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The implementation of multi-channels in Ad hoc networks and Wirelesses Mesh Networks has been widely investigated. It envisaged that the approach would increase the capacity of wireless access networks. Results show that the implementation of multi channels does increase the capacity of access networks. However, the use of either a temporary signalling channel or a dedicated control channel has raised many research questions. The use of a control channel is viewed as a challenge to multi-channel schemes and is considered to be a limiting factor. It has been argued that the capacity of a single dedicated channel causes system bottlenecks as its capacity saturates. Unfortunately, this challenge has been given little attention hence it requires further investigation. This paper explores the saturation problem using the analytical and simulation models. Under the two approaches, the saturation problem is investigated in different scenarios in which the number of data transmitting channels is increased steadily. The investigations show that the capacity of the control channel degrades steadily as the number of channels is increased. Both the simulation and analytical results exhibit similar behaviour of the control channel. However, this paper does not investigate the response of the data channel to the increasing data traffic.