Bandwidth estimation for aggregate traffic under delay QoS constraint based on supermartingale theory

Bandwidth estimation for network traffic plays an important role in various communication network applications. Due to the diversity presented by the network services, exploring theory and methods to measure bandwidth of superposition of traffic flows has great practical significance. In this paper, we propose a supermartingale approach to calculate bandwidth for aggregate traffic under delay Quality of Service (QoS) constraint. The concept of supermartingale bandwidth is put forward to define the required bandwidth of traffic, which measures bandwidth more accurately. The communication network carrying mixed services is modeled as a queuing system with aggregate arrival traffic. Supermartingale method enables the complex queuing system analysis. Based on the stopping time theory of supermartingale, remarkably tight bound of delay-violation probability for aggregate traffic is derived. Subsequently, we estimate the bandwidth according to delay QoS requirement and traffic characteristics. Searching program for bandwidth estimation is designed. Simulation results show that the estimated bandwidth through supermartingale model is more accurate and smaller than effective bandwidth, especially when arrival traffic has bursty feature. Although this approach is presented for the analysis of two typical arrivals, the proposed model is applicable to general aggregate traffic.