On the Flow-level Dynamics of a Packet-switched Network

The packet is the fundamental unit of transportation in modern communication networks such as the Internet. Physical layer scheduling decisions are made at the level of packets, and packet-level models with exogenous arrival processes have long been employed to study network performance, as well as design scheduling policies that more efficiently utilize network resources. On the other hand, a user of the network is more concerned with end-to-end bandwidth, which is allocated through congestion control policies such as TCP. Utility-based flow-level models have played an important role in understanding congestion control protocols. In summary, these two classes of models have provided separate insights for flow-level and packet-level dynamics of a network. In this paper, we wish to study these two dynamics together. We propose a joint flow-level and packet-level stochastic model for the dynamics of a network, and an associated policy for congestion control and packet scheduling that is based on alpha-weighted policies from the literature. We provide a fluid analysis for the model that establishes the throughput optimality of the proposed policy, thus validating prior insights based on separate packet-level and flow-level models. By analyzing a critically scaled fluid model under the proposed policy, we provide constant factor performance bounds on the delay performance and characterize the invariant states of the system.