First passage time analysis of stochastic process algebra using partial orders

This paper proposes a partial-order semantics for a stochastic process algebra that supports general (non-memoryless) distributions and combines this with an approach to numerically analyse the first passage time of an event. Based on an adaptation of McMillan's complete finite prefix approach tailored to event structures and process algebra, finite representations are obtained for recursive processes. The behaviour between two events is now captured by a partial order that is mapped on a stochastic task graph, a structure amenable to numerical analysis. Our approach is supported by the (new) tool Forest for generating the complete prefix and the (existing) tool Pepp for analysing the generated task graph. As a case study, the delay of the first resolution in the root contention phase of the IEEE 1394 serial bus protocol is analysed. 1