Tandem Brownian queues (Q2472190)

The authors analyze a two-node tandem queue with Brownian input. Section 2 presents a detailed description of the two-node tandem queue, as well as a closely related two-node parallel queue. It also gives formal implicit expressions for the over-flow probabilities, and contains a brief discussion of Schilder's sample-path large-deviations theorem. In Section 3 the two-node parallel system is analyzed. The authors derive an exact expression of the joint distribution function, large-buffer asymptotics, and the most probable path. Then they argue that the two-node parallel queue is closely related to the two-node tandem queue. Exploiting this property they obtain in Section 4 the desired results for the tandem systems. In Section 5 they discuss their results, and identify some open research questions.