One of the main features of the third Generation (3G) mobile networks is their capability to provide different classes of services; especially multimedia and real-time services in addition to the traditional telephony and data services. These new services, however, will require higher Quality of Service (QoS) constraints on the network mainly regarding delay, delay variation and packet loss. Additionally, the overall traffic profile in both the air interface and inside the network will be rather different than used to be in today?s mobile networks. Therefore, providing QoS for the new services will require more than what a call admission control algorithm can achieve at the border of the network. Continuous buffer control in both the wireless and the fixed part of the network ensures that higher priority traffic is treated in the proper way. This paper proposes and analytically evaluates a buffer management scheme that is based on multi-level priority and Partial Buffer Sharing (PBS) policy for all buffers at the border and inside the wireless network. The analytical model is based on the G/G/1/N censored queue with single server and R (R ≥ 2) priority classes under the Head of Line (HOL) service rule for the PBS scheme. The traffic is modelled using the Generalised Exponential distribution. The paper presents an analytical solution based on the approximation using the Maximum Entropy (ME) principle. The numerical results show the capability of the space prioritised buffer management scheme to provide higher QoS for the higher priority service classes.