 
Summary: Bounded Model Checking for GSMP Models of
Stochastic Realtime Systems
Rajeev Alur and Mikhail Bernadsky
Department of Computer and Information Science
University of Pennsylvania
{alur, mbernads}@cis.upenn.edu
Abstract. Model checking is a popular algorithmic verification technique for
checking temporal requirements of mathematical models of systems. In this pa
per, we consider the problem of verifying bounded reachability properties of sto
chastic realtime systems modeled as generalized semiMarkov processes (GSMP).
While GSMPs is a rich model for stochastic systems widely used in performance
evaluation, existing model checking algorithms are applicable only to subclasses
such as discretetime or continuoustime Markov chains. The main contribution
of the paper is an algorithm to compute the probability that a given GSMP sat
isfies a property of the form "can the system reach a target before time T within
k discrete events, while staying within a set of safe states". For this, we show
that the probability density function for the remaining firing times of different
events in a GSMP after k discrete events can be effectively partitioned into fi
nitely many regions and represented by exponentials and polynomials. We report
on illustrative examples and their analysis using our techniques.
