Higher Moment Analysis of a Spatial Stochastic Process Algebra

We introduce a spatial stochastic process algebra called MASSPA, which provides a formal behavioural description of Markovian Agent Models, a spatial stochastic modelling framework. We provide a translation to a master equation which governs the underlying transition behaviour. This provides a means of simulation and thus comparison of numerical results with simulation that was previously not available. On the theoretical side, we develop a higher moment analysis to allow quantities such as variance to be produced for spatial stochastic models in performance analysis for the first time. We compare the simulation results against resulting ODEs for both mean and standard deviations of model component counts and finish by analysing a distributed wireless sensor network model.

[1]  Miklós Telek,et al.  Mean Field Methods in Performance Analysis , 2008 .

[2]  Luca Bortolussi.  On the Approximation of Stochastic Concurrent Constraint Programming by Master Equation , 2008, Electron. Notes Theor. Comput. Sci..

[3]  Jean-Yves Le Boudec,et al.  A Generic Mean Field Convergence Result for Systems of Interacting Objects , 2007, Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007).

[4]  Diego Latella,et al.  Reconciling Population and Agent Models for Crowd Dynamics , 2010, LAM@LICS.

[5]  Robin Milner,et al.  Communicating and mobile systems - the Pi-calculus , 1999 .

[6]  Marco Gribaudo,et al.  Presenting Dynamic Markovian Agents with a road tunnel application , 2009, 2009 IEEE International Symposium on Modeling, Analysis & Simulation of Computer and Telecommunication Systems.

[7]  Diego Latella,et al.  Modelling Crowd Dynamics in Bio-PEPA – Extended Abstract – , 2010 .

[8]  D. Gillespie.  Exact Stochastic Simulation of Coupled Chemical Reactions , 1977 .

[9]  Miklós Telek,et al.  Analysis of Large Scale Interacting Systems by Mean Field Method , 2008, 2008 Fifth International Conference on Quantitative Evaluation of Systems.

[10]  Jane Hillston,et al.  A compositional approach to performance modelling , 1996 .

[11]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[12]  Ulf Dieckmann,et al.  On moment closures for population dynamics in continuous space. , 2004, Journal of theoretical biology.

[13]  Jeremy T. Bradley,et al.  Spatial extension of stochastic Pi calculus , 2009 .

[14]  Diego Latella,et al.  A Scalable Fluid Flow Process Algebraic Approach to Emergency Egress Analysis , 2010, 2010 8th IEEE International Conference on Software Engineering and Formal Methods.

[15]  Vashti Galpin,et al.  Modelling Network Performance with a Spatial Stochastic Process Algebra , 2009, 2009 International Conference on Advanced Information Networking and Applications.

[16]  Jeremy T. Bradley,et al.  Fluid computation of passage-time distributions in large Markov models , 2012, Theor. Comput. Sci..

[17]  Pietro Manzoni,et al.  A Markovian Agent Model for Fire Propagation in Outdoor Environments , 2010, EPEW.

[18]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[19]  Jane Hillston,et al.  Fluid flow approximation of PEPA models , 2005, Second International Conference on the Quantitative Evaluation of Systems (QEST'05).

[20]  Alan Bundy,et al.  Constructing Induction Rules for Deductive Synthesis Proofs , 2006, CLASE.

[21]  Otso Ovaskainen,et al.  Space and stochasticity in population dynamics , 2006, Proceedings of the National Academy of Sciences.

[22]  Allan Clark,et al.  State-Aware Performance Analysis with eXtended Stochastic Probes , 2008, EPEW.

[23]  Marco Gribaudo,et al.  Analysis of On-off policies in Sensor Networks Using Interacting Markovian Agents , 2008, 2008 Sixth Annual IEEE International Conference on Pervasive Computing and Communications (PerCom).

[24]  Jeremy T. Bradley,et al.  A fluid analysis framework for a Markovian process algebra , 2010, Theor. Comput. Sci..

[25]  Ulf Dieckmann,et al.  Relaxation Projections and the Method of Moments , 1999 .

[26]  C. Gillespie.  Moment-closure approximations for mass-action models. , 2009, IET systems biology.

[27]  Stefan Engblom,et al.  Computing the moments of high dimensional solutions of the master equation , 2006, Appl. Math. Comput..

[28]  Marco Gribaudo,et al.  Disaster Propagation in Heterogeneous Media via Markovian Agents , 2008, CRITIS.