Non-determinism in Probabilistic Timed Systems with General Distributions

Abstract

In this paper we address the problem of adequately handling non-deterministic choices in Generalised Semi-Markov Processes (GSMPs), i.e. probabilistic timed systems where durations of delays are expressed by means of random variables with a general probability distribution. In particular we want the probabilistic duration of a delay not to be decided all at once when the delay starts, but step by step in each system state (in the theory of GSMPs this corresponds to recording spent lifetimes instead of residual lifetimes of delays). In this way an adversary cannot take decisions a priori, based on the knowledge he may get about the future behavior of the system. In order to accomplish this, we consider Interactive Generalised Semi-Markov Processes (IGSMPs). We start by formalizing the class of well-named IGSMP models and the class of Interactive Stochastic Timed Transition Systems (ISTTSs) which are both closed under CSP parallel composition and hiding. Then, we introduce a semantics for IGSMPs which maps well-named IGSMP models onto ISTTSs by recording spent lifetimes of delays. Finally, we show that two weakly bisimilar IGSMPs give rise to two weakly bisimilar semantic models and that our semantic mapping is compositional with respect to both CSP parallel composition and hiding.