Lossy channel systems (LCSs for short) are models for communicating systems where the subprocesses are linked via unbounded FIFO channels which might lose messages. Link protocols, such as the Alternating Bit Protocol and HDLC can be modelled with these systems. The decidability of several verification problems of LCSs has been investigated by Abdulla & Jonsson [AJ93,AJ94], e.g. they have shown that the reachability problem for LCSs is decidable while LT L model checking is not. In this paper, we consider probabilistic LCSs (which are LCSs where the transitions are augmented with appropriate probabilities) as introduced by [IN97] and show that the question of whether or not a linear time property holds with probability 1 is deddable. More precisely, we show how LT L\x model checking for (certain types of) probabilistic LCSs can be reduced to a reachability problem in a (non-probabilistic) LCS where the latter can be solved with the methods of [AJ93].
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