Achievable throughput and queueing delay for imperfect cooperative retransmission MAC protocols

Cooperative retransmission (CR) for cellular uplink employs recovery epochs where colliding packets are retransmitted until all packets are recoverable by the base station. We consider a general class of queueing dynamics, appropriate for cellular uplink MAC protocols, where time slots are grouped into epochs, and each epoch results in some subset of the active nodes completing a transmission to the base station. Employing moment generating functions, we express the queue length in terms of the number of arrivals during each epoch, and from here we obtain general expressions for throughput and delay (queueing plus service). We specialize these general results for four MAC uplink protocols: i) independent queues with no collisions (providing an upper bound on performance), ii) slotted Aloha, iii) perfect cooperative retransmission (each time slot yields a new independent signal combination), and iv) imperfect cooperative retransmission (a time slot gives useful information with probability 1 - q).