PERFORMANCE EVALUATION, VOL.53, NO.1, PP.43-69, 2003.

TITLE: Iterative Disaggregation for a Class of Lumpable Discrete-Time 
Stochastic Automata Networks

AUTHORS: Oleg Gusak, Tugrul Dayar, and Jean-Michel Fourneau 

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.

KEY WORDS: Discrete-time stochastic automata networks; Ordinary lumpability;
Iterative disaggregation; Wireless asynchronous transfer mode system.