This paper presents the method of estimating of congestions in a partial mesh communication network comprises of many nodes such as the internet. The objectives are to characterize and model the non-stationary packet arrival process and to apply the model in adaptive routing algorithms. To achieve this, Bayesian estimation algorithms are implemented and used to determine the congestion of packet-queues in a prescribed interval time. The model is implemented in a state-space formation for estimating the arrival rate and occupancy at a network node. Bayesian method is used to predict the optimal size of the state vector in the proposed model with the aim to eliminate congestion through application of suitable adaptive routing algorithm.