Based on martingale theory, the authors explore a novel method to analyse the bound of delay violation probability for aggregate traffic in this study. The proposed arrival model, four-state Markov modulated multinomial process, describes the behaviour of mixed service flows, which depicts the packet arrival process of two interweaved services and highlights the arrival characteristics of the batch, bursty, and heterogeneous. The traffic of data service is modelled by the interrupted multinomial process to depict the randomness and discontinuity. Relying on martingale theory, arrival-supermartingales provide a model for integrating multiple heterogeneous services. They construct a supermartingale process of the backlog in the buffer, which enables the analysis of delay for the queuing system with multiple arrivals and a single server. Finally, the delay of aggregate traffic is featured by the parameters of its corresponding supermartingales. Based on the stopping time theory of martingales, the delay violation probability bound is derived, which matches the simulation results well and is tight.

中文翻译：

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基于mar理论的总交通延误分析

基于mar理论，作者探索了一种新颖的方法来分析本研究中总流量的延迟违规概率的界限。拟议的到达模型，四状态马尔可夫调制多项式过程，描述了混合服务流的行为，描述了两个交织服务的数据包到达过程，并突出了批处理，突发性和异构性的到达特性。数据服务的流量通过中断的多项式过程建模，以描述随机性和不连续性。依靠mar理论，到达超级市场提供了一个集成多种异构服务的模型。他们在缓冲区中构建了积压的超级市场流程，从而可以分析具有多个到达和单个服务器的排队系统的延迟。最后，总流量的延迟由其相应超级市场的​​参数来表征。基于of的停工时间理论，推导了延误违规概率界线，它与仿真结果吻合良好且紧密。