Router Buffer Behavior Analysis for Aggregate Traffic Based on Martingale Method

The buffer behavior of routers has an important influence on the quality of service of network services. Exploring theory and methods to analyze the characteristics of the buffer is an interesting job, especially when aggregate traffic is transmitted. This letter investigates the buffer behavior of a single server queuing system with multiple arrival flows, which models the operations of a router. A martingale analytical framework is proposed, which could evaluate buffer performance for aggregate traffic arrivals with different distributions. We use the processes of arrival and service to construct martingales, and analyze the queuing system with heterogeneous arrivals in martingale domain. Applying the stopping time theory of martingale, the transient performance of queue buffer is presented. The probability of buffer overflow and the expectation of buffer stopping time are derived together in this model. The simulations are given to validate the analytical results. This investigation provides a valuable reference for router buffer design.