Delay analysis for aggregate traffic based on martingales theory

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.