Postdoc: Teletraffic Modelling and Analysis of Communications Networks with Parallelizable Algorithms and Their Implementation

高速电信网络的设计、规划和控制需要对各类通信业务的流量特性有透彻的了解，并有能力利用这些特性进行性能评估。文献中现有的远程交通建模技术要么导致非常大规模的结构化马尔可夫链解决问题，可用的算法方法需要大量的CPU时间，要么导致目前没有实际分析结果用于排队分析的模型。基于离散时间批处理马尔可夫到达过程（D-BMAP）， pi采用简单、通用和系统的算法进行远程交通建模。建模过程需要捕获已知在远程通信性能中起主导作用的原始流量流的一阶和二阶统计量。此外，pi提出了并行建模算法，作为基于串行过程的大规模非线性优化问题技术的替代方法。当将这种流量模型输入到单个服务器队列中时，可以通过M/G/1或G/M/1型马尔可夫链范式进行分析。他们提出了基于矩阵符号函数的相关不变子空间计算算法。这些算法具有很高的收敛率（不像现有算法的线性收敛率），它们适合并行化，因此，现在可以有效地分析中等大小的M/G/1和G/M/1型马尔可夫链。

Design, dimensioning and control of high-speed telecommunication networks requires a thorough understanding of traffic characteristics of various types of communication services and the ability to use these characteristics for performance assessment. Teletraffic modeling techniques existing in the literature either lead to very large-scale structured Markov chain solution problems for which available algorithmic approaches suffer from huge CPU time requirements, or to models for which, at this time, there are no pratically analytical results for queuing analysis. The PIs do teletraffic modeling consisting of simple, general and systematic algorithms to model building based on D-BMAP's (discrete-time Batch Markovian Arrival Process). The modeling process is desired to capture the first and second order statistics of the original traffic streams that are known to play the dominant role in teletraffic performance. Moreover, the PIs propose parallel algorithms for modeling as an alternative to techniques based on serial procedures for large-scale nonlinear optimization problems. Such traffic models when fed into single server queues can be analyzed by the paradigm of M/G/1 or G/M/1 type Markov chains. They propose to use matrix sign function based algorithms for the associated invariant subspace computation . These algorithms have high convergence rates (unlike the linear convergence rates of existing algorithms), they are amenable to parallelization and, therefore, it is now possible to efficiently analyze moderately sized M/G/1 and G/M/1 type Markov chains.