In private telecommunication networks offering a call completion on busy link service, if a call request cannot be completed because of congestion of a link, and if setting up the call entails an overflow to the public network, the rights of the user may not be sufficient for subsequent completion of the call. To prevent this service being offered to a user whose rights are insufficient to enable subsequent call completion, because of the overflow, costs are assigned to the various links of the private network as a function of the overflows and access to the call completion on busy link service is monitored as a function of the rights of the user and the minimum total cost of completing the requested call. This prevents users with insufficient rights being queued indefinitely waiting for the call completion on busy link service.