Occupancy Distributions of Homogeneous Queueing Systems Under Opportunistic Scheduling

This paper analyzes opportunistic schemes for transmission scheduling from one of n homogeneous queues whose channel states fluctuate independently. Considered schemes consist of an LCQ policy that transmits from a longest connected queue in the entire system, and its low-complexity variant LCQ(d) that transmits from a longest queue within a randomly chosen subset of d ≥ 1 connected queues. A Markovian model is studied where mean packet transmission time is n-1 and packet arrival rate is λ <; 1 per queue. Transient and equilibrium distributions of queue lengths are obtained in the limit as the system size n tends to infinity. It is shown that under LCQ almost all queues are empty in equilibrium, maximum queue length is 1, and the overall system occupancy is Θ(1) as n → ∞. Limiting distribution of the system occupancy is characterized. Limiting queue length distributions under LCQ(d) are also given. It is shown that if d is fixed then the system occupancy is Θ(n) and the queue length distribution has infinite support. If d = ω(1) but d = o(n) then the maximum queue length is 1 and the system occupancy reduces to O(n/d). Numerical comparison of the obtained asymptotic mean packet delays suggests that LCQ and LCQ(d) may have comparable delay performance for moderate values of n and d.