Heavy-Traffic Analysis of Queueing Systems with No Complete Resource Pooling
Heavy-Traffic Analysis of Queueing Systems with No Complete Resource Pooling
复制标题
无完整资源池的排队系统大流量分析
DOI：
--
复制
发表时间：
2019
影响因子：
1.7
通讯作者：
S. T. Maguluri
中科院分区：
文献类型：
--
作者：
Daniela Hurtado;S. T. Maguluri
我们研究了在MaxWeight下运行的广义开关的重量限制，而不假设满足完整的资源合并条件并允许相关到达。本文的主要贡献是交通繁忙的队列长度线性组合的稳态平均值。我们通过将各种随机网络作为推论来展示我们的结果的普遍性，每个网络本身就是一个贡献。特别是，我们研究了带有相关到达的输入气味开关，并且我们表明，如果状态空间崩溃到全维子空间，则到达过程之间的相关性在繁忙的流量中无关紧要。我们用并行服务器系统，[公式：参见文本]系统和一个临时无线网络来体现最后一个情况。尽管这些结果是使用漂移方法获得的，但我们还提出了一个负面结果，显示了漂移方法的局限性。我们表明，不可能使用带有多项式测试函数的漂移方法获得单个队列长度。我们通过在线性方程系统方面呈现漂移方法的替代视图来做到这一点，并使用此方程系统来获得队列长度的任意线性组合的界限。
We study the heavy-traffic limit of the generalized switch operating under MaxWeight, without assuming that the complete resource pooling condition is satisfied and allowing for correlated arrivals. The main contribution of this paper is the steady-state mean of linear combinations of queue lengths in heavy traffic. We showcase the generality of our result by presenting various stochastic networks as corollaries, each of which is a contribution by itself. In particular, we study the input-queued switch with correlated arrivals, and we show that, if the state space collapses to a full-dimensional subspace, the correlation among the arrival processes does not matter in heavy traffic. We exemplify this last case with a parallel-server system, an [Formula: see text]-system, and an ad hoc wireless network. Whereas these results are obtained using the drift method, we additionally present a negative result showing a limitation of the drift method. We show that it is not possible to obtain the individual queue lengths using the drift method with polynomial test functions. We do this by presenting an alternate view of the drift method in terms of a system of linear equations, and we use this system of equations to obtain bounds on arbitrary linear combinations of the queue lengths.
具有按比例公平带宽共享的连接级数据传输模型中的大流量延迟不敏感
DOI：
10.1145/3199524.3199565
发表时间：
2018
期刊：
ACM SIGMETRICS Performance Evaluation Review
影响因子：
--
作者：
Wang, Weina;Maguluri, Siva Theja;Srikant, R.;Ying, Lei
通讯作者：
Ying, Lei