Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Modelling network performance with a spatial stochastic process algebra Vashti Galpin Laboratory for Foundations of Computer Science University of Edinburgh 26 May 2009 Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ related research Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ related research ◮ PEPA nets (Gilmore et al ) Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Introduction ◮ model network performance ◮ spatial concepts in a stochastic process algebra ◮ location can affect time taken ◮ analysis using continuous time Markov chains (CTMCs) ◮ no unnecessary increase in state space ◮ related research ◮ PEPA nets (Gilmore et al ) ◮ StoKlaim (de Nicola et al ) ◮ biological models – BioAmbients, attributed π -calculus Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Outline Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivating example 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 AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ PEPA [Hillston 1996] Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ PEPA [Hillston 1996] ◮ compact syntax, rules of behaviour ( α, r ) → P ′ P − − − ( α, r ) P + Q − − − → P ′ Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ PEPA [Hillston 1996] ◮ compact syntax, rules of behaviour ( α, r ) → P ′ P − − − ( α, r ) P + Q − − − → P ′ ◮ transitions labelled with ( α, r ) ∈ A × R + Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ PEPA [Hillston 1996] ◮ compact syntax, rules of behaviour ( α, r ) → P ′ P − − − ( α, r ) P + Q − − − → P ′ ◮ transitions labelled with ( α, r ) ∈ A × R + ◮ interpret as continuous time Markov chain Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ PEPA [Hillston 1996] ◮ compact syntax, rules of behaviour ( α, r ) → P ′ P − − − ( α, r ) P + Q − − − → P ′ ◮ transitions labelled with ( α, r ) ∈ A × R + ◮ interpret as continuous time Markov chain ◮ analyses to understand performance Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Motivation ◮ we want to model the performance of a network ◮ we know how to do this with stochastic process algebra ◮ PEPA [Hillston 1996] ◮ compact syntax, rules of behaviour ( α, r ) → P ′ P − − − ( α, r ) P + Q − − − → P ′ ◮ transitions labelled with ( α, r ) ∈ A × R + ◮ interpret as continuous time Markov chain ◮ analyses to understand performance ◮ new ingredient: general notion of location Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Locations ◮ L locations Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Locations ◮ L locations ◮ location names, cities Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Locations ◮ L locations ◮ location names, cities ◮ points in n -dimensional space Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Locations ◮ L locations ◮ location names, cities ◮ points in n -dimensional space ◮ collections of locations Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
Introduction Motivation Locations Syntax Semantics Measuring performance Conclusion Locations ◮ L locations ◮ location names, cities ◮ points in n -dimensional space ◮ collections of locations ◮ P L = 2 L , powerset Vashti Galpin Modelling network performance with a spatial stochastic process algebra AINA 2009
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