O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE H YBRID PERFORMANCE MODELLING OF OPPORTUNISTIC NETWORKS Luca Bortolussi 1 Vashti Galpin 2 Jane Hillston 2 1 Dipartimento di Matematica e Geoscienze Università degli studi di Trieste luca@dmi.units.it 2 Laboratory for Foundation of Computer Science University of Edinburgh Vashti.Galpin@ec.ac.uk Jane.Hillston@ec.ac.uk QAPL 2012, Tallinn, Estonia, April 1, 2012
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE O UTLINE 1 O PPORTUNISTIC NETWORKS 2 S TOCHASTIC HYPE 3 O PPORTUNISTIC N ETWORKS IN S HYPE
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE O PPORTUNISTIC NETWORKS characteristics and challenges disconnectedness: very low probability of direct path between any two nodes high latency and low data rate: due to lack of connectivity, queuing at intermediate nodes limited resources: battery-driven, hostile environment, constraints on storage and communication protocols approach: store-carry-forward main objective: maximise probabality of packet reaching destination secondary objectives: minimise delivery delay and resources usage
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE O PPORTUNISTIC NETWORKS : PROTOCOLS classification of protocols deterministic versus stochastic with or without infrastructure flooding versus forwarding flooding each packet is forwarded to many nodes epidemic routing prevents forwarding of already-seen packets forwarding each packet is forwarded to one node information gathered during communication used to choose example: historical information about path likelihood
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE S TOCHASTIC HYPE: OVERVIEW M AIN FEATURES OF HYPE Modelling of the continuous dynamics is focussed on the notion of flow. Control structure of events is modelled separately from the reaction of continuous dynamics to events. Events can either happen at stochastic times (exponentially distributed) or instantaneously, when guards become true. Modularity in the definition of the actual form of guards, resets, functions. In summary: compositionality.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE A SIMPLE ( FLUID ) BUFFER MODEL input output BUFFER on, off, empty on, off, full
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE HYPE A CTIONS AND A CTIVITIES E VENTS Events can either be instantaneous (buffer becomes full or empty: full , empty ∈ E d ) or they can happen at exponential random times (input/output of data in buffer: on in / out , off in / out ∈ E s ) A CTIVITIES OR INFLUENCES Description of flows: influences on continuous variables. For instance, the effect of data inflow in the buffer is α ( � X ) = ( in , r in , I ( � α ∈ A X )) ✟ ✯ ❍ ❨ ✟✟ ❍ ✻ ❍ influence type influence name rate here I ( � X ) := const where � X is a formal parameter.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE HYPE A CTIONS AND A CTIVITIES E VENTS Events can either be instantaneous (buffer becomes full or empty: full , empty ∈ E d ) or they can happen at exponential random times (input/output of data in buffer: on in / out , off in / out ∈ E s ) A CTIVITIES OR INFLUENCES Description of flows: influences on continuous variables. For instance, the effect of data inflow in the buffer is α ( � X ) = ( in , r in , I ( � α ∈ A X )) ✟ ✯ ❍ ❨ ✟✟ ❍ ✻ ❍ influence type influence name rate here I ( � X ) := const where � X is a formal parameter.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE HYPE A CTIONS AND A CTIVITIES E VENTS Events can either be instantaneous (buffer becomes full or empty: full , empty ∈ E d ) or they can happen at exponential random times (input/output of data in buffer: on in / out , off in / out ∈ E s ) A CTIVITIES OR INFLUENCES Description of flows: influences on continuous variables. For instance, the effect of data inflow in the buffer is α ( � X ) = ( in , r in , I ( � α ∈ A X )) ✟ ✯ ❍ ❨ ✟✟ ❍ ✻ ❍ influence type influence name rate here I ( � X ) := const where � X is a formal parameter.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE HYPE A CTIONS AND A CTIVITIES E VENTS Events can either be instantaneous (buffer becomes full or empty: full , empty ∈ E d ) or they can happen at exponential random times (input/output of data in buffer: on in / out , off in / out ∈ E s ) A CTIVITIES OR INFLUENCES Description of flows: influences on continuous variables. For instance, the effect of data inflow in the buffer is α ( � X ) = ( in , r in , I ( � α ∈ A X )) ✟ ✯ ❍ ❨ ✟✟ ❍ ✻ ❍ influence type influence name rate here I ( � X ) := const where � X is a formal parameter.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE HYPE A CTIONS AND A CTIVITIES E VENTS Events can either be instantaneous (buffer becomes full or empty: full , empty ∈ E d ) or they can happen at exponential random times (input/output of data in buffer: on in / out , off in / out ∈ E s ) A CTIVITIES OR INFLUENCES Description of flows: influences on continuous variables. For instance, the effect of data inflow in the buffer is α ( � X ) = ( in , r in , I ( � α ∈ A X )) ✟ ✯ ❍ ❨ ✟✟ ❍ ✻ ❍ influence type influence name rate here I ( � X ) := const where � X is a formal parameter.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE U NCONTROLLED S YSTEM S UBCOMPONENTS S ::= a : α. C s | S + S a ∈ E , α ∈ A C s ( � def X ) = S (simple looping agents) C OMPONENTS P ::= C ( � X ) | P ⊲ L P L ⊆ E ⊳ C ( � def X ) = P or subcomponent name U NCONTROLLED SYSTEM Σ ::= C ( � V ) | Σ ⊲ L Σ L ⊆ E ⊳
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE S IMPLE B UFFER IN S HYPE I NPUT OF D ATA def Input = on in :( in , r in , const ) . Input + off in :( in , 0 , const ) . Input + full :( in , 0 , const ) . Input + init :( in , 0 , const ) . Input O UTPUT OF DATA def Output = on out :( out , − r out , const ) . Output + off out :( out , 0 , const ) . Output + empty :( out , 0 , const ) . Output + init :( out , 0 , const ) . Output U NCONTROLLED SYSTEM def Sys = Input ⊲ { init } Output ⊳
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE S HYPE CONTROLLED SYSTEM C ONTROLLER M ::= a . M | 0 | M + M a ∈ E Con ::= M | Con ⊲ L Con L ⊆ E ⊳ C ONTROLLED SYSTEM ConSys ::= Σ ⊲ L Con L ⊆ E ⊳ W ELL - DEFINED HYPE SYSTEM Subcomponents are in bijection with influence names. init :( ι, _ , _ ) appears exactly once a :( ι, _ , _ ) appears at most once synchronisation on all shared events
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE S IMPLE B UFFER IN S HYPE ( CONTINUED ) C ONTROLLERS def Con in = on in . Con ′ in def Con ′ = off in . Con in + full . Con in in def Con out = on out . Con ′ out def Con ′ = off out . Con out + empty . Con out out C ONTROLLED SYSTEM def = Con in ⊲ Con ⊳ ∅ Con out S YSTEM def Buffer = Sys ⊲ M init . Con ⊳ with M = { init , on in , off in , on out , off out , empty , full }
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE E VENT CONDITIONS AND OTHER STUFF V is the set of system variables. ec associates event conditions to events. Event conditions for instantaneous events consist of an activation condition (a predicate/boolean formula on system variables) and a reset function. Event conditions for stochastic events consist of a rate function (of system variables) and a reset function.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE E VENT CONDITIONS AND OTHER STUFF V is the set of system variables. ec associates event conditions to events. Event conditions for instantaneous events consist of an activation condition (a predicate/boolean formula on system variables) and a reset function. Event conditions for stochastic events consist of a rate function (of system variables) and a reset function.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE E VENT CONDITIONS AND OTHER STUFF V is the set of system variables. ec associates event conditions to events. Event conditions for instantaneous events consist of an activation condition (a predicate/boolean formula on system variables) and a reset function. Event conditions for stochastic events consist of a rate function (of system variables) and a reset function.
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE S IMPLE B UFFER IN S HYPE ( CONTINUED ) System variable: B (buffer level). E VENT C ONDITIONS ( true , B ′ = b 0 ) ec ( init ) = ec ( full ) = ( B = max B , true ) ec ( empty ) = ( B = 0 , true ) ( k on ec ( on in ) = in , true ) ( k off ec ( off in ) = in , true ) ( k on ec ( on out ) = out , true ) ( k off ec ( off out ) = out , true )
O PPORTUNISTIC NETWORKS S TOCHASTIC HYPE O PPORTUNISTIC N ETWORKS IN S HYPE F ORMAL SEMANTICS OF S HYPE: STOCHASTIC HYBRID SYSTEMS A formal semantics of stochastic HYPE can be given in terms of a class of stochastic processes called Piecewise Deterministic Markov Processes.
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