A method comprising: selecting, by a network device, a prioritized sub-set of a plurality of routing protocol sessions based on peer priority information, each routing protocol session of the plurality of routing protocol sessions corresponding to a session with a respective peer network device of a plurality of peer network devices, wherein the peer priority information indicates a priority level of the routing protocol session; receiving, by the network device, configuration information defining a threshold number of established routing protocol sessions via a management interface; establishing, by the network device, one or more routing protocol sessions of the prioritized sub-set, wherein establishing the one or more routing protocol sessions of the prioritized sub-set comprises refraining from establishing one or more routing protocol sessions of the plurality of routing protocol sessions that are not included in the prioritized sub-set; determining, by the network device, that the number of established routing protocol sessions of the prioritized sub-set exceeds the threshold number of established routing protocol sessions; initiating, by the network device, a timer in response to determining that the number of established routing protocol sessions of the prioritized sub-set exceeds the threshold number of established routing protocol sessions; determining, by the network device, that a condition for establishing the prioritized subset of the plurality of routing protocol sessions is satisfied when the timer exceeds a threshold timer value; in response to determining that the condition for establishing the prioritized sub-set of the plurality of routing protocol sessions is satisfied, establishing, by the network device, one or more routing protocol sessions of the plurality of routing protocol sessions that are not included in the prioritized sub-set; and forwarding, by the network device, network traffic using the established one or more routing protocol sessions of the prioritized sub-set and the established one or more routing protocol sessions of the plurality of routing protocol sessions that are not included in the prioritized sub-set. selecting, by a network device, a prioritized sub-set of a plurality of routing protocol sessions based on peer priority information, each routing protocol session of the plurality of routing protocol sessions corresponding to a session with a respective peer network device of a plurality of peer network devices, wherein the peer priority information indicates a priority level of the routing protocol session; receiving, by the network device, configuration information defining a threshold number of established routing protocol sessions via a management interface; establishing, by the network device, one or more routing protocol sessions of the prioritized sub-set, wherein establishing the one or more routing protocol sessions of the prioritized sub-set comprises refraining from establishing one or more routing protocol sessions of the plurality of routing protocol sessions that are not included in the prioritized sub-set; determining, by the network device, that the number of established routing protocol sessions of the prioritized sub-set exceeds the threshold number of established routing protocol sessions; initiating, by the network device, a timer in response to determining that the number of established routing protocol sessions of the prioritized sub-set exceeds the threshold number of established routing protocol sessions; determining, by the network device, that a condition for establishing the prioritized subset of the plurality of routing protocol sessions is satisfied when the timer exceeds a threshold timer value; in response to determining that the condition for establishing the prioritized sub-set of the plurality of routing protocol sessions is satisfied, establishing, by the network device, one or more routing protocol sessions of the plurality of routing protocol sessions that are not included in the prioritized sub-set; and forwarding, by the network device, network traffic using the established one or more routing protocol sessions of the prioritized sub-set and the established one or more routing protocol sessions of the plurality of routing protocol sessions that are not included in the prioritized sub-set.