In large-scale Internet-based distributed systems, participants (consumers and providers) are typically autonomous, i.e. they may have special interests towards queries and other participants. In this context, a way to avoid a participant to voluntarily leave the system is satisfying its interests when allocating queries. However, participants satisfaction may also be negatively affected by the failures of other participants. Query replication is a solution to deal with providers failures, but, it is challenging because of autonomy: it cannot only quickly overload the system, but also it can dissatisfy participants with uninteresting queries. Thus, a natural question arises: should queries be replicated? If so, which ones? and how many times? In this paper, we answer these questions by revisiting query replication from a satisfaction and probabilistic point of view. We propose a new algorithm, called S b QR, that decides on-the-fly whether a query should be replicated and at which rate. As replicating a large number of queries might overload the system, we propose a variant of our algorithm, called S b QR+. The idea is to voluntarily fail to allocate as many replicas as required by consumers for low critical queries so as to keep resources for high critical queries during query-intensive periods. Our experimental results demonstrate that our algorithms significantly outperform the baseline algorithms from both the Communicated by M. Tamer Özsu. 2 Distrib Parallel Databases (2012) 30:1-26performance and satisfaction points of view. We also show that our algorithms automatically adapt to the criticality of queries and different rates of participant failures.