Stochastic automata network of modeling parallel systems

Abstract

Abstract-This paper is motivated by the study of the performance of parallel systems. The performance models of such systems are often complex to describe and hard to solve. The method presented here uses a modular representation of the system as a network of state-transition graphs. The state space explosion is handled by a decomposition technique. The dynamic behavior of the algorithm is analyzed under Markovian assumptions. The transition matrix of the chain is automatically derived using tensor algebra operators, under a format which involves a very limited storage cost.

Abstract Interpretation for Worst and Average Case Analysis

“…The coarsest abstraction α 1 : T 16 → T 1 computes in effect the average of all the values of f , i.e. the (constant) value of f A 1 G 1 is exactly the average of 5,5,6,7,8,4,3,2,8,6,6,7,9,8,8,7. In general we can always compute such an average via the one point abstraction:…”

“…There exist numerous formalisms to describe the semantics or dynamics of discrete as well as continuous time (stochastic) systems like for example: Stochastic Petri Nets (SPNs) [4], Stochastic Automata Networks (SANs) [5], etc.…”

“…Approaches based on stochastic modelling have become popular in recent years. Stochastic Petri Nets [4], Stochastic Automata Networks [5] and Stochastic State Machine Languages have all been used. Kwiatkowska [6] and co-workers have used the latter with PRISM and MAPLE to optimise average energy usage whilst bounding the average number of requests waiting to be served.…”

Compositionality for Markov reward chains with fast and silent transitions

“…This includes stochastic process algebras [2,3], (generalized) stochastic Petri nets [4,5], probabilistic I/O automata [6,7], stochastic automata networks [8], etc. The compositional modeling enables composing a bigger system from several smaller components.…”

“…In the process of compositional modeling, performance evaluation techniques produce intermediate constructs that are typically extensions of Markov chains featuring transitions with communication labels [2][3][4][5][6][7][8]. In the final modeling phase, all labels are discarded and communication transitions are assigned instantaneous behavior.…”