On deriving stable backlog bounds by stochastic network calculus

Network calculus is a powerful methodology of characterizing queueing processes and has wide applications. In this work¹, we focus on the fundamental problem of “under what condition can we derive stable backlog bounds using the current state of art of stochastic network calculus”. We model an network element (called a “node” here) as a single server with impairment service based on two best-known models in stochastic network calculus (one is first proposed by Cruz and the other is first proposed by Yaron and Sidi). We find that they actually derive equivalent stochastic service curves and backlog bounds. And we prove that stable backlog bounds can be derived by stochastic network calculus as long as the average rate of traffic arrival is less than that of service. This work suggests the effectiveness of stochastic network calculus in theory.