Occupancy Distributions of Homogeneous Queueing Systems Under Opportunistic Scheduling
Occupancy Distributions of Homogeneous Queueing Systems Under Opportunistic Scheduling
复制标题
机会调度下同质排队系统的占用分布
DOI：
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发表时间：
2008
影响因子：
2.5
通讯作者：
Maxim Dashouk
中科院分区：
文献类型：
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作者：
M. Alanyali;Maxim Dashouk
本文分析了 n 个信道状态独立波动的同质队列之一的传输调度机会方案。考虑的方案包括从整个系统中最长的连接队列进行传输的 LCQ 策略，以及从随机选择的 d ≥ 1 个连接队列子集中的最长队列进行传输的低复杂度变体 LCQ(d)。研究了马尔可夫模型，其中平均数据包传输时间为 n-1，数据包到达率为 λ <；每个队列 1 个。当系统规模n趋于无穷大时，在极限范围内得到队列长度的瞬态分布和均衡分布。结果表明，在 LCQ 下，均衡状态下几乎所有队列都是空的，最大队列长度为 1，当 n → ∞ 时，整个系统占用率为 θ(1)。系统占用的限制分布是有特征的。还给出了 LCQ(d) 下的限制队列长度分布。结果表明，如果d固定，则系统占用率为θ(n)，队列长度分布具有无限支持。如果 d = ω(1) 但 d = o(n)，则最大队列长度为 1，系统占用率降低至 O(n/d)。所获得的渐近平均数据包延迟的数值比较表明，对于中等的 n 和 d 值，LCQ 和 LCQ(d) 可能具有相当的延迟性能。
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.