A Matrix Pattern Compliant Strong Stochastic Bound

Stochastic bounds are a promising method to analyze QoS requirements. Indeed it is sufficient to prove that a bound of the real performance satisfies the guarantee. However, the time and space complexity issues are not well understood so far. We propose a new algorithm to derive a strong stochastic bound of a Markov chain, using a matrix pattern specifing the structural properties a bounding matrix should comply with. Thus we can obtain a simpler Markov chain bounding for which the numerical computation of the steady-state solution is easier.

[1]  J. Keilson,et al.  Monotone matrices and monotone Markov processes , 1977 .

[2]  Brigitte Plateau,et al.  On the stochastic structure of parallelism and synchronization models for distributed algorithms , 1985, SIGMETRICS '85.

[3]  J. Fourneau,et al.  Algorithms for an irreducible and lumpable strong stochastic bound , 2004 .

[4]  Audra E. Kosh,et al.  Linear Algebra and its Applications , 1992 .

[5]  Susanna Donatelli,et al.  Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution , 1994, Application and Theory of Petri Nets.

[6]  Jane Hillston,et al.  An Efficient Kronecker Representation for PEPA Models , 2001, PAPM-PROBMIV.

[7]  Donald F. Towsley,et al.  Bounding the Mean Response Time of the Minimum Expected Delay Routing Policy: An Algorithmic Approach , 1995, IEEE Trans. Computers.

[8]  Samuel S. Chiu,et al.  A Method to Calculate Steady-State Distributions of Large Markov Chains by Aggregating States , 1987, Oper. Res..

[9]  Jean-Michel Fourneau,et al.  Graphs and Stochastic Automata Networks , 1995 .

[10]  Mark A. McComb.  Comparison Methods for Stochastic Models and Risks , 2003, Technometrics.

[11]  Donald F. Towsley,et al.  Computing Performance Bounds of Fork-Join Parallel Programs Under a Multiprocessing Environment , 1998, IEEE Trans. Parallel Distributed Syst..

[12]  William J. Stewart,et al.  Introduction to the numerical solution of Markov Chains , 1994 .

[13]  John C. S. Lui,et al.  Bounding of performance measures for a threshold-based queueing system with hysteresis , 1997, SIGMETRICS '97.

[14]  Carl D. Meyer,et al.  Stochastic Complementation, Uncoupling Markov Chains, and the Theory of Nearly Reducible Systems , 1989, SIAM Rev..