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Phase transition phenomena between non-congested and congested phases in packet traffic have been observed in many packet switching networks (PSNs). Using the PSN model we investigate the nature of fluctuations in number of packets in transit from their source to their destination, when the mean flow density into the PSN model is close to the phase transition point. A meaningful parameter of PSN behaviour near this critical point is the Hurst exponent that when larger than 0.5 is revealing of a long memory process, i.e. a fractional Brownian motion. In this paper we have used Hurst exponents and long range dependence to analyse PSN model behaviour. We have found that the DFA analysis and several methods for estimating the Hurst exponent suggest the presence of a long memory process for the PSN model using adaptive routing. However, we have not observed this in the case of static routing for the same type of incoming traffic. Thus, the packet traffic is more correlated in PSN model with adaptive routing than the static one. We present our finding, outline the work underway and discuss its expansion.