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

高速电信网络的设计、规模确定和控制需要彻底了解各种类型通信服务的业务特性，并能够使用这些特性进行性能评估。文献中现有的电信业务建模技术要么导致可用算法方法遭受巨大CPU时间需求的超大规模结构化马尔可夫链解问题，要么导致此时没有用于排队分析的实际分析结果的模型。PI采用简单、通用和系统的算法建立基于D-BMAP(离散时间批马尔可夫到达过程)的交通模型。需要建模过程来捕获已知在电信业务性能中起主导作用的原始业务流的一阶和二阶统计量。此外，PI提出了用于建模的并行算法，作为大规模非线性优化问题的基于串行过程的技术的替代。当这种流量模型被送入单服务器队列时，可以用M/G/1或G/M/1类型的马尔可夫链来分析。他们提出使用基于矩阵符号函数的算法来进行相关的不变子空间计算。这些算法具有很高的收敛速度(不同于现有算法的线性收敛速度)，它们易于并行化，因此，现在可以有效地分析中等大小的M/G/1和G/M/1型马氏链。

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.