  In this paper we consider a stochastic model for a frequency-agile CSMA
protocol for wireless networks where multiple orthogonal frequency channels are
available. Even when the possible interference on the different channels is
described by different conflict graphs, we show that the network dynamics can
be equivalently described as that of a single-channel CSMA algorithm on an
appropriate virtual network. Our focus is on the asymptotic regime in which the
network nodes try to activate aggressively in order to achieve maximum
throughput. Of particular interest is the scenario where the number of
available channels is not sufficient for all nodes of the network to be
simultaneously active and the well-studied temporal starvation issues of the
single-channel CSMA dynamics persist. For most networks we expect that a larger
number of available channels should alleviate these temporal starvation issues.
However, we prove that the aggregate throughput is a non-increasing function of
the number of available channels. To investigate this trade-off that emerges
between aggregate throughput and temporal starvation phenomena, we propose an
analytical framework to study the transient dynamics of multi-channel CSMA
networks by means of first hitting times. Our analysis further reveals that the
mixing time of the activity process does not always correctly characterize the
temporal starvation in the multi-channel scenario and often leads to
pessimistic performance estimates.
