In this paper, we consider a time slotted cognitive radio network where multiple secondary users (SUs) contend to access wireless channels. We propose and analyze a channel access policy where each secondary user stochastically determines whether to access a wireless channel (or not) based on a given access probability. In our analysis we consider two extreme cases - where all SUs a) possess full information and b) have no information regarding idle channels. We propose to obtain the access probabilities that minimize the steady-state queue length tail probabilities in the two extreme cases based on Effective Bandwidth theory. Our analysis provides an insight on how to design optimal channel access policies in the two extreme cases. We also show how the optimal channel access policies of two extreme cases are related with each other. Some numerical examples are provided to validate our analysis and investigate the performance behaviors of the optimal channel access policies.