Hierarchical Markovian models: symmetries and reduction
Performance Evaluation - Special issue: 6th international conference on modelling techniques and tools for computer performance evaluation
The busy period in the fluid queue
SIGMETRICS '98/PERFORMANCE '98 Proceedings of the 1998 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Product form solution for a class of PEPA models
IPDS '98 Proceedings of the third IEEE international performance and dependability symposium on International performance and dependability symposium
Communicating sequential processes
Communications of the ACM
An Efficient Algorithm for Aggregating PEPA Models
IEEE Transactions on Software Engineering
IEEE Transactions on Software Engineering
The Möbius Framework and Its Implementation
IEEE Transactions on Software Engineering
Performance modelling of hierarchical cellular networks using PEPA
Performance Evaluation - Unified specification and performance evaluation using stochastic process algebras
Extended Markovian Process Algebra
CONCUR '96 Proceedings of the 7th International Conference on Concurrency Theory
Turning back time in Markovian process algebra
Theoretical Computer Science
The ipc/HYDRA Tool Chain for the Analysis of PEPA Models
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
Fluid Flow Approximation of PEPA models
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
An approximate compositional approach to the analysis of fluid queue networks
Performance Evaluation
A Generic Mean Field Convergence Result for Systems of Interacting Objects
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Invited Talk: A Process Algebra Master Equation
QEST '07 Proceedings of the Fourth International Conference on Quantitative Evaluation of Systems
Theoretical Computer Science
Journal of Computer and System Sciences
Relating continuous and discrete PEPA models of signalling pathways
Theoretical Computer Science
A class of mean field interaction models for computer and communication systems
Performance Evaluation
Fluid semantics for passive stochastic process algebra cooperation
Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Evaluating fluid semantics for passive stochastic process algebra cooperation
Performance Evaluation
Fluid analysis of energy consumption using rewards in massively parallel markov models
Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
Modelling non-linear crowd dynamics in bio-PEPA
FASE'11/ETAPS'11 Proceedings of the 14th international conference on Fundamental approaches to software engineering: part of the joint European conferences on theory and practice of software
On fluidization of discrete event models: observation and control of continuous Petri nets
Discrete Event Dynamic Systems
Fluid computation of passage-time distributions in large Markov models
Theoretical Computer Science
Fluid computation of the performance: energy tradeoff in large scale Markov models
ACM SIGMETRICS Performance Evaluation Review
Mean-field approximations for performance models with generally-timed transitions
ACM SIGMETRICS Performance Evaluation Review
Higher moment analysis of a spatial stochastic process algebra
EPEW'11 Proceedings of the 8th European conference on Computer Performance Engineering
Fluid limits of queueing networks with batches
ICPE '12 Proceedings of the 3rd ACM/SPEC International Conference on Performance Engineering
Mean-Field analysis of markov models with reward feedback
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Exact fluid lumpability for Markovian process algebra
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Moment closures for performance models with highly non-linear rates
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Formal performance modelling: from protocols to people
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Don't just go with the flow: cautionary tales of fluid flow approximation
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Moment closures for performance models with highly non-linear rates
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Formal performance modelling: from protocols to people
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Don't just go with the flow: cautionary tales of fluid flow approximation
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Continuous approximation of collective system behaviour: A tutorial
Performance Evaluation
Mean-field analysis of data flows in wireless sensor networks
Proceedings of the 4th ACM/SPEC International Conference on Performance Engineering
Bounds on the deviation of discrete-time Markov chains from their mean-field model
Performance Evaluation
Tackling continuous state-space explosion in a Markovian process algebra
Theoretical Computer Science
Hi-index | 5.23 |
Markovian process algebras, such as PEPA and stochastic @p-calculus, bring a powerful compositional approach to the performance modelling of complex systems. However, the models generated by process algebras, as with other interleaving formalisms, are susceptible to the state space explosion problem. Models with only a modest number of process algebra terms can easily generate so many states that they are all but intractable to traditional solution techniques. Previous work aimed at addressing this problem has presented a fluid-flow approximation allowing the analysis of systems which would otherwise be inaccessible. To achieve this, systems of ordinary differential equations describing the fluid flow of the stochastic process algebra model are generated informally. In this paper, we show formally that for a large class of models, this fluid-flow analysis can be directly derived from the stochastic process algebra model as an approximation to the mean number of component types within the model. The nature of the fluid approximation is derived and characterised by direct comparison with the Chapman-Kolmogorov equations underlying the Markov model. Furthermore, we compare the fluid approximation with the exact solution using stochastic simulation and we are able to demonstrate that it is a very accurate approximation in many cases. For the first time, we also show how to extend these techniques naturally to generate systems of differential equations approximating higher order moments of model component counts. These are important performance characteristics for estimating, for instance, the variance of the component counts. This is very necessary if we are to understand how precise the fluid-flow calculation is, in a given modelling situation.