Evaluating fluid semantics for passive stochastic process algebra cooperation

Fluid modelling is a next-generation technique for analysing massive performance models. Passive cooperation is a popular cooperation mechanism frequently used by performance engineers. Therefore having an accurate translation of passive cooperation into a fluid model is of direct practical application. We compare different existing styles of fluid model translations of passive cooperation in a stochastic process algebra and show how the previous model can be improved upon significantly. We evaluate the new passive cooperation fluid semantics and show that the first-order fluid model is a good approximation to the dynamics of the underlying continuous-time Markov chain. We show that in a family of possible translations to the fluid model, there is an optimal translation which can be expected to introduce least error. Finally, we use these new techniques to show how the scalability of a passively-cooperating distributed software architecture could be assessed.

[1]  Robert Holton,et al.  A PEPA Specification of an Industrial Production Cell , 1995, Comput. J..

[2]  Luca Cardelli,et al.  On process rate semantics , 2008, Theor. Comput. Sci..

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

[4]  Stephen Gilmore,et al.  Evaluating the Scalability of a Web Service-Based Distributed e-Learning and Course Management System , 2006, WS-FM.

[5]  Luca Bortolussi,et al.  Stochastic Concurrent Constraint Programming , 2006, QAPL.

[6]  Stephen Gilmore,et al.  Replicating Web Services for Scalability , 2007, TGC.

[7]  Jeremy T. Bradley,et al.  Stochastic analysis of scheduling strategies in a Grid-based resource model , 2004, IEE Proc. Softw..

[8]  Stephen Gilmore,et al.  Analysing distributed Internet worm attacks using continuous state-space approximation of process algebra models , 2008, J. Comput. Syst. Sci..

[9]  Alan Bain.  Stochastic Calculus , 2007 .

[10]  Alberto Policriti,et al.  Stochastic Concurrent Constraint Programming and Differential Equations , 2007, QAPL.

[11]  Fabrice Valois,et al.  Performance modelling of hierarchical cellular networks using PEPA , 2002, Performance evaluation (Print).

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

[13]  J. Norris,et al.  Differential equation approximations for Markov chains , 2007, 0710.3269.

[14]  Stephen Gilmore,et al.  Derivation of passage-time densities in PEPA models using ipc: the imperial PEPA compiler , 2003, 11th IEEE/ACM International Symposium on Modeling, Analysis and Simulation of Computer Telecommunications Systems, 2003. MASCOTS 2003..

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

[16]  Howard Bowman,et al.  Analysis of a Multimedia Stream using Stochastic Process Algebra , 2001, Comput. J..

[17]  Adam Duguid.  Coping with the Parallelism of BitTorrent: Conversion of PEPA to ODEs in Dealing with State Space Explosion , 2006, FORMATS.

[18]  Nil Geisweiller,et al.  Relating continuous and discrete PEPA models of signalling pathways , 2008, Theor. Comput. Sci..

[19]  T. Kurtz.  Solutions of ordinary differential equations as limits of pure jump markov processes , 1970, Journal of Applied Probability.

[20]  Luca Cardelli,et al.  From Processes to ODEs by Chemistry , 2008, IFIP TCS.

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

[22]  O. Kallenberg.  Foundations of Modern Probability , 2021, Probability Theory and Stochastic Modelling.

[23]  Jane Hillston,et al.  Process algebras for quantitative analysis , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).