基于鞅论的时延QoS分析
QoS Signal Delay Analysis Based on Martingale Theory

随着网络通信行业的迅速发展，出现了各种各样的数字移动终端，用户对服务质量的要求也不断提高，QoS (Quality of Service)应运而生。时延是QoS的指标之一，通过研究时延可以进一步分析网络的性能。基于排队论，主要研究单一业务到达时的系统性能，建立单一服务器服务的排队系统，在建模中，主要考虑突发性业务，使用突发性到达MMOO过程作为系统的输入，将服务过程建立为ALOHA。利用新的理论方法——鞅论，指数上鞅能够准确描述突发性到达对网络性能的影响，在鞅域中构建服务鞅和到达鞅的结构，通过鞅的停时定理，推导系统的时延违反概率不等式建模出在鞅结构下的时延违反概率界，利用MATLAB统计比较不同的负载率对应的时延违反概率界，发现在突发型的业务到达时，时延界随着负载率的减小更加紧致更加趋于真实值。
With the rapid development of network communication industry, various digital mobile terminals have emerged, and users’ requirements for service quality are also constantly improving, QoS (Quality of Service) comes into being. Delay is one of the QoS metrics and the performance of the network can be further analyzed by studying delay. Based on the queuing theory, the system per-formance when a single service arrives is mainly investigated, and establishes the queuing system of a single server service. In the modelling, the bursty service is mainly considered, and the bursty arrival MMOO process is used as the input of the system, and the service process is established as ALOHA. Using a new theoretical approach, the martingale theory, the exponential upper martingale is able to accurately describe the impact of bursty arrivals on network performance, construct the structure of the service martingale and the arrival martingale in the martingale theory, and through the stopping time theorem of the martingale, derive the system’s delay violation probability inequality to model the delay violation probability bounds under the martingale structure. Using MATLAB to statistically compare the delay violation probability bounds corresponding to different load rates, it is found that when bursty traffic arrives, the delay bound becomes tighter and tends to be closer to the true value as the load rate decreases.