Contention resolution in a non-synchronized multiple access channel

Multiple access channel is a well-known communication model that deploys properties of many network systems, such as Aloha multi-access systems, local area Ethernet networks, satellite communication systems, packet radio networks. The fundamental aspect of this model is to provide efficient communication and computation in the presence of restricted access to the communication resource: at most one station can successfully transmit at a time, and a wasted round occurs when more than one station attempts to transmit at the same time. In this work we consider the problem of contention resolution in a multiple access channel in a realistic scenario when up to k stations out of n join the channel at different times. The goal is to let at least one station to transmit alone, which results in successful delivery of the message through the channel. We present three algorithms: two of them working under some constrained scenarios, and achieving optimal time complexity Θ(klog⁡(n/k)+1), while the third general algorithm accomplishes the goal in time O(klog⁡nlog⁡log⁡n).