Compositional Analysis of Expected Delays in Networks
 		  of Probabilistic I/O Automata
 
 			  Eugene W. Stark
 
 	Probabilistic I/O Automata (PIOA's) form a model for probabilistic
 	concurrent systems that permits the hierarchical description
 	of a large system as the composition of a number of simpler
 	components.  Scott Smolka and I have recently been looking
 	into the problem of analyzing various properties of PIOA's
 	in a *compositional* fashion.  That is, we are interested in
 	determining whether a large, composite PIOA has a property of
 	interest by analyzing its components one at a time, rather than
 	by exhaustive search of the full, global state space.
 	Recently we have discovered such a compositional method for
 	calculating "expected delays" in a probabilistic PIOAs.
 	This method, which is suitable for automatic operation,
 	involves calculations with certain vectors and matrices of
 	rational functions that in a sense represent the behavior of a
 	PIOA.  In this talk, I will summarize the basic ideas and
 	results leading up to this method.