A novel analysis of queue length in differentiated services networks with self-similar arrival processes

It is well known that traditional analytic methods of queueing systems are based on the distributions of inter-arrival time and service time. However, it is quite inconvenient to employ these methods directly to he analysis of current self-similar traffic models. In this paper, we first derive, a novel analytic model based on the arrival rate and the service rate for single-class steady-state queueing systems. Then the derivations are extended to provide upper and lower boundary conditions for multi-priority queues in networks deploying differentiated services (DS). In addition, the analytical model is also applied to the analysis of DS effects on self-similar traffic. The results illustrate the performance gain in queue length of the priority classes that DS can provide compared to a network that does not deploy DS. Additionally, the upper lower boundary conditions of the queue lengths for each priority class also serves as a system design guideline.