Simulation of Scale-Free Networks

Gabriele D’Angelo <gda@cs.unibo.it> http://www.cs.unibo.it/gdangelo/ joint work with: Stefano Ferretti Department of Computer Science University of Bologna SIMUTOOLS 2009, Rome (Italy) Simulation of Scale-Free Networks

Presentation outline Scale-Free networks Simulation of scale-free networks Gossiping protocols fixed probability of dissemination fixed fanout probabilistic broadcast Scale-free network simulator: PaScaS / ARTÌS / GAIA Experimental evaluation sequential vs. parallel vs. adaptive parallel execution Conclusions and future work

Scale-Free networks : definition A graph can be used to represent a network and its connectivity Degree of a node = number of neighbor nodes attached to them A scale-free network is a network whose degree distribution follows a power law If p k is the probability that a node has a degree equal to k then: p k ~ k - α , for some constant value α ( usually: 2 < α < 3 )

Scale-Free networks : meaning and examples Quite good to model several types of real networks: computer networks (e.g. Web, Internet (?)) evolving networks in biology transmission of diseases citation graphs social networks, etc. This means: a few highly connected nodes, called hubs a very large number of poorly connected nodes

Simulation of scale-free networks Real networks are usually composed of a huge number of nodes Under the simulation point of view : large amount of memory used to represent the massively populated models huge amount of communication when simulating real-world protocols on top of such models nodes in real-world networks are very heterogeneous (i.e. hubs leaf nodes, different hardware and software characteristics) Lack of powerful tools to simulate such complex networks

Gossiping protocols : fixed probability Gossiping protocols have been implemented on top of the simulated scale-free networks, to build realistic case-studies Gossip #1: Fixed Probability For each message, the node randomly selects those edges through which the message must be propagated (v = threshold value) Algorithm function INITIALIZATION() v ← CHOOSE_PROBABILITY() function GOSSIP(msg) for all n j in Π j do if RANDOM() < v then SEND(msg, n j ) end if end for

Gossiping protocols : fixed fanout Gossip #2: Fixed Fanout Each message is sent to a fixed number of nodes ( fanout ), the receivers are selected at random among the neighbors Algorithm function INITIALIZATION() fanout ← RETRIEVE_FANOUT() function GOSSIP(msg) if fanout ≥ | Π j | then toSend ← Π j else SELECT_NODES() end if for all n j in toSend do SEND(msg, n j ) end for

Gossiping protocols : probabilistic broadcast Gossip #3: Probabilistic Broadcast If the message is locally generated then it is always broadcasted to all neighbors, otherwise it is randomly decided if it has to be broadcasted or ignored Algorithm function INITIALIZATION() p b ← PROBABILITY_BROADCAST() function GOSSIP(msg) if (RANDOM() < p b or FIRST_TRANSMISSION()) then for all n j in Π j do SEND(msg, n j ) end for end if

PaScaS : the scale-free network simulator Parallel and distributed Scale-free network Simulator (PaScaS) Implements the building of the scale-free networks (based on the preferential attachment algorithm ), the gossiping protocols and some data analysis utilities Based on the Advanced RTI System ( ARTÌS ), a middleware used to implement sequential/parallel/distributed simulations that follows an event-based approach It can exploit the adaptive simulation features provided by the Generic Adaptive Interaction Architecture ( GAIA ) PaScaS will be freely available as part of ARTÌS 2.0 , planned for release in the next weeks: http://pads.cs.unibo.it

Experimental evaluation : model parameters Model parameters and simulation scenario Parameter Value number of nodes 3000, 6000, 9000, 12000 message generation exponential distribution mean = 50 time-steps cache size (local to each node) 10 slots message Time To Live (TTL) 6 (fixed prob. and fanout) 4 (conditional broadcast) probability of dissemination (v) 0.5 (i.e. 50%) fanout value 5 probability of broadcast ( p b ) 0.5 (i.e. 50%) simulated time 1000 time-steps (after building)

Experimental evaluation : execution architecture Hardware : Dual processor unit, each processor equipped with a single-core Intel Xeon “Gallatin” CPU 2.80 GHz Hyper-Threading, 2 GB RAM Software : Debian GNU/Linux, Kernel 2.6.16.19 PaScaS 0.9, ARTÌS 1.9.3 Note : in case of monolithic (sequential) simulation, PaScaS uses only a single processor (also in presence of multiprocessors or multi-cores)

Experimental evaluation : sequential execution A single process is responsible to manage the whole simulation. The fixed probability has computational requirements higher than other gossip protocols

Experimental evaluation : parallel execution The simulation is obtained through the coordinated execution of a set of components ( Logical Processes, LPs ) Each LP manages the evolution of a part of the model and it is usually run by a different CPU Each node in the scale-free net is modeled as a Simulated Entity (SE) , therefore each LP manages a set of SEs SEs are randomly allocated in the LPs It is worth noting that the performance of a Parallel And Distributed Simulation (PADS) is a trade-off between: a) load parallelization; b) communication overhead in the parallel/distributed architecture (also including synchronization)

Experimental evaluation : parallel execution (fixed probability)

Experimental evaluation : parallel execution (fixed fanout)

Experimental evaluation : parallel execution (cond. broadcast)

Experimental evaluation : monolithic vs. parallel execution Performance gap (%) between LP=1 (monolithic) and LP=4 The parallel execution gives very unsatisfactory results The communication overhead introduced by the parallel execution does not balance the gain given by the load parallelization green = parallel faster than monolithic Nodes Gossip #1 Gossip #2 Gossip #3 3000 3.46 -12.22 -9.1 6000 0.19 -4.49 -6.23 9000 -5.35 -0.63 -3.36 12000 -9.07 -0.25 -2.42

Experimental evaluation : adaptive parallel execution The goal of this approach is to reduce the communication overhead Observation : in PADS the LP-to-LP (that is CPU-to-CPU) communication represents and overhead GAIA framework introduces an adaptive mechanism that: step by step analyzes the communication pattern of each Simulated Entity (SE) using a migration-based approach, clusters the highly interacting SEs in the same LP introduces a cost (i.e. migration) but in many cases reduces the communication overhead The mechanism dynamically reacts to the model behavior It is based on heuristics that controls the migrations and aims to good load balancing in the execution architecture

Experimental evaluation : adaptive parallel execution

Parallel execution vs. adaptive parallel execution Performance gap (%) between LP=1 and LP=4 GAIA ON The results obtained by adaptive parallel execution are quite good The best performances are obtained for gossip #1 and gossip #3, because both protocols are communication-bounded green = parallel faster than monolithic Nodes Gossip #1 Gossip #2 Gossip #3 3000 34.18 -1.33 19.75 6000 38.63 6.87 23.37 9000 30.97 11.07 24.59 12000 26.47 9.65 22.56

Conclusions and future work PaScaS is a novel freely available scale-free network simulator Parallel approach gives unsatisfactory results in the simulation of such complex networks An approach based on dynamic and adaptive clustering of the simulated entities can give valuable results Future work : more building algorithms for scale-free nets, more detailed heuristics for the clustering, support for multi-core processors , detailed evaluation of the performances of the gossip protocols in very heterogeneous networks

For more information PaScaS / ARTÌS software : http://pads.cs.unibo.it Adaptive parallel/distributed simulation : G. D'Angelo, M. Bracuto. Distributed Simulation of Large Scale and Detailed Models . To appear, International Journal of Simulation and Process Modelling (IJSPM), Special issue on "Parallel and Distributed Simulation“, InderScience, 2009. (email to: [email_address] for the draft)

Simulation of Scale-Free Networks

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Simulation of Scale-Free Networks