Leader Election for Multi-channel Radio Networks - Dependent versus Independent Trials

We consider access scheduling to a shared radio channel in networks where a set of stations tries to get exclusive rights to transmit over a shared radio channel. A frequent strategy to solve this problem is that each station independently tosses an asymmetric coin and transmits in case of tails. The trials are executed some number of times and the first station that sends alone in a trial gets the right to broadcast over the shared channel. We consider here a multi-channel case: during onetime slot a station may transmit on k different channels.In this case trials can be arranged in two slightly different ways. The first method is that in each trial a station decides whether to participate in it; if it is so, then the station decides independently for each channel whether to transmit on it. According to the second method a station makes one decision whether to send and if the decision is positive it chooses a single channel for transmission. The second method guarantees a limited energy cost for each station but,as we show, turns out to be inferior regarding success probability. We consider these algorithms for a realistic number of stations. We analyze subtle differences between both algorithms regarding success probability.