Delay scaling in many-sources wireless networks without queue state information

We examine a canonical scenario where several wireless data sources generate sporadic delay-sensitive messages that need to be transmitted to a common access point. The access point operates in a time-slotted fashion, and can instruct the various sources in each slot with what probability to transmit a message, if they have any. When several sources transmit simultaneously, the access point can detect a collision, but is unable to infer the identities of the sources involved. While the access point can use the channel activity observations to obtain estimates of the queue states at the various sources, it does not have any explicit queue length information otherwise. We explore the achievable delay performance in a regime where the number of sources n grows large while the relative load remains fixed. We establish that, under any medium access algorithm without queue state information, the average delay must be at least of the order of n slots when the load exceeds some threshold ?^* < 1. This demonstrates that bounded delay can only be achieved if a positive fraction of the system capacity is sacrificed. Furthermore, we introduce a scalable Two-Phase algorithm which achieves a delay upper bounded uniformly in n when the load is below e^-1, and a delay of the order of n slots when the load is between e^-1 and 1. Additionally, this algorithm provides robustness against correlated source activity.