireless sensor networks ◮ actual physical location Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates ◮ wireless sensor networks ◮ actual physical location ◮ weights capture performance characteristics over distance Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates ◮ wireless sensor networks ◮ actual physical location ◮ weights capture performance characteristics over distance ◮ scope for many other scenarios Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates ◮ wireless sensor networks ◮ actual physical location ◮ weights capture performance characteristics over distance ◮ scope for many other scenarios ◮ different types of networks Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Different concrete process algebras ◮ multiple packets ◮ each located node in network is one or more buffers ◮ similar approach ◮ throughput, loss rates ◮ wireless sensor networks ◮ actual physical location ◮ weights capture performance characteristics over distance ◮ scope for many other scenarios ◮ different types of networks ◮ virus transmission in vineyards Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous behaviour Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous behaviour ◮ semantic model ◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous behaviour ◮ semantic model ◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata ◮ delay-tolerant networks Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous behaviour ◮ semantic model ◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata ◮ delay-tolerant networks ◮ packets modelled as a continuous flow Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous behaviour ◮ semantic model ◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata ◮ delay-tolerant networks ◮ packets modelled as a continuous flow ◮ periods of connectivity modelled stochastically Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous behaviour ◮ semantic model ◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata ◮ delay-tolerant networks ◮ packets modelled as a continuous flow ◮ periods of connectivity modelled stochastically ◮ full buffers modelled discretely Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion And now for something slightly different ◮ Stochastic HYPE, joint with Jane Hillston and Luca Bortolussi ◮ process algebra to model discrete, stochastic and continuous behaviour ◮ semantic model ◮ piecewise deterministic Markov processes ◮ transition-driven stochastic hybrid automata ◮ delay-tolerant networks ◮ packets modelled as a continuous flow ◮ periods of connectivity modelled stochastically ◮ full buffers modelled discretely ◮ determine storage required at nodes Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance ◮ further research Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance ◮ further research ◮ explore how it can be applied in modelling networks Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance ◮ further research ◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance ◮ further research ◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere ◮ comparison with other location-based formalism Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance ◮ further research ◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere ◮ comparison with other location-based formalism ◮ theoretical results for abstract process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion Conclusion and further work ◮ conclusion ◮ stochastic process algebra with location ◮ designed to be flexible ◮ useful for modelling network performance ◮ further research ◮ explore how it can be applied in modelling networks ◮ explore how it can be applied elsewhere ◮ comparison with other location-based formalism ◮ theoretical results for abstract process algebra ◮ behavioural equivalences Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
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
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus ◮ locations and collections of location Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus ◮ locations and collections of location ◮ P L = 2 L , powerset Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus ◮ locations and collections of location ◮ P L = 2 L , powerset ◮ P L = L ∪ ( L × L ), singletons and ordered pairs Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus ◮ locations and collections of location ◮ P L = 2 L , powerset ◮ P L = L ∪ ( L × L ), singletons and ordered pairs ◮ different choices for P L give different semantics Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus ◮ locations and collections of location ◮ P L = 2 L , powerset ◮ P L = L ∪ ( L × L ), singletons and ordered pairs ◮ different choices for P L give different semantics ◮ locations associated with processes and/or actions Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus ◮ locations and collections of location ◮ P L = 2 L , powerset ◮ P L = L ∪ ( L × L ), singletons and ordered pairs ◮ different choices for P L give different semantics ◮ locations associated with processes and/or actions ◮ singleton locations versus multiple locations Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
Introduction Motivation Syntax and semantics Example Other approaches Conclusion More comments ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus ◮ locations and collections of location ◮ P L = 2 L , powerset ◮ P L = L ∪ ( L × L ), singletons and ordered pairs ◮ different choices for P L give different semantics ◮ locations associated with processes and/or actions ◮ singleton locations versus multiple locations ◮ longer terms aims Vashti Galpin Modelling network performance with a spatial stochastic process algebra June 2010
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