Self-adaptive congestion control for multi-class intermittent connections in a communication network

A Markovian model of the evolution of intermittent connections of various classes in a communication network is established and investigated. Any connection evolves in a way which depends only on its class and the state of the network, in particular as to the route it uses among a subset of the network nodes. It can be either active (ON) when it is transmitting data along its route, or idle (OFF). The congestion of a given node is defined as a functional of the transmission rates of all ON connections going through it, and causes losses and delays to these connections. In order to control this, the ON connections self-adaptively vary their transmission rate in TCP-like fashion. The connections interact through this feedback loop. A Markovian model is provided by the states (OFF, or ON with some transmission rate) of the connections. The number of connections in each class being potentially huge, a mean-field limit result is proved with an appropriate scaling so as to reduce the dimensionality. In the limit, the evolution of the states of the connections can be represented by a non-linear system of stochastic differential equations, of dimension the number of classes. Additionally, it is shown that the corresponding stationary distribution can be expressed by the solution of a fixed-point equation of finite dimension.

💡 Research Summary

The paper presents a rigorous stochastic framework for analyzing congestion control in communication networks that host a massive number of intermittent connections belonging to several service classes. Each connection alternates between an OFF (idle) state and an ON (active) state; when active it transmits data along a predetermined route with a certain transmission rate. The rate is not fixed: it evolves according to a TCP‑like self‑adaptive rule (additive increase, multiplicative decrease) that reacts to the congestion level observed at the nodes traversed by the connection. Congestion at a node is defined as a functional of the aggregate transmission rates of all ON connections that pass through that node, and it induces packet losses and delays that feed back into the rate‑adjustment mechanism.

Because the number of connections per class can be extremely large, a direct Markovian description of the whole system would be intractable. The authors therefore introduce a mean‑field scaling: for class (k) with (N_k) connections, each individual transmission rate is scaled by (1/N_k) while the transition intensities (OFF→ON and ON→OFF) remain of order one. As (N_k\to\infty) for all classes, the empirical distribution of the states of connections in each class converges to a deterministic limit. This limit is captured by a system of (K) coupled non‑linear stochastic differential equations (SDEs), where (K) is the number of classes. The SDE for class (k) reads schematically

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