On power-of-choice in downlink transmission scheduling

A low-complexity guiding principle is considered for transmission scheduling from n homogeneous queues whose channel states fluctuate independently. The scheduler transmits from a longest queue within d randomly chosen queues with eligible channel states. A Markovian model is studied where mean packet transmission time is n^-1 and packet arrival rate is lambda < 1 per queue. Equilibrium distribution of queue occupancy is obtained in the limit as n rarr infin and it is shown to have tails that decay as Theta((lambda/d)^k). If transmissions are scheduled from a longest eligible queue in the entire system then almost all queues are empty in equilibrium; the number of queues with one packet is Theta(1) and the number of queues with more than one packet is o(1) as n rarr infin. Equilibrium distribution of the total number of packets in the system is also characterized in this latter case.