The use of queue thresholds is a well known technique for network traffic congestion control. This motivates the study of a single server queue with R(R  2) distinct priority classes under Head of Line (HoL) service priority discipline, Partial Buffer Sharing (PBS) scheme and a finite capacity vector N, representing a sequence of thresholds (N₁, N₂, … , N_R) for each class jobs. The external traffic is modelled using the compound Poisson process or generalised exponential (GE) distribution which can capture the bursty property of the network traffic. The transmission times have also been modelled using the GE distribution to depict the bulk departures from the system. Using a GE/GE/1/N approximation, a closed form cost-effective analytical solution is obtained using the principle of maximum entropy (ME). The forms of the joint, aggregate and marginal state probabilities, as well as basic performance measures such as utilisation and blocking probabilities are analytically established at equilibrium via appropriate mean value constraints and the generating function approach. Consequently, efficient recursive expressions of low computational cost are determined. Typical numerical experiments are included to illustrate the credibility of the proposed mechanism in the context of different QoS grades for various network traffic classes. This model, therefore, can be used as a powerful tool to provide a required grade of service to a particular class of traffic in any heterogeneous networks.