A system for controlling, in a multi-resource communication network, the delivery of services by at least one resource capable of simultaneously delivering, within a maximum joint service capacity, at least one first type of service to a first set of users and a second type of service to a second set of users. The increase in the first set of users is capable of causing a decrease in the capacity to serve new users of the second set of users. At least one module for estimating a parameter representing the probability that, in a given time interval, the number of service requests of said second type is such as not to cause the maximum service capacity to be reached. In the presence of a service request of the first type, the estimation module compares the parameter with a respective threshold value and indicates the acceptability of the service request of the first type if that parameter exceeds the respective threshold. If the parameter is lower than the threshold value, then the estimation module evaluates the possible decrease in the capacity to serve new users of the second set of users which can be induced by the acceptance of the request of the first type of service and then compares the possible decrease with a respective decrease threshold value. The service request of the first type is then accepted or blocked.