In a cognitive radio network, a Primary User (PU) may vacate a channel for intermissions of an unknown length. A substantial amount of research has been devoted to minimizing the disturbance a Secondary User (SU) may cause the PU. We take another step and optimize the throughput of an SU, even when assuming that the disturbance to the PU is indeed avoided using those other methods. We suggest new optimization parameters the lengths of SU packets. That is, the SU fills up the intermission with consecutive packets. Each packet is associated with some fixed overhead. Hence, using a larger number of smaller packets increases the overhead ratio for each SU packet. On the other hand, it reduces the loss of throughput the SU suffers with the loss of a packet in a collision at the end of the intermission. As opposed to previous studies, we optimize also the case where the distribution of the channel intermission is unknown. That is, we develop optimal competitive protocols. Those seek to minimize the ratio of the SU's profit compared to a hypothetical optimal algorithm that knows the intermission length in advance. We show how to compute the optimal present packets' sizes for the case that the distribution is known (for a general distribution). Finally, we show several interesting properties of the optimal solutions for several popular distributions.
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