Example embodiments provide various techniques for distributing connections within a connectional parallelism architecture. In one embodiment, a method is provided where resource utilizations of connection groups are measured. Here, each connection group is assigned to one of multiple processors. A probability distribution is accessed that maps probabilities assigned to relative resource utilizations. A relative resource utilization of one of the connection groups is determined based on a resource utilization of the one connection group relative to other resource utilizations of other connection groups. A probability from the probability distribution is identified based on the determined relative resource utilization, and based on the identified probability, a connection is assigned to this connection group for execution by one of the processors assigned to this connection group.