Low Power and Lossy Networks (LLNs) represent one of the interesting research areas in recent years. The IETF ROLL and 6LoWPAN working groups have developed new IP based protocols for LLNs such as the RPL routing protocol. In LLNs e.g. 6LoWPANs, heavy data traffic causes congestion which significantly degrades network performance. In this paper, we explore the impact of congestion on 6LoWPAN networks where an extensive analysis is carried out with different scenarios and parameters. Analysis results show that when congestion occurs, the majority of packets are lost due to buffer overflow as compared to channel loss. Also, we found that when the application payload length is increased since IPv6 packets are fragmented, the reassembly timeout parameter value has a significant effect on network performance. Thus, it is important to consider buffer occupancy and the reassembly timeout parameter in protocol design, e.g. RPL, to improve network performance when congestion does occur.