The focus of this work is on how the congestion experienced on the GSM network can be minimized. The voice calls is broken into sub-classes of services and a level of priority is established among the classes so that the most urgent and important service will have access to the channel by preempting the lower priority services during congestion. The voice communications over the GSM network using the different classes of subscribers were analyzed with Markov chain’s model. The steady state probabilities for voice services were derived. The blocking and dropping probabilities models for the different services were developed using the Multi-dimensional Erlang B. To give a new call a fair sharing of the channel, Time-Threshold scheme is employed. This scheme classifies handoff call as either prioritised call or new call according to its associated elapsed real time value. The models were implemented based on the blocking and dropping probabilities models to show how the congestion can be minimised for different subscribers based on their priority levels. The work shows that the models used gave significant reduction in congestion when compared to the traditional Erlang-B model used in GSM.