Occupancy Distribution of Queueing Systems with Opportunistic Scheduling in the Downlink

We consider a block-fading homogeneous broadcast channel with n users each receiving packets randomly and independently with a rate of lambda. Packets are stored in separate queues to await transmission using an opportunistic scheduling which exploits the multiuser diversity of the channel by serving the user with the most favorable channel condition at each coherence interval. In this paper, we consider a stochastic model in which mean packet transmission time is n^-1 and establish a convergence result for the occupancy distribution of all n queues under opportunistic scheduling. It is shown that if lambda < 1 then the expected length of the longest queue is less than log_1/lambda n + O(1) for large n. In order to improve the occupancy distribution while exploiting the multiuser diversity, we also study a scheme that serves the user with the longest queue among the d users with the most favorable channel conditions. It is shown that upper bound on the expected length of the longest queue improves to log_d/lambda n + O(1). Simulation results are presented to validate our asymptotic results.