Optimal Rate Scheduling via Utility-Maximization for J-User MIMO Markov Fading Wireless Channels with Cooperation
Optimal Rate Scheduling via Utility-Maximization for J-User MIMO Markov Fading Wireless Channels with Cooperation
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DOI：
10.1287/opre.2013.1224
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发表时间：
2011-06
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影响因子：
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通讯作者：
W. Dai
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作者：
W. Dai
针对一类生活在随机环境中的广义处理器共享队列，设计了一种马尔可夫型的动态速率调度策略，该调度策略通过随机演化容量集上效用最大化问题的解（社会最优纳什均衡点）来实现，其任务到达每个队列遵循双随机更新过程（DSRP）.每个DSRP的随机环境和随机到达率都由有限状态连续时间马尔可夫链（FS-CTMC）驱动。鉴于调度策略相对于每个队列和环境状态以贪婪的方式进行优化，并且由于难以获得在该策略下的这种调度系统的性能的封闭形式的解，我们建立了一个带有状态转换的反射扩散模型（RDRS），模型的性能指标，并证明其渐近最优通过推导相应的系统的随机流体和扩散限制在繁忙的交通和识别成本函数相关的效用函数，这是最小化通过最小化工作量过程中的扩散限制。更重要的是，我们的调度模型包括J-用户多输入多输出（MIMO）多址接入信道（MAC）和广播信道（BC）的合作和准入控制的特殊情况。在这些无线系统中，来自MAC中的J个用户的数据或去往BC中的J个用户的数据在根据FS-CTMC衰落的公共信道上发送。用于MAC或BC的J用户容量区域是随着FS-CTMC衰落而切换的集值随机过程。在任何特定的信道状态下，我们表明，每个J-用户容量区域是一个凸集的线性或光滑的曲面的数量为界。因此，我们的模型可以完美地匹配这些无线系统的动态。
We design a dynamic rate scheduling policy of Markov type via the solution (a social optimal Nash equilibrium point) to a utility-maximization problem over a randomly evolving capacity set for a class of generalized processor-sharing queues living in a random environment, whose job arrivals to each queue follow a doubly stochastic renewal process (DSRP). Both the random environment and the random arrival rate of each DSRP are driven by a finite state continuous time Markov chain (FS-CTMC). Whereas the scheduling policy optimizes in a greedy fashion with respect to each queue and environmental state and since the closed-form solution for the performance of such a queueing system under the policy is difficult to obtain, we establish a reflecting diffusion with regime-switching (RDRS) model for its measures of performance and justify its asymptotic optimality through deriving the stochastic fluid and diffusion limits for the corresponding system under heavy traffic and identifying a cost function related to the utility function, which is minimized through minimizing the workload process in the diffusion limit. More importantly, our queueing model includes both J-user multi-input multi-output (MIMO) multiple access channel (MAC) and broadcast channel (BC) with cooperation and admission control as special cases. In these wireless systems, data from the J users in the MAC or data to the J users in the BC is transmitted over a common channel that is fading according to the FS-CTMC. The J-user capacity region for the MAC or the BC is a set-valued stochastic process that switches with the FS-CTMC fading. In any particular channel state, we show that each of the J-user capacity regions is a convex set bounded by a number of linear or smooth curved facets. Therefore our queueing model can perfectly match the dynamics of these wireless systems.