Abstract Analysis of networks of queues under repetitive service blocking mechanism has been presented in this paper. Nodes are connected according to an arbitrary configuration and each node in the networks employs an active queue management (AQM) based queueing policy to guarantee certain quality of service for multiple class external traffic. This buffer management scheme has been implemented using queue thresholds. The use of queue thresholds is a well known technique for network traffic congestion control. The analysis is based on a queue-by-queue decomposition technique where each queue is modelled as a GE/GE/1/ N queue with single server, R ( R ⩾ 2) distinct traffic classes and { N = N 1 , N 2 , … , N R } buffer threshold values per class under first-come-first-serve (FCFS) service rule. The external traffic is modelled using the generalised exponential (GE) distribution which can capture the bursty property of network traffic. The analytical solution is obtained using the maximum entropy (ME) principle. The forms of the state and blocking probabilities are analytically established at equilibrium via appropriate mean value constraints. The initial numerical results demonstrate the credibility of the proposed analytical solution.