Modeling with Parallel DEVS

Serialization in DEVS models Select function Implicit serialization of parallel models E-DEVS: internal transition first, external transition after Inadequate representation of DEVS models with parallel components

Parallel DEVS Atomic Models ta(s) (1) s DEVS = < X b, S, Y b,  int,  ext,  conf, ta,   s  y b (3) s ’ =  int  s    x b (5) s ’ =  ext ( s,e,x b ) (6a) (6a) s ’ =  conf ( s,e,x b ) (6b)

Parallel DEVS Atomic models ta(s) (1) s DEVS = < X b, S, Y b,  int,  ext,  conf, ta,   s  y b (3) s ’ =  int  s   

Parallel DEVS Atomic models ta(s) (1) s DEVS = < X b, S, Y b,  int,  ext,  conf, ta,  x b (5) s ’ =  ext ( s,e,x b ) (6a) (6a)

Parallel DEVS Atomic models ta(s) (1) s DEVS = < X b, S, Y b,  int,  ext,  conf, ta,  x b (5) s ’ =  conf ( s,e,x b ) (6b)

Parallel-DEVS Coupled models Components Couplings –Internal –External Inputs –External Outputs FallowfieldKingstonOttawa departure arrival departure arrival passengers Ottawa-Toronto

Simulation mechanism Simulation advanced through message exchange –Synchronization messages TypeAction t ) Output execution ( *, t )State transition ( done, t )End of action –Content messages ( y, t )Output event ( q, t )External event

Simulator Drives atomic models State tN = time of next transition tL = time of last transition message bag Upon receivingDo y =  s  send ( y, t ) t ) y =  s  send ( y, t ) Add q to message bag –(q, t) Add q to message bag –( *, t ) s  ext ; tN = ta(s) ; tL = t if t < tN s   ext ; tN = ta(s) ; tL = t s  int ; tN = ta(s) ; tL = t if t = tN  bag =  s  int ; tN = ta(s) ; tL = t s  conf ; tN = ta(s) ; tL = t if t = tN  bag   s  conf ; tN = ta(s) ; tL = t

Coordinator Coordinates processor’s activities Coordinator tN = 10 tN = 20 10) ( y, 10) y =  s  ( done, 10) ( y, 10 )

Coordinator tN = 10 tN = 20 ( *, 10) (q, 10) s =  int s =  ext s =  conf ( done, 30) ( done, 20) (done, 15) ( *, 10)

Coordinator tN = 30 tN = 20 tN = 15 15)

Parallel CD++ A tool to execute Parallel DEVS and Parallel Cell-DEVS models in parallel/distributed environments Layered architecture based on Warped MPI (Message Passing Interface) Warped Parallel CD++

Parallel - DEVS simulation Independent of the modelling technique Different simulators can be applied according to the needs. Examples of existing simulators: –Hierarchical –Flat –Centralized –Distributed –Real-Time

Parallel DEVS simulation Processors –Simulator:Atomic model –Coordinator:Coupled model Processor hierarchy = model hierarchy Cellular model : a coupled model of 16 cell Coord. Simulator Processors: 1 coordinator 16 simulators Simulator

CD++ Parallel simulator Model partitioned among available CPUs –Atomic models Each atomic model assigned to a CPU –Coupled models Coordinator is placed on each CPU where there is a component CPU 1CPU 2 Coord. Simulator Coord. Simulator

Parallel simulation mechanism CPU 1CPU 2 Simulator Master coord. Simulator Slave coord. (y,10) (done,10) (y,10) (done,10)

Parallel simulation mechanism CPU 1CPU 2 simulator Master coord. simulator Slave coord. (*,10) (done,tN) (done, min tN) (q,10) (done,tN) (*,10)

Extensions to CD++

Extensions (cont.)

Partition Files

RADS (Carleton University) – Alpha network and Gamma network

Simulation Results GPT Generator transducer queue processor throughput cpuusage out arrive in done solvedout Generator- Processor-Transducer –Multiple instances (12, 48 and 96) –1 to 12 CPUs(different machines)

Results Generator - Processor - Transducer

Results Heat diffusion model –100 x 100 surface –Each cell holds a temperature value –Temperature is update periodically Partitions –1, 2, 4 and 8 CPUs Quantization –Quantum sizes: 0 ; 0,001 ; 0,01 y 0,

Results Heat diffusion - Linux cluster

Results Heat diffusion - 4 processors SMP