Markovian Petri Nets protocols with product form solution
Performance Evaluation
A compositional approach to performance modelling
A compositional approach to performance modelling
Theoretical Computer Science
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
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Mean-Value Analysis of Closed Multichain Queuing Networks
Journal of the ACM (JACM)
Linearizer: a heuristic algorithm for queueing network models of computing systems
Communications of the ACM
An Efficient Algorithm for Aggregating PEPA Models
IEEE Transactions on Software Engineering
A Calculus of Communicating Systems
A Calculus of Communicating Systems
IEEE Transactions on Software Engineering
Aggregation Methods for Large Markov Chains
Proceedings of the International Workshop on Computer Performance and Reliability
Turning back time in Markovian process algebra
Theoretical Computer Science
Optimal state-space lumping in Markov chains
Information Processing Letters
Fluid Flow Approximation of PEPA models
QEST '05 Proceedings of the Second International Conference on the Quantitative Evaluation of Systems
Journal of Systems and Software
A class of mean field interaction models for computer and communication systems
Performance Evaluation
Enhanced Modeling and Solution of Layered Queueing Networks
IEEE Transactions on Software Engineering
ACM SIGMETRICS Performance Evaluation Review
A fluid analysis framework for a Markovian process algebra
Theoretical Computer Science
Mean-field framework for performance evaluation of push-pull gossip protocols
Performance Evaluation
Approximate Mean Value Analysis of Process Algebra Models
MASCOTS '11 Proceedings of the 2011 IEEE 19th Annual International Symposium on Modelling, Analysis, and Simulation of Computer and Telecommunication Systems
Fluid computation of passage-time distributions in large Markov models
Theoretical Computer Science
Scalable Differential Analysis of Process Algebra Models
IEEE Transactions on Software Engineering
Reduced base model construction methods for stochastic activity networks
IEEE Journal on Selected Areas in Communications
Exact fluid lumpability for Markovian process algebra
CONCUR'12 Proceedings of the 23rd international conference on Concurrency Theory
Hi-index | 5.23 |
Fluid or mean-field methods are approximate analytical techniques which have proven effective in tackling the infamous state-space explosion problem which typically arises when modelling large-scale concurrent systems based on interleaving semantics. These methods are particularly suitable in situations which present large populations of simple interacting objects characterised by small local state spaces, since they require the analysis of a problem which is insensitive to the population sizes but is dependent only on the size of the local state spaces. This paper studies the case when the replicated objects are best described as composites which consist of smaller simple objects. A congenial formal modelling framework for situations of this kind may be given by stochastic process algebra. Using PEPA as a representative case, we find that fluid models with replicated copies of composite processes do not scale well with increasing population sizes, thus rendering intractable the analysis of the underlying system of ordinary differential equations (ODEs). We call this problem continuous state-space explosion, by analogy with its counterpart phenomenon in discrete state spaces. The main contribution of this paper is a result of equivalence that simplifies, in an exact way, the potentially massive ODE system arising in those circumstances to one whose size is independent from all the multiplicities in the model. As a byproduct, we find that these simplified ODEs turn out to characterise the fluid behaviour of a family of PEPA models whose elements cannot be related to each other through any known equivalence relation. A substantial numerical assessment investigates the relationship between the different underlying Markov chains and their unique fluid limit, demonstrating its generally good accuracy for all practical purposes.