Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks

Authors:
Oleg Gusak;Tuǧrul Dayar;Jean-Michel Fourneau
Affiliations:
School of Interdisciplinary Computing and Engineering, University of Missouri-Kansas City, 5100 Rockhill Road, Kansas City, MO;Department of Computer Engineering, Bilkent University, 06533 Bilkent, Ankara, Turkey;Lab. PRiSM, Université de Versailles, 45 Av. des États Unis, 78035 Versailles Cedex, France
Venue:
Performance Evaluation
Year:
2003

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Abstract

Stochastic automata networks (SANs) have been developed and used in the last 15 years as a modeling formalism for large systems that can be decomposed into loosely connected components. In this work, we concentrate on the not so much emphasized discrete-time SANs. First, we remodel and extend an SAN that arises in wireless communications. Second, for an SAN with functional transitions, we derive conditions for a special case of ordinary lumpability in which aggregation is done automaton by automaton. Finally, for this class of lumpable discrete-time SANs we devise an efficient aggregation-iterative disaggregation algorithm and demonstrate its performance on the SAN model of interest.