1. A method of distributing connections within a connectional parallelism architecture, the method comprising: measuring resource utilizations for each of multiple connection groups, each connection group being assigned to one of multiple processors; accessing a probability distribution that maps probabilities with relative resource utilizations, wherein the probabilities decrease as the relative resource utilizations increase; determining a relative resource utilization of one of the connection groups based on a resource utilization of the one connection group relative to other resource utilizations of other connection groups; identifying, from the probability distribution, a probability of assigning a connection to the one connection group based on the determined relative resource utilization of the one connection group; and based on the identified probability, making a determination to assign the connection to the one connection group for execution by one of the multiple processors assigned to the one connection group or to assign the connection to another connection group.