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Extending the Gillespie's Stochastic Simulation Algorithm for Integrating Discrete-Event and Multi-Agent Based Simulation

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Whereas Multi-Agent Based Simulation (MABS) is emerging as a reference approach for complex system simulation, the event-driven approach of Discrete-Event Simulation (DES) is the most used approach in the simulation mainstream.
In this talk, we elaborate on two intuitions: 1) event-based systems and multi-agent systems are amenable of a coherent interpretation within a unique conceptual framework; 2) integrating MABS and DES can lead to a more expressive and powerful simulation framework.
Accordingly, we propose a computational model integrating DES and MABS, based on an extension of the Gillespie's stochastic simulation algorithm.
Then, we discuss a case of a simulation platform (Alchemist) specifically targeted at such a kind of complex models, and show an example of urban crowd steering simulation.

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Extending the Gillespie's Stochastic Simulation Algorithm for Integrating Discrete-Event and Multi-Agent Based Simulation

  1. 1. Extending the Gillespie’s Stochastic Simulation Algorithm for Integrating Discrete-Event and Multi-Agent Based Simulation Sara Montagna, Andrea Omicini, Danilo Pianini {sara.montagna, andrea.omicini, danilo.pianini}@unibo.it Alma Mater Studiorum—Universit`a di Bologna a Cesena The XVI International Workshop on Multi-Agent Based Simulation May 5, 2015 - Istanbul, Turkey Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 1 / 22
  2. 2. Outline 1 Background Discrete Event Simulation (DES) Agent Based Modelling (ABM) and Simulation (MABS) 2 Motivation 3 A Unified Stochastic Computational Model Model Simulation algorithm 4 Tools: The ALCHEMIST Platform 5 Conclusion Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 2 / 22
  3. 3. Background Discrete Event Simulation (DES) DES . . . The most used approach in the simulation mainstream Instantaneous events responsible for the changes in the system state In between events, no change to the system is assumed to occur All events are ordered (even if they happen at the exact same time) It is normally very efficient since it allows to jump in time from one relevant event Defining a DES means to model the behaviour of a system as an ordered sequence of non-continuous events, by specifying for each of them the perturbations in the system state it provokes, and the exact point in time when it has to be triggered. Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 3 / 22
  4. 4. Background Agent Based Modelling (ABM) and Simulation (MABS) MABS I MABS (Multi-Agent Based Simulation) was introduced as a novel and alternative approach to Discrete Event Simulation (DES) and to Systems Dynamic (SD) Rather than a simulation method, it is a simulation paradigm ABM models the system at the micro-level active entity are autonomous and interacting agent dynamic environment global system-level behaviour as a result of the agent-to-agent interactions Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 4 / 22
  5. 5. Background Agent Based Modelling (ABM) and Simulation (MABS) MABS II The simulation platform Various platforms were developed for the purpose [All10], tools for developing, editing, and executing ABM, as well as for visualising the simulation dynamic. How do they operate over a timeline? How are agents and environment behaviours coupled and scheduled? Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 5 / 22
  6. 6. Background Agent Based Modelling (ABM) and Simulation (MABS) Crucial Issue: Time How to deal with the evolution of time? Continuous approaches Rare Specifically used for modelling the endogenous dynamic of the environment coupled with discrete agent internal processes. Discrete approaches Time-driven most widely used fixed time steps Event-driven Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 6 / 22
  7. 7. Motivation Motivation: Why not Time-driven? Efficiency Time passes fixed time steps even if no action changes the state happen in between Carefully choice of temporal granularity low granularity may ruin results high granularity may lead to a waste of computational resources Accuracy, validity, coherency All the events happening in the same ∆t are executed together possible loss of order and changes on the system outcome to be as close as possible to the MAS paradigm, actions and interactions should be conducted concurrently Congruence Simultaneous updates of system entities is far from reality Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 7 / 22
  8. 8. Motivation From the Time-driven Drawbacks to Our Contribution Based on two intuitions a unified conceptual framework [Omi15] coherent interpretation of event-driven and multi-agent systems powerful simulation framework [Mey14] from the integration of DES and MABS . . . and one observation Gillespie’s SSA [Gil77] as an event-driven algorithm Our proposal A computational model integrating DES and MABS based on an extension of the Gillespie’s stochastic simulation algorithm. Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 8 / 22
  9. 9. A Unified Stochastic Computational Model Gillespie’s SSA as an Event-driven Algorithm Gillespie’s algorithm Gillespie first proposed an event driven stochastic simulation algorithm (SSA) for the exact stochastic simulation of chemical systems Gibson and Bruck [GB00] improved its performance Next reaction selection not by propensity (function of concentration of reagents and a markovian rate) but by generated putative times Dependency graph meant to update only the events whose scheduling time might have changed because of other events Building on their work, we extended the algorithm in order to be able to shift from the world of chemistry to the richer MABS world Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 9 / 22
  10. 10. A Unified Stochastic Computational Model Model Generalised Chemistry Pure chemistry vs. agent-based systems Single, static compartment versus multiple, possibly mobile, and interconnected agents whose ability to communicate may depend on environmental and technological factors Molecules are described by concentrations (an integer), agents may carry and process any kind of data Reactions “scheduling” in nature follows a Poisson distribution whose rate equation depends on reagents’ concentration [Gil77]. Events in an agent-based simulation may be influenced by any of the environment components and follow any probability distribution (triggers, timers, events with memory) Agents live in an environment, such abstraction is absent in chemistry A huge leap, indeed Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 10 / 22
  11. 11. A Unified Stochastic Computational Model Model Close the Gap: Environment ReactionA proactive behaviour Linking Rule A function of the environment that decides wether or not two nodes are connected Moleculetoken representing a chunk of data (think of it as a pointer) ConcentrationActual data associated with a "molecule" Environment Riemannian manifold where nodes live NodeA container of reactions and molecules situated in the environment Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 11 / 22
  12. 12. A Unified Stochastic Computational Model Model Close the Gap: Reactions Number of neighbors<3 Node contains something Any other condition about this environment Rate equation: how conditions influence the execution speed Conditions Probability distribution Actions Any other action on this environment Move a node towards... Change concentration of something Reaction Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 12 / 22
  13. 13. A Unified Stochastic Computational Model Model Flexibility and Data Types Abstract Concentration Concentration can be any data type Pick integers, the result is a simulator for (bio)chemistry, with multiple intercommunicating compartments situated in an environment [MPV12] Pick “set of tuples matching a tuple template”, the result is a simulator of network of programmable tuple spaces Pick “any object”, the result is flexibile enough to simulate a network of devices running their own program [PVB15] For each type of concentration, a specific set of legal conditions and actions can (must) be defined All the other entities can be defined in a generic fashion, and reused Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 13 / 22
  14. 14. A Unified Stochastic Computational Model Simulation algorithm Extended SSA—Phase 1: Pick the Next Event How to select the next event? Most high-performance SSAs presume an underlying model that only includes memoryless events [STP08] Gibson/Bruck’s “next reaction” uses putative times instead We extended it adding support for addition and removal of events at runtime Agents may join and leave the system at runtime, new agents may be equipped with novel behaviours Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 14 / 22
  15. 15. A Unified Stochastic Computational Model Simulation algorithm Extended SSA—Phase 2: Dependency Management How to select the next event? The dependency graph is key for the high performance of SSAs [STP08] In general, it is very hard to build a dependency graph in an open environment composed of multiple entities We extended the original concept of (static) dependency graph with: Events can be added and removed at runtime, the graph is dynamically updated Execution contexts: local, neighborhood, global Separation of influencing context and context of influence (input and output) Overall, the dependency graph is greatly pruned, with positive impact on performance Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 15 / 22
  16. 16. Tools: The ALCHEMIST Platform The ALCHEMIST Platform as a Tool 1 ALCHEMIST: A chemistry-inspired meta-simulator Based on the machinery already described Java written Provides out of the box support for simulating distributed programmable tuple spaces and Protelis [PVB15] devices Supports mobility and complex environments, both indoor and outdoor (with data from OpenStreetMap) Available as Maven artifact (it.unibo.alchemist:alchemist) 1 http://alchemist.apice.unibo.it Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 16 / 22
  17. 17. Tools: The ALCHEMIST Platform Architecture of ALCHEMIST Dynamic Dependency Graph Dynamic Reaction Manager Discrete Event Engine Core Environment (model) Reporting Graphical Output Logging System Interactive UI XML Bytecode Environment Builder Language Chain DSL to XML Compiler Domain Specific Language Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 17 / 22
  18. 18. Tools: The ALCHEMIST Platform Case Study: Crowd-sensitive User Steering in London (a) Initial (b) Ongoing (c) Near-end Figure: Three snapshots of the simulation. Our altered distance metric (the gradient) goes from green (most favourable and close to destination) to red (unpleasant or far from destination). Agents (in black) climb this structure towards greener values. Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 18 / 22
  19. 19. Tools: The ALCHEMIST Platform Case Study: Crowd-sensitive User Steering in London Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 19 / 22
  20. 20. Conclusion Conclusion Integration of DES and MABS We adopted an extension of Gillespie’s SSA as stochastic event-driven algorithm We extended it to support the inherent complexity of multiagent systems, still retaining the performance optimisations We extended the chemical model towards higher flexibility, introducing the environment, generalising the concept of reaction and allowing arbitrary data to be a “concentration” We implemented those concepts inside the ALCHEMIST framework A non-trivial example was provided: crowd steering in London Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 20 / 22
  21. 21. References References I Rob Allan. Survey of agent based modelling and simulation tools. Technical Report DL-TR-2010-007, Computational Science and Engineering Department, October 2010. Michael A. Gibson and Jehoshua Bruck. Efficient exact stochastic simulation of chemical systems with many species and many channels. J. Phys. Chem. A, 104:1876–1889, 2000. Daniel T. Gillespie. Exact stochastic simulation of coupled crfreactions. The Journal of Physical Chemistry, 81(25):2340–2361, December 1977. Ruth Meyer. Event-driven multi-agent simulation. In Electronic Proceedings of the Fifteenth International Workshop on Multi-Agent-Based Simulation, 2014. Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 21 / 22
  22. 22. References References II Sara Montagna, Danilo Pianini, and Mirko Viroli. A model for drosophila melanogaster development from a single cell to stripe pattern formation. In Proceedings of the 27th Annual ACM Symposium on Applied Computing, SAC ’12, pages 1406–1412, New York, NY, USA, 2012. ACM. Andrea Omicini. Event-based vs. multi-agent systems: Towards a unified conceptual framework. In 2015 19th IEEE International Conference on Computer Supported Cooperative Work in Design (CSCWD2015). IEEE Computer Society, May 2015. Danilo Pianini, Mirko Viroli, and Jacob Beal. Protelis: Practical aggregate programming. In 30th Symposium On Applied Computing (SAC 2015). ACM, 2015. Alexander Slepoy, Aidan P. Thompson, and Steven J. Plimpton. A constant-time kinetic monte carlo algorithm for simulation of large biochemical reaction networks. The Journal of Chemical Physics, 128(20):205101, 2008. Montagna, Omicini, Pianini (UNIBO) Gillespie’s SSA to Integrate DES and MABS 2015-05-15 MABS 22 / 22

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