Probabilistic duration automata for analyzing real-time systems

Abstract

1 We present a novel methodology and tools for analyzing real-time systems that use probability density functions (pdfs) to represent the durations of operations within the system. We introduce the concept of a probabilistic duration automaton in which clocks are defined by pdfs rather than by explicit times. A state of a probabilistic duration automaton is a set of active clocks, and a transition is triggered by the expiration of one or more of these clocks. We present an algorithm for determining the probability that a clock in a state expires, the residual pdfs for the unexpired clocks, the probability of each transition, the probability of each state, and the duration of each state represented as a pdf. The algorithm also calculates the pdfs for durations of intervals between pairs of states within the automaton. These pdfs are used to determine whether a real-time system can meet its probabilistic timing constraints. An example application illustrates the use of this methodology in analyzing the real-time behavior of a four-phase handshaldng protocol used in input/output systems.